Swaminath Venkateswaran
email: swaminath.venkateswaran@ls2n.fr

Matthieu Furer
email: matthieu.furet@ls2n.fr

Damien Chablat
email: damien.chablat@ls2n.fr

Philippe Wenger
email: philippe.wenger@ls2n.fr

Design and analysis of a tensegrity mechanism for a bio-inspired robot

Piping inspection robots are of greater interests in industries such as nuclear, chemical and sewage. The design of such robots is highly challenging owing to factors such as locomotion inside pipes with varying diameters, cable management,and complex pipe bends (or) junctions. A rigid bio-inspired caterpillar type piping inspection robot was developed at LS2N, France. By introducing tensegrity mechanisms and four-bar wheel mechanisms, the design of this robot is modified into a reconfigurable system. The tensegrity mechanism employs a passive universal joint with three tension springs and three cables for actuation. The positioning of the end effector with respect to the base of the mechanism plays an important role in determining the maximum tilt angle (or) bending limit of the system. By workspace analysis of three case studies, the best solution is chosen which generates the maximum tilt. A static force analysis is then performed on the mechanism to determine its stability under the influences of preload. By the modification of design parameters, stable configurations are determined followed by which cable actuation of mechanism is analyzed for estimating applied forces.

INTRODUCTION

Piping inspection robots have a major attraction in the scientific research community. They could be used in applications for industries such as nuclear, chemical and sewage where it is usually cumbersome for a human being to perform the desired inspection activity. Some of the main design criteria that have to be kept in mind for these robots are their locomotion principle, contact system with pipeline walls, cable management and articulation units for facilitating the robot to pass through curvilinear pipe profiles. During locomotion, at any instant the diameter of pipeline is unknown and it is essential for the robot to have deployable or retracting modules that can work in such unknown diameter ranges. Several researches have been proposed and developed in this area of robotics for varying diameter pipelines. For example, Ankit et al. [START_REF] Nayak | Design of a new in-pipe inspection robot[END_REF] proposed a screw type robot that is capable of working inside 127-152 mm diameter pipes. Zhang et al. [START_REF] Zhang | Design and motion analysis of a flexible squirm pipe robot[END_REF] developed an inchworm-type robot that can adapt itself to varying pipe diameters. Kwon et al. [START_REF] Kwon | Design and motion planning of a two-moduled indoor pipeline inspection robot[END_REF] developed an inspection robot that employs a caterpillar module with four bar linkages to work inside 100 mm diameter pipes having bends and junctions. However, the main challenge lies in the development of a robot for pipelines having diameters less than 100 mm. As the diameter of the pipeline reduces, careful attention has to be given to the selection of mechanical systems that can adapt itself to make tight contacts with the walls. A bio-inspired caterpillar type piping inspection robot was developed by Henry et al [START_REF] Henry | Multi-objective design optimization of the leg mechanism for a piping inspection robot[END_REF]. This robot is capable of working inside 50-94 mm diameter pipelines. However, the robot is a rigid prototype which limits its application inside pipelines having bends (or) junctions. Also, the velocity of the motors used in the robot is very low and the cable management issues were not addressed.

In this article, we focus extensively on the modification of the caterpillar type robot into a reconfigurable system. A tensegrity type mechanism that employs a passive universal joint with three tension loaded springs is proposed to be introduced in the robot. Prior to the design and analysis of this articulation unit, some key design criteria is addressed which is essential for a robot to pass through pipe bends or junctions. With the help of Maple, the vector equations are generated for the tensegrity mechanism. The tilting of the mechanism is first studied to understand its posture under the influence of a cable force. For the estimation of the maximum bend (or) tilt angles, three possible case studies are generated for the mechanism. By workspace analysis, the best configuration is chosen which will facilitate the robot to bend upto maximum angle possible when passing through a pipe bend or junction. A static force analysis is performed on the mechanism in order to determine its stability with zero applied forces and with a preload. With the stable configurations determined, the necessary forces that have to be applied to the mechanism for working through curved pipe profiles are analyzed.

The outline of the article is as follows. The key design factors for a robot to pass through pipe bends and the architecture of modified robot design is discussed. Followed by that the design of the tensegrity mechanism is presented. Analysis of the mechanism is then done for determining the ideal base orientation and then a workspace analysis is performed for three case studies of the system. The subsequent section deals with the static force analysis and estimation of forces to be applied to the mechanism. The article then ends with conclusions and future works.

ARCHITECTURE OF THE ROBOT

A bio-inspired robot for the inspection of pipelines has been designed and developed at LS2N, France by Henry et al. and Chablat et al [START_REF] Henry | Multi-objective design optimization of the leg mechanism for a piping inspection robot[END_REF][START_REF] Chablat | Mechanical design optimization of a piping inspection robot[END_REF]. This robot accomplishes the locomotion of a caterpillar in six steps for moving inside pipes. Using leg mechanisms and EC-Motors, the prototype was developed and tested. However, this robot is a rigid model and it cannot be used for pipelines having bends or junctions. By the addition of suitable articulation units, the design of the robot can be modified into a reconfigurable mechanism. Before the design of articulation unit, some key issues have to be addressed for a robot that has to pass through pipe bends or junctions which are: the passive compliance, the active compliance,and tilt angle limits. Passive compliance could be imagined for a robot that has to pass through a pipe bend at 90 degrees or less. For addressing this compliance, the articulation unit need not be necessarily active. An example would be the robot of Zhang et al. [START_REF] Zhang | Design and motion analysis of a flexible squirm pipe robot[END_REF] which uses a passive flexible helical axle to pass through 90-degree bends. In the case of active compliance, it is necessary for the articulation unit to be active. For a robot to pass through a T-junction or an elbow, the articulation unit needs to be actuated in order to decide the best path to be followed as well as maintain contact with pipeline walls. The third important factor is the tilt or bending angle limit of the articulation unit. As a robot passes through a pipe bend of 90 degrees or less, it is necessary for the articulation unit to bend up to a certain angle. The tilt angle range is generally defined by a cone of ± x degrees. The three factors are represented in Fig. 1.

a b c

Modified design of the robot

The existing bio-inspired robot is made reconfigurable by introducing articulation units and four-bar wheel mechanisms. The outline of the modified bio-inspired robot is shown in Fig. 2. The caterpillar module represented by O C A B is retained in the modified design for having contact with pipeline wall during static and dynamic phases. OABCD represents a spring-loaded four-ball wheel mechanism. They ensure contact with the pipeline wall at all instances of locomotion. Also, this mechanism can assist the robot to smoothly enter and exit pipe bends or junctions. The parameters ρ and ρ c represents the clamping and central system actuation units. The joint J represents the new articulation unit that will be introduced in the robot. In the existing prototype, the front and central modules were bolted together but in the proposed design all the modules are being made independent. As the robot moves through a pipe bend, it resembles an "Elephant Trunk". By ensuring tight contact with pipeline walls using the caterpillar module, the force is transmitted from the front to rear end of the robot which will allow the robot to pass through or overcome the pipe bend.

Design of a tensegrity mechanism

In this article, we focus on the design of a suitable articulation unit that could address the issues of compliances and tilt limits discussed in the previous section. A tensegrity type mechanism is proposed to be introduced between the motor modules which can facilitate the robot to pass through 90-degree bends or junctions by bending up to a certain angle. In the existing design of the robot, the motor units were coupled rigidly. Between each unit, a universal joint and three tension springs are introduced. The universal joint remains passive and the issue of passive compliance could be addressed by this joint and springs for a 90-degree pipe bend. For active compliance, cables will be introduced that can pass through the springs. From a central control unit, the cables can be actuated and the robot can be made to move or bend along a fixed direction while encountering a junction. The proposed tensegrity mechanism is represented in Fig. 3.

Tension springs of length 'l' 3 holes for springs & cables

Cables for actuation of mechanism 3 holes for motor wires r f

Front View Side View

Figure 3: The proposed tensegrity mechanism with universal joint, springs and cables

The tensegrity system resembles the robot analyzed by Yigit et al. [START_REF] Yigit | Design and modelling of a cable-driven parallel-series hybrid variable stiffness joint mechanism for robotics[END_REF] but in the proposed design three tensions springs are used over a single compression spring of [START_REF] Yigit | Design and modelling of a cable-driven parallel-series hybrid variable stiffness joint mechanism for robotics[END_REF]. The flanges used for spring mounting is carried over from the existing prototype. The three springs are mounted at an angle of 120 degrees between each other. Three tension springs are used because they ensure stability of the system as well as the bending limit of the universal joint is controlled when the robot works through 3D pipe profiles. Three cables for actuation of the system passes through the springs. The other three holes on the flange can be used for routing the wires coming out from the motors used in the caterpillar module. The springs are mounted at radius r f from the central axis of the flange. Using CATIA software, a 3D model of the tensegrity system is created by referencing dimensions from standard parts available at LS2N. The flanges are produced by 3D printing. With a standard universal coupling and three tension springs of stiffness k = 0.2 N/mm, the prototype is realized and it is depicted in Fig. 4. Figure 4: A prototype of the tensegrity mechanism created using 3D printing and standard parts without cables In order to determine the maximum tilt limits, the radius r f and the distance l between the flanges have to be considered for analysis which will be exploited in the next section.

ANALYSIS OF THE TENSEGRITY MECHANISM

In order to identify the constraints of the tensegrity mechanism, the equations of the system have to be derived. The complete tensegrity mechanism represented in Fig. 3 could be correlated to a parallel manipulator of type 3-SPS-U [START_REF] Alici | Topology optimisation and singularity analysis of a 3-sps parallel manipulator with a passive constraining spherical joint[END_REF]. The 3D and 2D views of the correlation are represented in Fig. 5.

b i = R z (θ) n i , with i = 1, 2, 3 (1)
where

R z (θ) =     c θ -s θ 0 s θ c θ 0 0 0 1     & n i =     r f cos 2π(i-1) 3 r f sin 2π(i-1) 3 -r f h    
where n i are the coordinates of B i in the local reference frame. The rotation matrix R z with respect to θ is used for determining the rotation/orientation of mechanism about z-axis inside the pipe. The parameter h is a constant and it can assume values greater than zero. In order to estimate the positions of end-effector C i , the theory of tilt & torsion (T&T) is employed. The T&T theory is employed mainly for parallel manipulators where the robot platform is mobile and asymmetric [START_REF] Bonev | Advantages of the modified euler angles in the design and control of pkms[END_REF]. Since the universal joint is passive, the tilt and azimuth angles would be sufficient to calculate the positions of end-effectors as there is no torsion. The tilt and azimuth angles of the tensegrity mechanism are represented in Fig. 6.

β represents the azimuth angle between the x-axis and face of the z-axis. Rotation about M causes a shift of the axis xyz to x * y * z * . The angle between z and z * represents the tilt, α. The rotation matrix R for the tilt and azimuth angles is given by the equation:

R = R z (β)R x (α)R z (-β) (2) R =    (c α + c 2 β (1 -c α ) -c β s β (c α -1) s β s α -c β s β (c α -1) 1 + (c α -1)c 2 β -c β s α -s β s α c β s α c α    (3)
In order to obtain the position of end-effector, Eqn. ( 3) is multiplied by the vector coordinates of positions C i and the equation is given by:

c i = R z (θ) R o i , with i = 1, 2, 3 (4)
where

o i =     r f cos 2π(i-1) 3 r f sin 2π(i-1) 3 r f γ    
where o i are the coordinates of C i in the local reference frame of the mobile platform. The parameter γ is a scalar value that determines the position of end-effector from the origin A. The workspace analysis for various values of γ will be analyzed in the upcoming section. The length of the mechanism l i which provides the solution for the inverse kinematic problem can be solved and it is given by the equations below:

b i = [b ix , b iy , b iz ] T , c i = [c ix , c iy , c iz ] T with i = 1, 2, 3 l i = (b ix -c ix ) 2 + (b iy -c iy ) 2 + (b iz -c iz ) 2 (5)

Tilting direction of the mechanism

For an applied force, the tensegrity mechanism has to tilt along the direction of force. The position of β is identified where the mechanism tilts along the applied force. The 2D representation of the tensegrity mechanism shown in Fig. 5b will be used for calculations. The force vectors on Fig. 5b can be calculated by the equation:

f i = λ i di di with i = 1, 2, 3 (6)
where

d i = b i -c i & f i = [f ix , f iy , f iz ] T
In Eqn. [START_REF] Yigit | Design and modelling of a cable-driven parallel-series hybrid variable stiffness joint mechanism for robotics[END_REF], λ i represents the magnitude of applied forces. About the origin or central point A, there exist moments that are generated by the cables (m c ) as well as the springs (m s ) whose equations are given by:

m c = 3 i=1 (c i × f i ) (7)
m s = 3 i=1 (k c i × d i ) (8)
where k represents the stiffness of spring. We assume same stiffness for the three springs. The resultant moment m can be found by summing up the results of Eqn. ( 7) & Eqn. [START_REF] Bonev | Advantages of the modified euler angles in the design and control of pkms[END_REF]. For attaining stable postures, the sum of components in the resultant moment m is equal to zero. As an example, if we assume h = 1, γ = 1, k = 0.2 N/mm, θ = 0 radians and λ 2 = λ 3 = 0, the values of λ 1 could be estimated with respect to α. The equation of λ 1 is generated using Maple and it is given by:

λ 1 (θ=0,β=π/2) = -33s α √ 1 -s α 10c α (9)
A tilt of α= 0 to π/3 radians is applied on the mechanism. For β = 0, the first cable cannot produce any moment to rotate around the y axis. Only the other cables can be used. For β = π/2, from Eqn. ( 9), it could be observed that the efforts generated have negative values and the mechanism tilts along the opposite direction of applied forces which is represented in Fig. 7. The home-pose position of end-effector is represented in gray lines and points C1 -C2 -C3 in Fig. 7. The final position is represented by C1 -C2 -C3. Thus, in order to have m = 0, preloading forces have to be applied which will ensure the stability of the mechanism.

Estimation of tilt limits

The feasible tilt range for the tensegrity mechanism has to be calculated. In Eqn. (4), the parameter γ in o i can assume three values: γ < 0, γ = 0 and γ > 0. These are called as the Pendulum, the Neutral pose, and the Inverse-pendulum. We set h = 1 for this analysis. The estimation of tilt range also permits us to calculate the geometrical workspace of the mechanism. The tilt limits can be estimated by taking into account the articulation or joint limits of the mechanism. The equations of the robot and its associated constraint equations can be generated using the SIROPA [START_REF] Jha | Workspace, joint space and singularities of a family of delta-like robot[END_REF][START_REF] Moroz | Cusp points in the parameter space of rpr-2prr parallel manipulators[END_REF] package of Maple. By using the CreateM anipulator syntax of SIROPA in Maple, the tensegrity mechanism is constructed. The tilt and azimuth angles are used as the pose variables and the lengths (l 1 , l 2 and l 3 ) are employed as the articular variables. By using the ConstraintEquations of SIROPA, six constraint equations are generated, with first three equations at the lower limit of lengths and the next three equations at the upper limit of lengths. The equations are given by:

C 1+3i : 2r 2 f c α (c 2 β -1) -2s β s α r 2 f (1 + γ) + 2c α r 2 f γ -2r 2 f c 2 β +r 2 f γ 2 + 3r 2 f -l 2 j (10) C 2+3i : -2 √ 3r 2 f c α c β s β + 2 √ 3r 2 f s α c β γ -2c α c 2 β r 2 f + 2 √ 3r 2 f c β s β + 2 √ 3r 2 f c β s α + 2s α s β r 2 f γ + 2r 2 f c 2 β + 2s α s β r 2 f + 4c α r 2 f γ +2r 2 f γ 2 -r 2 f c α + 3r 2 f -2l 2 j ( 11
)
C 3+3i : 2 √ 3r 2 f c α c β s β -2 √ 3r 2 f s α c β γ -2c α c 2 β r 2 f -2 √ 3r 2 f c β s β - 2 √ 3r 2 f c β s α + 2s α s β r 2 f γ + 2r 2 f c 2 β + 2s α s β r 2 f + 4c α r 2 f γ +2r 2 f γ 2 -r 2 f c α + 3r 2 f -2l 2 j ( 12
)
where for i = 0 and 1, l j = l min and l max These equations are generated using SIROPA by the projection of variables in a polynomial form [START_REF] Jha | Workspace, joint space and singularities of a family of delta-like robot[END_REF]. For γ, three values are assumed -1/4, 0 and 1 and they are employed in Eqn. [START_REF] Moroz | Cusp points in the parameter space of rpr-2prr parallel manipulators[END_REF] to Eqn. [START_REF] Chablat | Working modes and aspects in fully parallel manipulators[END_REF]. The value r f is retained as 11 mm from existing prototype [START_REF] Chablat | Mechanical design optimization of a piping inspection robot[END_REF]. In order to estimate the geometric workspace range, the CellDecompositionP lus feature of the SIROPA package is employed. The CellDecompositionP lus uses the Cylindrical Algebraic Decomposition (CAD) technique and parametric root finding technique of Maple for estimating the regions where there exists real solutions to the inverse or direct kinematic problem [START_REF] Chablat | A comparative study of 4-cable planar manipulators based on cylindrical algebraic decomposition[END_REF]. For isolating the aspects around home-pose, we transform Eqn. [START_REF] Moroz | Cusp points in the parameter space of rpr-2prr parallel manipulators[END_REF] to Eqn. ( 12) as inequality equations [START_REF] Chablat | Working modes and aspects in fully parallel manipulators[END_REF] which will be used as inputs for CellDecompositionP lus in Maple. For the constraint equations, it is also necessary to set the length limits of l i as it plays a vital role in the estimation of the maximum tilt angle. At the home-pose as represented in Fig. 5b, the length between B -C is found to be 9 mm, 11 mm and 22 mm for γ= -1/4, 0 and 1. The constraint limits for these lengths under maximum tilt is assumed to be l min = 7 mm and l max = 31 mm for the analysis. The results of the geometric workspace are then generated for the three cases of γ and they are represented in Fig. 8.

It could be observed from the results that the maximum tilt range varies for the three case studies. The blue regions represents the feasible working range for the tensegrity mechanism. The values of tilt with azimuth angles at the joint limits are provided in Table 1.

Table 1: MAXIMUM TILT POSITIONS WITH AZIMUTH'S AT JOINT LIMITS

γ β α min β α max -1/4 [±π/3,±π] -π/18 [±2π/3, 0] π/18 0 -π/6 π/6 1 -π/3 π/3
From Table 1 and the results of Maple from Fig. 8, it can be deduced that the pendulum configuration is not ideal as the tilt range is narrow and cannot be feasible for pipes having angled or 90 degree bends. Better solutions are obtained in the other two cases but the inverse pendulum case is considered for further analysis as it could be potentially used for pipelines having bends up to 90 degrees as it has higher tilt ranges.

STATIC FORCE ANALYSIS OF THE MECHANISM

With the inverse pendulum configuration being a suitable solution for the tensegrity mechanism, it is important to analyze its stability. In the case of pipelines with junctions, the active compliance has to be employed where the stability of tensegrity mechanism could be controlled through cables and the robot can be made to follow the right direction. For passive compliance, the cable actuation is not required and the objective of the mechanism will be to overcome the bend under passive mode. In this scenario, the static stability of the mechanism has to be determined and it should be capable of working passively without cable actuation. As the suitable tilt and azimuth ranges have Figure 8: Geometric workspace range for the three case studies around the home-pose been determined, the forces to be applied for the system can be estimated. According to Lagrange, for a moving system, the equation of motion [START_REF] Meirovitch | Fundamentals of vibrations[END_REF] is given by:

τ = d dt ∂T ∂ q - ∂T ∂q + dU dq where q = [α, β] T ( 13
)
where T and U are the kinetic and potential energies of the system. τ represents the generalized torques on the system. Under static conditions, the velocity of the system is zero and there exists no kinetic energies. Thus in Eqn. [START_REF] Meirovitch | Fundamentals of vibrations[END_REF] only the potential energy derivative with respect to the tilt and azimuth angles exists. The mass of the mechanism is also not taken into account as it vanishes along with the kinetic energy term. The potential energy of the system is contributed by the springs and cables. For this calculation, we assume the magnitudes of applied forces along the three cables as F 1 , F 2 , F 3 and equal stiffness for the three springs as k. The total potential energy can be estimated by summing up the energies of springs and cables. The equations are given by:

U cable = 3 i=1 F i l i U spring = 3 i=1 1 2 kl 2 i ( 14
)
U tot = U cable + U spring (15)
The springs are considered massless and have zero free lengths. By substituting the results of Eqn. [START_REF] Furet | Workspace and cuspidality analysis of a 2-x planar manipulator[END_REF] in Eqn. ( 13), the forces required to actuate the mechanism can be calculated.

Stability of the tensegrity mechanism

Under zero-applied forces or under the presence of a preload, the mechanism can deform due to the springs. The stability of mechanism has to be analyzed under static modes. Arsenault et al. [START_REF] Arsenault | Kinematic, static and dynamic analysis of a planar 2-dof tensegrity mechanism[END_REF] analyzed that for a tensegrity mechanism to be stable under static modes, the second order derivative or the stiffness of the mechanism K has to be positive. The U tot equation is first derived. Since the inverse pendulum configuration is used in the analysis, we fix γ = 1. U tot depends on the applied forces as well as design parameters of the system and it can be expressed as:

U tot = 3 i=1 f (F i (α, β, r f , h)) + ζ (16)
where

ζ = 3 kr f 2 h 2 -1 2 c α + h 2 + 1 2
At the home-pose condition as represented in Fig. 5b where we have α and β equal to zero and no applied forces, only the constant term ζ of Eqn. ( 16) exists as it depends on the spring stiffness k, mounting radius r f , parameter h and the cosine of tilt. The stability of the system can be found by plotting the total potential energy against the estimated tilt ranges. The parameters k, r f and h is considered as 0.2 N/mm, 11 mm and 1. The stability plot for the system is depicted in Fig. 9. It could be observed that the mechanism remains unstable and has maximum potential energy with no forces being applied. Since U tot has a direct dependency on the applied forces, the system continues to remain unstable when the preload is considered. Under the influence of zero applied forces, the mechanism has no dependencies on the azimuth 16)). The second order derivative of U tot with respect to α which gives the mechanism stiffness K α has to be studied for determining stable configuration [START_REF] Arsenault | Kinematic, static and dynamic analysis of a planar 2-dof tensegrity mechanism[END_REF]. The applied forces are considered equal and are taken as

F 1 = F 2 = F 3 = F .
The stiffness equation is generated using Maple with β & α at 0 radians and is given by:

K α = -3r f 2 kr f h 2 + h F -kr f 2 (17)
It can be seen that the mechanism stiffness depends on the parameters r f , h, F and k. By fixing one or several parameters, it is possible to determine a stable configuration. In this study, we fix the spring stiffness as per the prototype of Fig. 4 positive zone of K α is higher. However, K α transforms into negative values when r f increases. By retaining r f as 11 mm from the existing design of the robot, a value of h = 1/2 is chosen such that stiffness K α is always positive with the preload. The geometric workspace is calculated for this new inverse pendulum by using Eqn. [START_REF] Moroz | Cusp points in the parameter space of rpr-2prr parallel manipulators[END_REF] to Eqn. [START_REF] Chablat | Working modes and aspects in fully parallel manipulators[END_REF] and the results are depicted in Fig. 11. From the results of Fig. 11, it can be seen that the tilt range has been reduced stable configuration has been obtained. The system is also found to be stable with the consideration of preload. The new parameter of h = 1/2 will be considered for further analysis.

Estimation of forces to be applied and influences of azimuth β

In order to make the tensegrity mechanism to tilt upto a given angle, it is necessary to apply at least one force on the system. However, in order to obtain a given azimuth angle at a given tilt angle, at least two forces must be applied on the mechanism. The force equations can be solved by differentiating U tot with respect to α & β and equating them to zero and fixing a positive value of 1 N.mm/rad for K a . The forces can be expressed as:

F i = f (α, β, K α , h, r f , k) with i = 1, 2, 3 (18)
In Eqn. (18), the new inverse pendulum parameters identified in the previous section is considered. The azimuth angle β can vary from 0 to 2π radians and it can be controlled to attain a certain value based on the profile of pipeline encountered by the robot. The three force values of Eqn. (18) are plotted against the azimuth range at the maximum tilt angle of π/6 radians which is depicted in Fig. 13. In Fig. 13 for each azimuth phase of 2π/3 radians one of the forces remain redundant. During the azimuth phase of 0 -2π/3, F 3 remains redundant and there exists no significant changes to the system by this force. On the other hand, the force F 1 continues to drop while F 2 starts increasing in this azimuth range. The dotted horizontal line in Fig. 13 separates the region of redundancy and below this line, one of the three forces always remain redundant. The influences of each azimuth phase on the three forces are provided in Table 2.

(β) range F 1 F 2 F 3 0 -2π/3
Decreasing Increasing Redundant 2π/3 -4π/3

Redundant Decreasing Increasing 4π/3 -2π

Increasing Redundant Decreasing However at azimuth angles of 0, 2π/3 and 4π/3 radians, the forces F 1 , F 2 and F 3 are at a maximum while the other two forces will remain equal and low. Based on the profile of the pipeline, the cables used in the tensegrity mechanism could be actuated to attain an azimuth angle that will facilitate the robot to have better contact with the walls. For a curvilinear pipe profile in 3D space, at least one or maximum two forces have to be actuated while the third one always remains redundant.

CONCLUSIONS AND FUTURE WORKS

The tensegrity mechanism proposed in this article can be implemented as a solution to the rigid prototype of [START_REF] Henry | Multi-objective design optimization of the leg mechanism for a piping inspection robot[END_REF][START_REF] Chablat | Mechanical design optimization of a piping inspection robot[END_REF] in order to work through pipelines with bends and junctions. By the study of compliances and tilt angle limits, the tensegrity mechanism was designed. For pipelines with 90 degrees bends, the universal joint can remain passive and it can address the issue of passive compliance. In the case of a junction, the cables can be actuated which will allow the robot to bend to a given tilt and azimuth to follow a given path. By correlating the tensegrity mechanism to a parallel manipulator, the orientation of mechanism was determined and the maximum tilt ranges were exploited by decomposition of the mechanism into three case studies. The inverse pendulum configuration was chosen as it provided the maximum tilt range. However, with the static force analysis, this system was found to be unstable under zero applied forces. By fixing several parameters, the parameter h was modified to obtain a stable configuration under the presence of preload. The variation of azimuth β on the mechanism was studied in order to determine the necessary forces to be applied while working through curved pipe profiles.

With the modification of h, the maximum tilt range was reduced from ±π/3 to ±π/6 radians . This range might not be sufficient to pass through a pipe bend of 90 degrees. This could be overcome by stacking a second tensegrity module over the existing mechanism. Kinematics and workspace analysis was performed by Furet et al. [START_REF] Furet | Workspace and cuspidality analysis of a 2-x planar manipulator[END_REF][START_REF] Furet | Kinematic analysis of planar tensegrity 2-x manipulators[END_REF] on stacked tensegrity system for 2D case. This problem will be extended for the 3D case because a stacked model can provide higher tilt angles. Also with stacked modules, it will be essential to check stability as there will be two tilt angles. In this case, the Hessian matrix will be derived and stability can be attained when the determinant of the Hessian matrix is always positive. The CATIA model of the robot with stacked tensegrity modules that resembles an "Elephant Trunk" is depicted in Fig. 14. Force analysis will further be extended on the stacked models assembled with the robot for various postures inside pipeline namely: vertical, horizontal and angled configurations for understanding the stability of the entire robot. An alternate approach will be proposed which deals with the study of variation of spring stiffness k and its impact on the mechanism stiffness K α . An optimization technique will also be carried out for the determination of spring stiffness by taking into account the general design equations of a tension spring.

Figure 1 :

 1 Figure 1: Representation of the passive (a) & active compliance's (b) and tilt angle range (c)

Figure 2 :

 2 Figure 2: Outline of the modified bio-inspired piping inspection robot inside a pipeline of radius r

Figure 5 :Figure 5

 55 Figure 5: 3D (left) and 2D (right) representations of the tensegrity mechanism to a 3-SPS-U parallel manipulator (home-pose)

Figure 6 :

 6 Figure 6: Representation of Tilt (α) and Azimuth (β) angles on the tensegrity mechanism

Figure 7 :

 7 Figure 7: Representation of mechanism with applied force λ 1 along C 1 -B 1 with α = 0 to π/3 radians and β = π/2 radians

Figure 9 :

 9 Figure 9: Plot of total potential energy versus the tilt with zero applied forces

Figure 10 :

 10 Figure 10: Projection of K α with respect to r f and h for α & β = 0 radians

Figure 11 :Figure 12 :

 1112 Figure 11: Geometric workspace for the new inverse pendulum configuration with h=1/2 and r f = 11 mm

Figure 13 :

 13 Figure 13: Variation of forces for β = 0 to 2π radians at α= π/6 radians

Figure 14 :

 14 Figure 14: Modified architecture of the robot with stacked tensegrity structures in CATIA

Table 2 :

 2 INFLUENCES OF AZIMUTH PHASES ON THE FORCES

	Azimuth

NOMENCLATURE

Mechanism stiffness with respect to tilt α


Adrien Cambier
email: adrien.cambier@orange.com

Matthieu Chardy

Rosa Figueiredo

Adam Ouorou

Michael Poss

Optimizing the investments in mobile network technologies and designing of offers

Context and stakes

).

 is that each telecommunication site is associated with its own pool of subscribers, which assumes that there is no overlapping between sites coverage. This assumption leads to overdimensioning since sites coverage overlapping exists in real networks and hence a technology installed on a neighbor site could have been sufficient to serve the subscribers. Allowing the possibility of installing new sites and assessing the earnings due to sites coverage overlapping in dimensionning, are hence important stakes for an operator.

Contributions

Our modeling contribution over our previous work [START_REF] Cambier | Optimizing the investments in mobile networks and subscriber migrations for a telecommunication operator[END_REF] is two-fold. First, we model the sites coverage overlapping. We consider that the territory is divided in areas. Subscribers from an area can be served by a given technology on a given site if the range condition is satisfied. We introduce a multi bipartite graph to model this range condition, with an edge (labeled with a network technology) between an area and a site if this area can be served by the site for this technology. Second, we model the possibility of installing new sites (equipped only with the newest technology) on the areas not yet equipped. We provide a mixed integer formulation that tackles the two cases, and linearize it in a classical way. We reinforce the model with several valid inequalities. We prove the NP-hardness of our formulation, even in the case of a single generation, single module and mono period framework, by a reduction to the set covering problem.

Computational tests have been performed on real life instances. On the one hand, we have shown taking into account the overlapping reduces computational times and gaps despite a large number of optimization variables in the formulation. On the other hand, the use of micro-cells has shown the scalability limits of the Branch-and-Bound approach for modeling the problem. Beyond this limit, heuristics have to be designed since the problem becomes out of memory. On a business point of view, our results enlighten the important savings allowed by sites coverage overlappings.


Sami Jannin

Jean-Nicolas Dumez

Patrick Giraudeau

Dennis Kurzbach
email: dennis.kurzbach@univie.ac.at

Application and methodology of dissolution dynamic nuclear polarization in physical, chemical and biological contexts

Dissolution dynamic nuclear polarization (d-DNP) is a versatile method to enhance nuclear magnetic resonance (NMR) spectroscopy. It boosts signal intensities by four to five orders of magnitude thereby providing the potential to improve and enable a plethora of applications ranging from the real-time monitoring of chemical or biological processes to metabolomics and in-cell investigations. This perspectives article highlights possible avenues for developments and applications of d-DNP in biochemical and physicochemical studies. It outlines how chemists, biologists and physicists with various fields of interest can transform and employ d-DNP as a powerful characterization method for their research.

Introduction

Dissolution dynamic nuclear polarization (d-DNP) is a technique that aims at overcoming experimental limitations of solution state nuclear magnetic resonance (NMR) spectroscopy imposed by its intrinsically low sensitivity. Weak signal intensities in NMR are a major bottleneck that often impede rapid detection schemes by necessitating signal averaging or high (e.g., nonphysiological) concentrations of target molecules. d-DNP [START_REF] Ardenkjaer-Larsen | Increase in Signal-to-Noise Ratio of > 10,000 Times in Liquid[END_REF] mitigates these constraints by providing hyperpolarized nuclear spin states, which feature dramatic signal intensity boosts by several orders of magnitude. It is probably the most versatile method among other established hyperpolarization techniques, such as para-hydrogen induced polarization (PHIP), [START_REF] Buljubasich | Parahydrogen Induced Polarization by Homogeneous Catalysis: Theory and Applications[END_REF] signal amplification by reversible exchange (SABRE) [START_REF] Rayner | Signal Amplification by Reversible Exchange (SABRE): From Discovery to Diagnosis[END_REF] or spin exchange or metastability exchange optical pumping (SEOP or MEOP) [START_REF] Barskiy | NMR Hyperpolarization Techniques of Gases[END_REF] . Several reviews describing these methods are already available [START_REF] Kovtunov | Hyperpolarized NMR Spectroscopy: D -DNP, PHIP, and SABRE Techniques[END_REF] .

d-DNP is based on the general concepts of DNP 6 making use of the high polarization of electron spins by transferring it to nuclear spins through microwave irradiation at low temperatures. The original idea behind d-DNP [START_REF] Ardenkjaer-Larsen | Increase in Signal-to-Noise Ratio of > 10,000 Times in Liquid[END_REF] consists in a fast dissolution of the sample after DNP, which preserves most of the hyperpolarization. This approach enables a plethora of solutionstate applications in analytical NMR or magnetic resonance imaging (MRI). Here again several reviews are available in the literature. [START_REF] Bornet | Optimizing Dissolution Dynamic Nuclear Polarization[END_REF][START_REF] Ardenkjaer-Larsen | On the Present and Future of Dissolution-DNP[END_REF][START_REF] Jähnig | Conceptual and Instrumental Progress in Dissolution DNP[END_REF][START_REF] Keshari | Chemistry and Biochemistry of 13 C Hyperpolarized Magnetic Resonance Using Dynamic Nuclear Polarization[END_REF] d-DNP provides the potential to boost signal intensities by three to four orders of magnitude thereby opening possibilities to access materials and properties that cannot be studied by conventional NMR. [START_REF] Lumata | DNP by Thermal Mixing under Optimized Conditions Yields >60 000-Fold Enhancement of 89 Y NMR Signal[END_REF][START_REF] Vuichoud | Measuring Absolute Spin Polarization in Dissolution-DNP by Spin PolarimetrY Magnetic Resonance (SPY-MR)[END_REF] Hence, potential applications in various fields of research ranging from physical chemistry over nuclear physics to biochemistry are imaginable.

While one of the currently most prominent applications of d-DNP relies on the use of hyperpolarized biomolecular imaging tracers for in-vivo metabolic MRI [START_REF] Nelson | Metabolic Imaging of Patients with Prostate Cancer Using Hyperpolarized [1-13C]Pyruvate[END_REF][START_REF] Wilson | Hyperpolarized 13C MR for Molecular Imaging of Prostate Cancer[END_REF] , this article targets the in-vitro analytical, physiochemical and biochemical applications and perspectives of d-DNP thereby trying to raise the attention of a multidisciplinary community. After a brief introduction, current uses in biochemical, chemical and physical contexts will be outlined and perspectives will be developed for future applications, such as real-time chemical reaction monitoring, investigation of biological substrates, metabolomics and nuclear spin physics of solids. Subsequently, based on the current state-ofthe-art a perspective on future instrumentation and methods improvements will be developed in view of improving dDNP to make it more efficient, general, or transportable.

The d-DNP methodology -merits and pitfalls d-DNP goes back to an invention by Ardenkjaer-Larsen, Golman and co-workers in 2003, [START_REF] Ardenkjaer-Larsen | Increase in Signal-to-Noise Ratio of > 10,000 Times in Liquid[END_REF] who combined DNP of frozen liquids at low-temperatures (see [START_REF] Jannin | Dynamic Nuclear Polarization by Thermal Mixing Under Partial Saturation[END_REF] and references therein for a detailed discussion of DNP mechanisms) with a subsequent dissolution and rapid transition to ambient temperatures to increase signal intensities in liquid state NMR spectroscopy. The combination of temperature jumps with DNP can spectacularly increase nuclear spin polarizations 𝑃I (vide infra for a more detailed definition), yet such an experi-ment also requires peculiar instrumentation and workflows. Currently, a prototypical d-DNP experiment for hyperpolarized NMR consists of three principal steps: i) Dynamic nuclear polarization of a sample at a low temperature 𝑇 #$% ≤ 4.2 K within a dedicated DNP apparatus that maintains a static magnetic field 3.35 T < 𝐵 * #$% < 11.8 T; ii) rapid heating and dissolution of the sample to the liquid state prior to fast transfer to an NMR spectrometer operating at typical magnetic fields 𝐵 * $+, > 7 T or dedicated low-field devices; iii)

NMR detection at close to ambient temperature 𝑇 $+, > 273 K. The basic setup of such an experiment is sketched in Fig. 1, which depicts a DNP apparatus connected to a conventional NMR spectrometer via a dissolution and transfer system. To give the reader an overview over the requirements of a d-DNP experiment, a brief description of steps i) , ii) and iii) is provided in the following:

i) The experiment starts with the preparation of a sample that contains paramagnetic molecules that are often coined polarization agents (PAs). Stable radicals such as nitroxides or tri-aryl methyl compounds often serve as PAs. After freezing of the sample, partial saturation of the electron paramagnetic resonance (EPR) line of a PA by slightly off-resonant microwave irradiation will entail an increased nuclear spin polarization 𝑃 due to a transfer of polarization from the unpaired electrons of the PAs to the nuclei in their vicinity (the ratio of gyromagnetic ratios is g(e -)/g( 1 H) » 668). This process normally takes place in a dedicated DNP apparatus, as it requires probes with microwave irradiation and often NMR capabilities (see for example references [START_REF] Ardenkjaer-Larsen | Increase in Signal-to-Noise Ratio of > 10,000 Times in Liquid[END_REF][START_REF] Baudin | A Cryogen-Consumption-Free System for Dynamic Nuclear Polarization at 9[END_REF][START_REF] Ardenkjaer-Larsen | Cryogen-Free Dissolution Dy-namic Nuclear Polarization Polarizer Operating at 3.35 T, 6.70 T and 10[END_REF] ). A more or less homogeneous distribution of PAs in the DNP samples usually leads to optimal hyperpolarization. Therefore, crystallization, which leads to uncontrolled local PA-enriched and -depleted phases needs to be avoided, if necessary enforced by addition of vitrification agents such as glycerol. [START_REF] Weber | Sample Ripening through Nanophase Separation Influences the Performance of Dynamic Nuclear Polarization. Angew[END_REF] The sections "Sample Throughput" and "Transportable Hyperpolarization" provide a closer look at current developments concerning instrumentation and state-of-the-art PAs. For the moment it is sufficient to consider that microwave irradiation induces DNP by means of various mechanisms, most prominent, the cross effect and thermal mixing. [START_REF] Guarin | Characterizing Thermal Mixing Dynamic Nuclear Polarization via Cross-Talk between Spin Reservoirs[END_REF][START_REF] Shimon | Dynamic Nuclear Polarization in the Solid State: A Transition between the Cross Effect and the Solid Effect[END_REF] The effectiveness of the different mechanisms depends on various factors such as the EPR line-shape, the concentration and the electron T1e of the PA. In d-DNP applications, one typically operates at temperatures close to 1 K, where mixtures of several mechanisms may be operative. A detailed description of these processes and their relation to d-DNP is beyond the scope of this perspective article. The reader is referred to the seminal work by Abragam and Goldman 6 as well as to monographs [START_REF] Wenckebach | Essentials of Dynamic Nuclear Polarization[END_REF] , articles [START_REF] Jannin | Dynamic Nuclear Polarization by Thermal Mixing Under Partial Saturation[END_REF][START_REF] Hovav | Theoretical Aspects of Dynamic Nuclear Polarization in the Solid State -Spin Temperature and Thermal Mixing[END_REF][START_REF] Serra | Electron and Nuclear Spin Dynamics in the Thermal Mixing Model of Dynamic Nuclear Polarization[END_REF][START_REF] Wenckebach | Spectral Diffusion and Dynamic Nuclear Polarization: Beyond the High Temperature Approximation[END_REF][START_REF] Lumata | Electron Spin Resonance Studies of Trityl OX063 at a Concentration Optimal for DNP[END_REF][START_REF] Weber | Anisotropic Longitudinal Electronic Relaxation Affects DNP at Cryogenic Temperatures[END_REF] and reviews. [START_REF] Kovtunov | Hyperpolarized NMR Spectroscopy: D -DNP, PHIP, and SABRE Techniques[END_REF][START_REF] Zhang | Applications of Dissolution Dynamic Nuclear Polarization in Chemistry and Biochemistry[END_REF] Yet, for the following perspectives the reader should keep in mind that DNP of samples that contain millimolar quantities of PAs entails a transfer of polarization from a PA to nuclear spins in its vicinity causing a boost in NMR signal intensity by increasing the nuclear polarization 𝑷 𝑰 . The resulting spin state is then denoted as "hyperpolarized".

ii) After the hyperpolarization procedure is complete, the sample is rapidly dissolved and diluted in hot heavy water and transferred to a conventional NMR spectrometer. The influence of the temperature jump during a d-DNP experiment can directly be deduced from eq. 1:

𝑃 1 #$% = 𝜀 #$% × 𝜀 5678 = 𝜀 #$% × 9:;< = ℏ?@ A BCD EF @ G HIJ K 9:;< = ℏ?@ A CLM EF @ G INO K ~ 𝜀 #$% × Q A BCD R INO Q A CLM R HIJ (1)
with 𝜀 #$% the polarization enhancement brought about by DNP, and ℏ and 𝑘 Q the Planck and Boltzmann constants, respectively, and 𝛾 the gyromagnetic ratio of the nuclear spin 𝐼. The lower the temperature 𝑇 #$% at which the DNP process takes place, the higher the thermal equilibrium polarization. The large signal enhancement in a d-DNP experiment can therefore be traced back to the multiplicative effects of DNP and the temperature jump.

The speed of the dissolution and transfer process is critical due to two major factors. Firstly, large fractions of hyperpolarization can be lost during the dissolution/heating process, if it proceeds to slowly. The target substance may pass through a regime in which nuclear spin relaxation is very effective (e.g., through slow tumbling of the molecule during the dissolution and exacerbate paramagnetic relaxation) causing a rapid decay of the hyperpolarization. Secondly, the sample needs to be rapidly transferred from the DNP apparatus to the detection NMR device during a transfer time t trans through the magnetic field B trans . The latter might be uncontrolled or too low, which may cause enhanced losses of hyperpolarization via enhanced paramagnetic relaxation [START_REF] Miéville | Relaxometry of Insensitive Nuclei: Optimizing Dissolution Dynamic Nuclear Polarization[END_REF] or scalar relaxation of the first and second kind. [START_REF] Chiavazza | Earth's Magnetic Field Enabled Scalar Coupling Relaxation of 13C Nuclei Bound to Fast-Relaxing Quadrupolar 14N in Amide Groups[END_REF][START_REF] Elliott | Nuclear Singlet Relaxation by Scalar Relaxation of the Second Kind in the Slow-Fluctuation Regime[END_REF] Several recent developments try to mitigate this bottleneck of the d-DNP technology. For example, the use of magnetic tunnels [START_REF] Milani | A Magnetic Tunnel to Shelter Hyperpolarized Fluids[END_REF] that maintain a stable magnetic field B trans during the trans-fer or high-pressure transfer systems in which the sample is propelled within only 0.5 to 2 s (depending on the setup) from the DNP apparatus to the NMR spectrometer. [START_REF] Bowen | Rapid Sample Injection for Hyperpolarized NMR Spectroscopy[END_REF][START_REF] Olsen | Optimizing Water Hyperpolarization and Dissolution for Sensitivity-Enhanced 2D Biomolecular NMR[END_REF] Additionally, it has recently been proposed that the dissolution process can take place in the detection NMR spectrometer after the cold solid sample has been transferred and not as usual within the DNP apparatus before the transfer. [START_REF] Kouřil | Dissolution-Dynamic Nuclear Polarization with Rapid Transfer of a Polarized Solid[END_REF] Several developments and perspectives in this regard will be discussed in more detail below in section "Solid transfer, liquid transfer".

iii) After the sample has been dissolved and transferred, NMR detection proceeds. The hyperpolarized spin states can be exploited in NMR experiments if their duration does not exceed the lifetime of the hyperpolarization. A single pulse experiment with a 90˚detection pulse will yield maximum sensitivity in a single scan (see Fig. 2), but it is also very common to detect the hyperpolarized magnetization with a train of small angle detection pulses, especially when the experiment aims at monitoring kinetic or dynamic processes. in thermal equilibrium by means of a 90˚ detection pulse that reads the entire polarization. Subsequently, one waits for rebuild-up of the nuclear spin polarization to repeat the experiment. Typical, recovery delays are between a few hundreds of milliseconds to minutes. In contrast, in d-DNP the entire experiment is executed during a single period (b, c). One may use a single read-out pulse, which yields a single very intense spectrum. Yet, typically for 1D NMR by dDNP, the experiment starts with such an intense polarization that allows for small angle detection such that only small shares of the polarization are used to read the signal (or Ernst angles in cases of continuously replenished intermetdaites). The detection can be repeated rapidly, e.g. every 100 ms, before the hyperpolarization has decayed to thermal equilibrium polarization. This strategy is useful for monitoring dynamic/kinetic processes on a T1 timescale, but if sensitivity enhancement is the main goal, a single 90° can likewise be applied to obtain a maximum signal in a single detection.

In contrast to conventional NMR, where the experiment may last indefinitely within spectrometer stability and schedule constraints, signal detection in a d-DNP experiment needs to be completed within a short time interval after the sample has been transferred (see Fig. 1). The hyperpolarization has a limited lifetime as it inevitably decays towards thermal equilibrium with the time constant of longitudinal nuclear relaxation T1.

The limited lifetime of hyperpolarization and the irreversible nature of d-DNP imposes limitations in the application of conventional 2D and 3D experiments, which typically take longer then 2 min. Several approaches have been developed to resolve this dilemma. They will be discussed in more detail in the section "High-resolution d-DNP vs. high-resolution NMR" as well as "d-DNP and ultrafast NMR detection". While, on the one hand, a d-DNP experiment is time-constrained, it is, on the other hand, boosted by signal enhancements e d-DNP of three to four orders of magnitude. e d-DNP is here understood as the ratio between nuclear spin polarization P d-DNP of a hyperpolarized sample and corresponding polarization in thermal equilibrium P TE . This ratio can reach over 1 000 in proton NMR and over 10 000 in NMR of heteronuclei. [START_REF] Lumata | DNP by Thermal Mixing under Optimized Conditions Yields >60 000-Fold Enhancement of 89 Y NMR Signal[END_REF][START_REF] Vuichoud | Measuring Absolute Spin Polarization in Dissolution-DNP by Spin PolarimetrY Magnetic Resonance (SPY-MR)[END_REF] Hence, novel detection strategies for higher-dimensional or time-resolved NMR become conceivable.

Small angle detection pulses of typically 1 -30˚ are sufficient to observe an intense signal although only a small share of the nuclear polarization is used for detection. The readout can therefore be repeated rapidly, e.g. every 100 ms, before the polarization has vanished. In contrast, conventional NMR typically employs longer waiting times between every detection together with a readout of the entire polarization by 90˚pulses. These relations are visualized in Fig. 2.

Applications of d-DNP for chemists, biologists and physicists

With a general outline of the d-DNP method at hand, we will highlight in following selected state-ofthe-art examples and extrapolate these with respect to potential avenues to future d-DNP applications. The selection of examples in this article is of course of limited extent and does not claim to cover all important recent developments in the field. Top: To couple D-DNP with high-resolution protein NMR applications, hyperpolarized aqueous buffers are produced and subsequently mixed with a protein solution. Rapid exchange of hyperpolarized protons between the water in the buffer and the target proteins introduced hyperpolarization into the protein. As proton exchange is quite efficient at pH 7.4 and 37˚C, NMR under near-physiological is feasible by this approach. Bottom: 1 H-15 N HMQC of ubiquitin detected through hyperpolarized 96% deuterated PBS buffer (red) superimposed to a conventional HSQC in 10% deuterated PBS (black). Evidently, not all residues can be detected by hyperpolarization-based detection as the signal intensity depends on the efficiency of the exchange of hyperpolarization between the solvent and the protein. The resulting spectra are, hence, sparse and reminiscent of selective labeling techniques based on selectively isotope enriched amino acids.

High-resolution d-DNP vs. high-resolution NMR -Applications to structural biology of proteins

The established solution to overcome the intrinsically low sensitivity in conventional NMR is signal averaging. To this end, a spectrum is several times sequentially acquired such that the result features an improved signal-to-noise ratio (SNR). Obviously, the higher the desired SNR, the longer is the necessary acquisition time. d-DNP is -to a large extent -not limited anymore by signal intensities such that the need for signal accumulation becomes outdated and novel possibilities emerge.

Due to the necessity for rapid detection, often only one-dimensional spectra are recorded by means of d-DNP. However, recently it has been shown that highresolution multidimensional NMR of proteins by d-DNP is also possible by using hyperpolarized solvents as vectors to transport hyperpolarization from the low-temperature conditions within a DNP apparatus to a protein solution and finally into a protein (see Fig. 3 for a sketch of the approach). [START_REF] Olsen | Optimizing Water Hyperpolarization and Dissolution for Sensitivity-Enhanced 2D Biomolecular NMR[END_REF][START_REF] Szekely | High-Resolution 2D NMR of Disordered Proteins Enhanced by Hyperpolarized Water[END_REF][START_REF] Kurzbach | Investigation of Intrinsically Disordered Proteins through Exchange with Hyperpolarized Water[END_REF][START_REF] Kadeřávek | High-Resolution NMR of Folded Proteins in Hyperpolarized Physiological Solvents[END_REF][START_REF] Chappuis | Hyperpolarized Water to Study Protein-Ligand Interactions[END_REF][START_REF] Vuichoud | Filterable Agents for Hyperpolarization of Water, Metabolites, and Proteins[END_REF] Indeed, by dissolving a well-folded or intrinsically disordered protein (IDP) in a buffer that contains labile hyperpolarized protons, the hyperpolarization is introduced into the protein by chemical exchange between labile protein side-chain or backbone protons and the solvent. With this technique, multidimensional NMR spectra with increased intensity can be measured due to two key points: 1) The approach is applicable to any watersoluble protein, as only the buffer must undergo the d-DNP procedure. This renders this approach broadly applicable to a plethora of substrates. The major limitation is imposed by the proton exchange rate between solvent and the protein's backbone amide protons, which needs to ranging between ca. 0.5 s -1 and 100 s -1 to provide substantial signal enhancements. [START_REF] Szekely | High-Resolution 2D NMR of Disordered Proteins Enhanced by Hyperpolarized Water[END_REF][START_REF] Kadeřávek | High-Resolution NMR of Folded Proteins in Hyperpolarized Physiological Solvents[END_REF] 2) The hyperpolarization of the protons in a protein buffer decays with a time constant T1 that is much longer than the one of protons attached to the protein, which is of the order of 1 s. Typically, partially deuterated buffers are employed to prolong T1 times and hyperpolarization lifetimes of ca. 2 min. can be achieved with this approach. Hence, rapid multidimensional, high-resolution detection schemes become feasible.

It was shown that 1 H- [START_REF] Jannin | Dynamic Nuclear Polarization by Thermal Mixing Under Partial Saturation[END_REF] N correlation spectroscopy (HMQC) of >200 amino acid long IDPs is possible at residue resolution. Very recently, the approach has been extended to three-dimensional NMR (HNCO) and carbon-direct detection in [START_REF] Nelson | Metabolic Imaging of Patients with Prostate Cancer Using Hyperpolarized [1-13C]Pyruvate[END_REF] C- [START_REF] Jannin | Dynamic Nuclear Polarization by Thermal Mixing Under Partial Saturation[END_REF] N correlation experiments (H N -CON). [START_REF] Olsen | Hyperpolarized 3D NMR for Biomolecular Applications[END_REF] Enhancement factors e in such experiments vary between ca. 10 to 500 with respect to signal intensities in thermal equilibrium ceteris paribus. The signal enhancements translate into a squared reduction in experimental time.

The result of a hyperpolarized multidimensional protein NMR experiment differs from a conventional NMR experiment. As the hyperpolarization of the protein is introduced through exchange between hyperpolarized solvent protons and labile protein protons (or through exchange-relayed nuclear Overhauser effects) [START_REF] Kadeřávek | High-Resolution NMR of Folded Proteins in Hyperpolarized Physiological Solvents[END_REF] , the signal enhancement is -like the exchange rate -residue-dependent. For example, in 1 H- [START_REF] Jannin | Dynamic Nuclear Polarization by Thermal Mixing Under Partial Saturation[END_REF] N correlation spectra only such proton-nitrogen pairs are detected that exchange hyperpolarization efficiently with the solvent during the recovery delay between each detection. Hence, only a subset of signals is detected in comparison to the conventional counterpart of a 1 H-15 N correlation spectrum. The "hyperpolarization-selective" detection can be compared with selective labeling approaches, such as targeted [START_REF] Nelson | Metabolic Imaging of Patients with Prostate Cancer Using Hyperpolarized [1-13C]Pyruvate[END_REF] C or [START_REF] Jannin | Dynamic Nuclear Polarization by Thermal Mixing Under Partial Saturation[END_REF] N-enrichment of selected amino acids. [START_REF] Lichtenecker | Selective Isotope Labelling of Leucine Residues by Using α-Ketoacid Precursor Compounds[END_REF][START_REF] Tugarinov | Isotope Labeling Strategies for the Study of High-Molecular-Weight Proteins by Solution NMR Spectroscopy[END_REF] Such techniques render spectra sparse and, hence, allow for residue-specific analysis of larger proteins, for which uniform labeling would lead to strong signal overlap. Similar applications are concievable for large proteins, where signal broadening due to relaxation would be mitigated. The hyperpolarization exchange approach In the ligand free form, OPN populates a compacted core (red and blue patches). When heparin binds to the positively charged part of the core (blue), the negatively charged part of the core (red) becomes more solvent exposed, which leads to the detection of glycine situated within the red marked stretch by means of hyperpolarization-boosted 1 H- [START_REF] Jannin | Dynamic Nuclear Polarization by Thermal Mixing Under Partial Saturation[END_REF] N HMQC (right). In the absence of heparin, these glycines could not be detected.

to high-resolution NMR might turn out to be very powerful supplement to established techniques, which suffer from overlapping signals.

Reducing concentrations, NMR optimized conditions

Hyperpolarized protein NMR is not likely to be superior to conventional NMR, instead it is of a complementary nature. For example, it can be employed to support NMR under physiological conditions (pH 7.4, 37˚C), where conventional techniques may suffer from too low signal intensities. Such penalties can be compensated by hyperpolarization.

Another potential of hyperpolarized protein NMR lies in the possible reduction of substrate concentrations. Typically, NMR of proteins requires that substrate concentrations in the micromolar range (>50 µM). However, physiological concentrations are often much lower, even nanomolar and such variations can lead to significant shifts in the conformational ensemble of a protein. For example, the transcription factor MAX exists predominantly as a well-folded homodimer at higher, NMR-typical concentrations, but at physiological concentrations it mostly adopts an intrinsically disordered conformation. [START_REF] Kizilsavas | Hydrophobic Collapse of the Intrinsically Disordered Transcription Factor Myc Associated Factor X[END_REF] Hyperpolarized protein NMR can enable a reduction of the necessary substrate quantities to physiological concentrations to mitigate such biases. Possibly even in-cell NMR at physiological protein concentrations can be envisaged for future developments of d-DNP rendering this method even more versatile and a possible tool for characterization of low-concentrated and low-yield substrates.

Applications of hyperpolarized NMR to protein interactions

As the nature of hyperpolarized protein NMR is somewhat differing from established applications, novel possibilities to investigate protein interactions become conceivable. [START_REF] Chappuis | Hyperpolarized Water to Study Protein-Ligand Interactions[END_REF][START_REF] Ragavan | Real-Time Analysis of Folding upon Binding of a Disordered Protein by Using Dissolution DNP NMR Spectroscopy[END_REF][START_REF] Karlsson | Hyperpolarized 133 Cs Is a Sensitive Probe for Real-Time Monitoring of Biophysical Environments[END_REF] Among other excellent examples, this has recently been demonstrated at hand of the binding of the extracellular matrix protein osteopontin (OPN) to its ligand heparin. OPN is an intrinsically disordered protein (IDP) that features a disordered yet compacted core region. While the core's increased level of compression shields it from the solvent, other regions of the protein are strongly exposed to the solvent. Binding of heparin to OPN leads to dissolution of the core and consequently changed solvent exposure of the core residues. [START_REF] Kurzbach | Compensatory Adaptations of Structural Dynamics in an Intrinsically Disordered Protein Complex[END_REF] As a consequence, hyperpolarization-selective detection leads to an observation of residues that are localized in the core region only in the heparin-bound state. This relation is visualized in Fig. 4.

Glycine residues located between aa 100 and 180, which take part in the formation of OPN's core region cannot be detected by means of hyperpolarized solvents in the heparin-free form. However, in the presence of heparin, the proton exchange between the core residues and the solvent is accelerated and the glycines become observable. [START_REF] Kurzbach | Investigation of Intrinsically Disordered Proteins through Exchange with Hyperpolarized Water[END_REF] Hence, the set of residues that pass the "hyperpolarization-selective" filter varies due to conformational changes induced by the binding event. This feature provides an accurate indication for a protein interaction and can reveal adaptions of structural dynamics due to population shifts in conformational spaces of IDPs. Such a method might develop into a complement to conventional approaches, such as chemical shift perturbations in ligand titration experiments. Due to the rapid nature of the experiment, which typically takes no longer than 2 min. it also appears to be especially well-suited for metastable targets or transient intermediates allowing for residue-resolved interaction studies in short periods of time.

Potential of d-DNP for metabolomics

Metabolomics is a growing application field that could benefit in the near future from the sensitivity boost offered by d-DNP. Metabolomics -which aims at identifying and quantifying as many metabolites as possible in biological samples-currently relies on mass spectrometry (MS) and NMR as analytical tools. However, the metabolomics field is largely dominated by MS due to the much higher sensitivity of this technique. NMR is still popular thanks to its ease-of-use and to its higher reproducibility and identification capabilities, but the MS/NMR complementarity in metabolomics would certainly be reinforced by more sensitive NMR methods. Recent studies highlighted the potential of d-DNP for the analysis of biological samples such as those commonly encountered in metabolomics. This requires to successfully hyperpolarize complex mixtures and to detect the multiple corresponding signals with a sufficient analytical performance to monitor biological variations between samples from different groups. A first approach consists in incubating the targeted biological samples with [START_REF] Nelson | Metabolic Imaging of Patients with Prostate Cancer Using Hyperpolarized [1-13C]Pyruvate[END_REF] C-labeled substrates, followed by d-DNP on the resulting samples. [START_REF] Lerche | Stable Isotope-Resolved Analysis with Quantitative Dissolution Dynamic Nuclear Polarization[END_REF] This approach was applied to determine the concentration of several metabolites in cell extracts. Since it is based on isotope labeling, this method aims at targeting specific metabolic pathways. An untargeted strategy has also been suggested, which consists in hyperpolarizing samples at natural [START_REF] Nelson | Metabolic Imaging of Patients with Prostate Cancer Using Hyperpolarized [1-13C]Pyruvate[END_REF] C abundance by applying cross-polarization (CP) from 1 H to [START_REF] Nelson | Metabolic Imaging of Patients with Prostate Cancer Using Hyperpolarized [1-13C]Pyruvate[END_REF] C spins. This approach has the double advantage that it does not require [START_REF] Nelson | Metabolic Imaging of Patients with Prostate Cancer Using Hyperpolarized [1-13C]Pyruvate[END_REF] C labeling and that a high and reproducible [START_REF] Nelson | Metabolic Imaging of Patients with Prostate Cancer Using Hyperpolarized [1-13C]Pyruvate[END_REF] C polarization of metabolites can in principle be reached within a few tens of minutes (versus a few hours for the direct [START_REF] Nelson | Metabolic Imaging of Patients with Prostate Cancer Using Hyperpolarized [1-13C]Pyruvate[END_REF] C hyperpolarization of labeled samples). Dumez et al. demonstrated the potential of this approach on plant and cancer cell extracts at natural abundance, both with 1D and ultrafast (UF) 2D NMR detection. 48 While these recent papers open interesting perspectives, several challenges must be addressed before d-DNP can be applied to real metabolomic studies. A notable characteristic of the approaches mentioned above is that only quaternary carbons could be detected thanks to their longer relaxation times. Faster injection systems that could enable the detection of broadband [START_REF] Nelson | Metabolic Imaging of Patients with Prostate Cancer Using Hyperpolarized [1-13C]Pyruvate[END_REF] C spectra of hyperpolarized metabolite mixtures will certainly enhance the applicability of the method. Another key requirement for metabolomics is the precision of the method in terms of repeatability and reproducibility. The signal variation between successive experiments must be significantly smaller than the targeted biological variations (generally of at least 20%). An encouraging result has recently been obtained by Bornet al., who demonstrated the very good repeatability (3.6% in average for signals above the limit of quantification) of d-DNP assisted by CP on tomato extracts (Fig. 5). [START_REF] Bornet | Highly Repeatable Dissolution Dynamic Nuclear Polarization for Heteronuclear NMR Metabolomics[END_REF] Note that the trueness of d-DNP is not an issue since only relative concentration variations between samples are sought. In particular, the T1-weighting of metabolite signals is unavoidable but is not an issue if the T1 variations between samples within a metabolomics study are negligible and if the experiment is reproducible. Still, absolute metabolite concentrations can in principle be measured by applying adequate correction factors determined with refernce samples. 36 [START_REF] Nelson | Metabolic Imaging of Patients with Prostate Cancer Using Hyperpolarized [1-13C]Pyruvate[END_REF] C NMR evaluated on 8 successive experiments performed on identical tomato extracts. The average precision, expressed in terms of repeatability, is 6.4% for all buckets containing signals above the limit of detection (LOD), and 3.6% when only the 16 buckets with signals above the limit of quantification (LOQ) are taken into account. The dashed orange bars correspond to the average SNR of the corresponding buckets, showing that the repeatability is proportional to the inverse of the SNR. The buckets are numbered from 1 to 26, indicated by lines on top of the spectra. Those in bold indicate buckets containing signals above the LOQ. Reproduced with permission from Reference [START_REF] Bornet | Highly Repeatable Dissolution Dynamic Nuclear Polarization for Heteronuclear NMR Metabolomics[END_REF] .

While these studies pave the way towards hyperpolarized NMR metabolomics, future work will need to explore if d-DNP can bring more than conventional 1 H metabolomics, both in terms of sample classification and biological interpretation. Such exploration will require embedding d-DNP in a meticulous analytical workflow including careful sample preparation, hyperpolarized NMR and data analysis.

Interaction monitoring -Applications to General Chemistry and Biochemistry

The potential of real-time monitoring has given rise to some remarkable studies in the recent past. For example, tracking of fast folding-upon-binding processes of proteins, of in-cell metabolic conversion, [START_REF] Harris | Kinetics of Hyperpolarized 13C1-Pyruvate Transport and Metabolism in Living Human Breast Cancer Cells[END_REF] enzyme kinetics [START_REF] Sadet | Rates of Chemical Reactions Embedded in a Metabolic Network by Dissolution Dynamic Nuclear Polarisation NMR[END_REF] , pH jumps [START_REF] Nardi-Schreiber | Biochemical Phosphates Observed Using Hyperpolarized 31P in Physiological Aqueous Solutions[END_REF] or biomineralization processes. [START_REF] Weber | Real-Time Monitoring of Calcium Phosphate Pre-Nucleation Clusters for-Mation by Dissolution Dynamic Nuclear Polarization[END_REF] The general principle in all these applications is to hyperpolarize one interaction partner and to mix it with another interaction partner upon dissolution and transfer to the detection spectrometer followed by real-time NMR detection by either low-dimensional or higher-dimensional (ultrafast-detected) techniques (cf. Fig. 6) to follow the event in time. Among many excellent examples, one very interesting demonstration by Hilty and co-workers [START_REF] Lee | Detection of Living Anionic Species in Polymerization Reactions Using Hyperpolarized NMR[END_REF] is based on monitoring signal intensities of live anionic chain ends in the polymerization of polystyrene. The d-DNP approach allowed to deduce details about reaction mechanisms and kinetic parameters with high precision. Another example by Abergel and co-workers is based on enzymatic conversion of hyperpolarized metabolites that are mixed upon dissolution with a protein cocktail that mimics parts of the physiological metabolic network. [START_REF] Sadet | Rates of Chemical Reactions Embedded in a Metabolic Network by Dissolution Dynamic Nuclear Polarisation NMR[END_REF][START_REF] Miclet | Toward Quantitative Measurements of Enzyme Kinetics by Dissolution Dynamic Nuclear Polarization[END_REF] The conversion of the metabolite can then be monitored by following the build-up of NMR signals of the reaction products. Such, parts of the pentose phosphate pathway (PPP) have been studied by using hyperpolarized glucose (GLU) as tracer molecule that is mixed with a mixture of hexokinase (HA) and adenosine-triphosphate (ATP). By analyzing the decay of the educt GLU signal and the signal build-up of the product glucose-6-phosphate (G6P) with elaborate kinetic models, unprecedented insights (e.g. that phosphorylation of both α and β glucose anomers proceeds with comparable efficiencies) into kinetics and mechanism behind the PPP could be revealed. d-DNP is a tool with potentially universal scope for reaction monitoring on milliseconds to seconds time scales and it might possibly develop into a versatile technique to monitor and study the early onset of a plethora of chemical processes.

Perspective on instrumentation and methods developments

Like NMR spectroscopy in general, d-DNP devices and techniques are undergoing continuous developments. In the following, we will give an account of the current state-of-the-art and possible future avenues as well as consequences for possible applications of d-DNP.

d-DNP and ultrafast NMR detection

The fast decaying and, more importantly, non-renewable nature of DNP-enhanced polarization, once in solution, makes it challenging, and in many cases, impossible, to collect multidimensional NMR spectra with classic time-incremented experiments. An important exception is the HMQC experiment, which is compatible with multi-scan acquisition when implemented with small-tip angle excitation pulses. [START_REF] Zeng | Sequentially Acquired Two-Dimensional NMR Spectra from Hyperpolarized Sample[END_REF] A general solution to the problem of collecting 2D spectra from hyperpolarized substrates is to use single-scan, so called "ultrafast" NMR methods, based on the principle of spatial encoding. This was demonstrated early on by Frydman and co-workers with the acquisition of HSQC spectra. [START_REF] Frydman | Ultrafast Two-Dimensional Nuclear Magnetic Resonance Spectroscopy of Hyperpolarized Solutions[END_REF] Further demonstrations include the acquisition of [START_REF] Nelson | Metabolic Imaging of Patients with Prostate Cancer Using Hyperpolarized [1-13C]Pyruvate[END_REF] C-1 H spectra from hyperpolarized natural products or complex metabolic mixtures. [START_REF] Giraudeau | Multiple Ultrafast, Broadband 2D NMR Spectra of Hyperpolarized Natural Products[END_REF]48 Spatial encoding is also the basis for ultrafast Laplace NMR (UFLNMR), where diffusion and/or relaxation information is encoded spatially. [START_REF] Frydman | Ultrafast Two-Dimensional Nuclear Magnetic Resonance Spectroscopy of Hyperpolarized Solutions[END_REF] UFLNMR was used by Telkki and co-workers to obtain chemical information in heterogeneous media from hyperpolarized compounds, or to speed up the acquisition of water diffusivity and relaxation data in low-field NMR using single-sided magnets. [START_REF] Frydman | Ultrafast Two-Dimensional Nuclear Magnetic Resonance Spectroscopy of Hyperpolarized Solutions[END_REF] Diffusion data can also be obtained in a single scan with chemical shift resolution from hyperpolarized substrates. This requires the use of convection-compensated diffusion encoding schemes. (Fig. 6). [START_REF] Frydman | Ultrafast Two-Dimensional Nuclear Magnetic Resonance Spectroscopy of Hyperpolarized Solutions[END_REF] Overall, single-scan 2D NMR offers many promising options to increase the information content of DNP-enhanced experiments, although these have been little exploited so far. One limitation of the approach is that many single-scan 2D methods are not compatible with the acquisition of multiple consecutive spectra, while most applications of d-DNP concern time-evolving samples. While the sensitivity penalty associated with the gradient-based acquisition of UF2DNMR may also be a concern, it is counter-balanced in d-DNP by the single vs multi scan nature of the experiment. 59 Several strategies have also been reported to obtain effectively multidimensional information from a small number of scans, in a way that is compatible with new renewable hyperpolarized signals. For example, Hilty and co-workers have used off resonance [START_REF] Nelson | Metabolic Imaging of Patients with Prostate Cancer Using Hyperpolarized [1-13C]Pyruvate[END_REF] C decoupling to scale the apparent [START_REF] Nelson | Metabolic Imaging of Patients with Prostate Cancer Using Hyperpolarized [1-13C]Pyruvate[END_REF] C-1 H coupling in 1 H 1D spectra and provide access to the chemical shift of the coupled carbon for each proton. [START_REF] Bowen | Chemical Shift Correlations from Hyperpolarized NMR by Off-Resonance Decoupling[END_REF] They also showed how the selective inversion of a signal can result in a new type of correlation between, e.g. reactant and product, for systems undergoing a chemical reaction. [START_REF] Bowen | Temporal Chemical Shift Correlations in Reactions Studied by Hyperpolarized Nuclear Magnetic Resonance[END_REF] This strategy was used to help in the mechanistic analysis of metal catalyzed polymerization reactions. [START_REF] Chen | In Situ Determination of Tacticity, Deactivation, and Kinetics in [ Rac -(C 2 H 4 (1-Indenyl) 2 )ZrMe[END_REF]

Sample throughput

A main shortcoming of the d-DNP state-of-the-art is its low sample throughput. Hyperpolarization buildup times are often on the order of hours such that only few experiments are possible per day. To overcome this bottleneck, an instrumentation workaround has recently been developed that allows one to hyperpolarize several samples at the same time, but to dissolve them sequentially such that high experimental repetition rates and multi-shot experiments become possible. [START_REF] Krajewski | A Multisample Dissolution Dynamic Nuclear Polarization System for Serial Injections in Small Animals: Multisample Dissolution DNP Polarizer for Small Animals[END_REF][START_REF] Hu | Rapid Sequential Injections of Hyperpolarized [1-13C]Pyruvate in Vivo Using a Sub-Kelvin, Multi-Sample DNP Polarizer[END_REF] Another effective way of enhancing sample throughput consists in the use of 1 H- [START_REF] Nelson | Metabolic Imaging of Patients with Prostate Cancer Using Hyperpolarized [1-13C]Pyruvate[END_REF] C cross polarization together with a rapid and efficient hyperpolarization of [START_REF] Ardenkjaer-Larsen | Increase in Signal-to-Noise Ratio of > 10,000 Times in Liquid[END_REF] H spins with broad lines PAs such as nitroxides. [START_REF] Batel | Dissolution Dynamic Nuclear Polarization Efficiency Enhanced by Hartmann-Hahn Cross Polarization[END_REF][START_REF] Bornet | Cross Polarization for Dissolution Dynamic Nuclear Polarization Experiments at Readily Accessible Temperatures 1.2 < T < 4.2 K[END_REF] By further increasing the polarizing magnetic field [START_REF] Vuichoud | Hyperpolarization of Deuterated Metabolites via Remote Cross-Polarization and Dissolution Dynamic Nuclear Polarization[END_REF] , implementing suitable frequency modulation of the microwave irradiation [START_REF] Bornet | Microwave Frequency Modulation to Enhance Dissolution Dynamic Nuclear Polarization[END_REF] and performing microwave gating during CP [START_REF] Bornet | Microwave-Gated Dynamic Nuclear Polarization[END_REF] , record [START_REF] Nelson | Metabolic Imaging of Patients with Prostate Cancer Using Hyperpolarized [1-13C]Pyruvate[END_REF] C polarizations > 60% have been achieved in less than 10 minutes. It is most likely that these advances will be further improved in the near future by better radiofrequency coil designs. (CP experiments are currently performed with B1 < 20 kHz whereas > 50 kHz values would be desirable.) Another route to improve the throughput would be the use of more efficient PAs that would polarize 1 H-nuclei faster and higher, possibly even at higher temperatures. For the moment, the best PAs for proton DNP are simplest forms of nitroxide radicals (such as TEMPO, amino-TEMPO, or TEMPOL) but one can hope that well-chosen or newly designed PAs may surpass the existing ones (see for example the current effort to improve PAs in MAS-DNP). [START_REF] Lesage | Surface Enhanced NMR Spectroscopy by Dynamic Nuclear Polarization[END_REF][START_REF] Rosay | Solid-State Dynamic Nuclear Polarization at 263 GHz: Spectrometer Design and Experimental Results[END_REF][START_REF] Shimon | Static 1 H Dynamic Nuclear Polarization with the Biradical TOTAPOL: A Transition between the Solid Effect and the Cross Effect[END_REF] These developments may pave the way towards applications of d-DNP with enhanced sample throughput such as compound screening applications in combinatorial research.

Solid transfer, liquid transfer -Applications to spin physics

Typically for d-DNP, samples are dissolved within the DNP apparatus and subsequently transferred in the liquid state to the detection NMR spectrometer. However recently, it has been demonstrated that a transfer of some solid samples is likewise feasible if the transfer is very rapid, i.e. on the order of 100 ms, and the magnetic field B trans does not drop below a critical values where nuclear thermal mixing occurs. [START_REF] Kouřil | Dissolution-Dynamic Nuclear Polarization with Rapid Transfer of a Polarized Solid[END_REF] While, d-DNP of solutes in liquid state samples is currently further developed and applicable to various NMR active nuclei, the solid-transfer development opens new avenues for applications of d-DNP, not only with respect to NMR of hyperpolarized liquids and solids, [START_REF] Eills | Preservation of Nuclear Spin Order by Precipitation[END_REF] but also with respect to hyperpolarized NMR of dissolved gases. Fig. 7 displays a sketch of the setup developed to transfer a DNP hyperpolarized solid sample to the NMR spectrometer. The transfer of solids is a promising method to study the effect of temperature jumps on spin dynamics, as has been shown in a recent example where the para-to-ortho conversion of proton nuclear spins was studied in hyperpolarized water molecules enclosed in C60 fullerene cages (H2O@C60). Such conversions have been subject to many speculations due to the omnipresence of ortho-and para-water, [START_REF] Mammoli | Challenges in Preparing, Preserving and Detecting Para-Water in Bulk: Overcoming Proton Exchange and Other Hurdles[END_REF] but have so far been cumbersome to access due to fast proton exchange in water. Yet, Meier and co-wokers showed that hyperpolarized H2O@C60 facilitated the access to these states and to study their properties, albeit somewhat artificial conditions. [START_REF] Meier | Spin-Isomer Conversion of Water at Room Temperature and Quantum-Rotor-Induced Nuclear Polarization in the Water-Endofullerene H 2 O @ C 60[END_REF] After rapid transfer of solid H2O@C60 from cold temperatures close to 1 K to an NMR spectrometer operating at ambient temperatures T NMR , a conversion of para water to ortho water can be observed at hand of the intensity of the water NMR signal. Similar principles can be applied to a plethora of other substrates to study the effect of rapid temperature changes on nuclear polarizations and dynamics. Especially in highly symmetric systems interesting results can be anticipated. [START_REF] Dumez | Theory of Long-Lived Nuclear Spin States in Methyl Groups and Quantum-Rotor Induced Polarisation[END_REF][START_REF] Jhajharia | Communication: Dissolution DNP Reveals a Long-Lived Deuterium Spin State Imbalance in Methyl Groups[END_REF] Another potential provided by the transfer-thendissolution approach lies in the study of dissolved gases. The traditional dissolution-then-transfer strategy often suffers from imminent degassing of the solution. Typically, pressurized helium is used to rapidly push the dissolved sample in the liquid state through a capillary towards the detection NMR spectrometer. This process has undergone intense optimization in recent years. [START_REF] Bowen | Rapid Sample Injection for Hyperpolarized NMR Spectroscopy[END_REF] However, the applied pressure leads to a removal of the gas from the solution. This problem could be overcome by first transferring a hyperpolarized frozen gas pellet to the detection NMR spectrometer and then dissolving it in a suitable liquid in-situ within the spectrometer. Such, NMR of important substances such as methane, ethylene or 15 N2, might become possible. [START_REF] Vuichoud | Hyperpolarization of Frozen Hydrocarbon Gases by Dynamic Nuclear Polarization at 1.2 K[END_REF] This might render dDNP more versatile and applicable to a broader range of scientific problems.

Transportable hyperpolarized substrates

The concept of solid-state transfer of the DNP sample is also currently opening new avenues for remote transport of hyperpolarized samples, which will ultimately make the presence of a DNP machine at the point of the NMR experiment unnecessary. Three proof of concept papers that were recently published indeed demonstrated that transport of hyperpolarized substances could be possible over tens of hours timescales. This was done either by brute force polarization (with PA-free sample formulation) [START_REF] Hirsch | Transport and Imaging of Brute-Force 13 C Hyperpolarization[END_REF] , by 1 H- [START_REF] Nelson | Metabolic Imaging of Patients with Prostate Cancer Using Hyperpolarized [1-13C]Pyruvate[END_REF] C CP-DNP (on sub-micron heterogenous sample formulations) [START_REF] Ji | Transportable Hyperpolarized Metabolites[END_REF] , or by thermal annihilation of photo-induced radicals (using UV excitation) [START_REF] Capozzi | Thermal Annihilation of Photo-Induced Radicals Following Dynamic Nuclear Polarization to Produce Transportable Frozen Hyperpolarized 13C-Substrates[END_REF] . The key in these approaches always is the absence of paramagnetic relaxation during the transport step. It is likely that in the next couple of years, these methods will develop further and enable remote hyperpolarized applications (such as real-time metabolic imaging, metabolomics, drug discovery, etc.). The prospect of hyperpolarization in dedicated DNP centers may raise the question of a scaling-up of DNP sample quantities and throughput to much higher extents than today, which may lead to a radical transformation of the DNP instrumentation towards high volume cryostats, high power microwave sources, lower cryogenic fluid consumption, etc.

Outlook

This article tried to outline selected possible applications of d-DNP that might be of interest for a broader community covering physical, chemical and biological research. Many potentials emerged up to now due to the progress d-DNP has undergone since its invention in 2003, and its future developments seem promising in view of the current state-of-the-art. However, d-DNP remains a complicated method, which is often cumbersome to use, and expert operators are often necessary as many factors need to be considered ranging from low-temperature nuclear physics, over hydrodynamics to rapid NMR detection. A possible avenue for a more widespread application of d-DNP could be hyperpolarization user facilities, where external users can apply and be supported by local expert staff. Examples in this direction are (among others) the d-DNP facilities at EPFL and CRMN Lyon 48,[START_REF] Gajan | Hybrid Polarizing Solids for Pure Hyperpolarized Liquids through Dissolution Dynamic Nuclear Polarization[END_REF][START_REF] Jannin | Kinetics of Yttrium-Ligand Complexation Monitored Using Hyperpolarized 89 Y as a Model for Gadolinium in Contrast Agents[END_REF] , at the ENS Paris, [START_REF] Guarin | Characterizing Thermal Mixing Dynamic Nuclear Polarization via Cross-Talk between Spin Reservoirs[END_REF][START_REF] Guduff | Single-Scan 13 C Diffusion-Ordered NMR Spectroscopy of DNP-Hyperpolarised Substrates[END_REF][START_REF] Ivanov | Relaxation of Long-Lived Modes in NMR of Deuterated Methyl Groups[END_REF] and at the MagLab in Talahassee where numerous biologically, physically and chemically oriented projects of external users of d-DNP have been successfully executed with the help of local operators. If such direction were to be pursued, developments that NMR spectroscopy has undergone in the last 40 years, from an expert method to almost completely automated facilities could be envisaged for future developments of d-DNP. Alternatively, the prospects of transportable hyperpolarization might also definitely eliminate the need for an on-site d-DNP access and simply transform hyperpolarization into a consumable (such as PET tracers).

Figure 1 .

 1 Figure 1. Principle setup of a d-DNP experiment. The DNP apparatus (left) typically operates at comparable or slightly lower magnetic fields than the NMR spectrometer used for detection (right). Qualitative magnetic field, B, and temperature, T, profiles as a function of time are sketched below together with the association of the different phases (i, ii and iii) of a d-DNP experiment with the different parts of the setup.

Figure 2 .

 2 Figure 2. Comparison of a conventional NMR experiment with a d-DNP experiment. a) Traditionally, NMR detects the nuclear spin polarization in thermal equilibrium by means of a 90˚ detection pulse that reads the entire polarization. Subsequently, one waits for rebuild-up of the nuclear spin polarization to repeat the experiment. Typical, recovery delays are between a few hundreds of milliseconds to minutes. In contrast, in d-DNP the entire experiment is executed during a single period (b, c). One may use a single read-out pulse, which yields a single very intense spectrum. Yet, typically for 1D NMR by dDNP, the experiment starts with such an intense polarization that allows for small angle detection such that only small shares of the polarization are used to read the signal (or Ernst angles in cases of continuously replenished intermetdaites). The detection can be repeated rapidly, e.g. every 100 ms, before the hyperpolarization has decayed to thermal equilibrium polarization. This strategy is useful for monitoring dynamic/kinetic processes on a T1 timescale, but if sensitivity enhancement is the main goal, a single 90° can likewise be applied to obtain a maximum signal in a single detection.

  Figure 2. Comparison of a conventional NMR experiment with a d-DNP experiment. a) Traditionally, NMR detects the nuclear spin polarization in thermal equilibrium by means of a 90˚ detection pulse that reads the entire polarization. Subsequently, one waits for rebuild-up of the nuclear spin polarization to repeat the experiment. Typical, recovery delays are between a few hundreds of milliseconds to minutes. In contrast, in d-DNP the entire experiment is executed during a single period (b, c). One may use a single read-out pulse, which yields a single very intense spectrum. Yet, typically for 1D NMR by dDNP, the experiment starts with such an intense polarization that allows for small angle detection such that only small shares of the polarization are used to read the signal (or Ernst angles in cases of continuously replenished intermetdaites). The detection can be repeated rapidly, e.g. every 100 ms, before the hyperpolarization has decayed to thermal equilibrium polarization. This strategy is useful for monitoring dynamic/kinetic processes on a T1 timescale, but if sensitivity enhancement is the main goal, a single 90° can likewise be applied to obtain a maximum signal in a single detection.

Figure 3 .

 3 Figure 3.Experimental strategy for hyperpolarized multi-dimensional NMR of proteins. Top: To couple D-DNP with high-resolution protein NMR applications, hyperpolarized aqueous buffers are produced and subsequently mixed with a protein solution. Rapid exchange of hyperpolarized protons between the water in the buffer and the target proteins introduced hyperpolarization into the protein. As proton exchange is quite efficient at pH 7.4 and 37˚C, NMR under near-physiological is feasible by this approach. Bottom: 1 H-15 N HMQC of ubiquitin detected through hyperpolarized 96% deuterated PBS buffer (red) superimposed to a conventional HSQC in 10% deuterated PBS (black). Evidently, not all residues can be detected by hyperpolarization-based detection as the signal intensity depends on the efficiency of the exchange of hyperpolarization between the solvent and the protein. The resulting spectra are, hence, sparse and reminiscent of selective labeling techniques based on selectively isotope enriched amino acids.

Figure 4 .

 4 Figure 4. Sketch of the IDP OPN.In the ligand free form, OPN populates a compacted core (red and blue patches). When heparin binds to the positively charged part of the core (blue), the negatively charged part of the core (red) becomes more solvent exposed, which leads to the detection of glycine situated within the red marked stretch by means of hyperpolarization-boosted 1 H-[START_REF] Jannin | Dynamic Nuclear Polarization by Thermal Mixing Under Partial Saturation[END_REF] N HMQC (right). In the absence of heparin, these glycines could not be detected.

Figure 5 .

 5 Figure 5. Potential of CP-assisted D-DNP for metabolomics. (a) Quaternary region of a[START_REF] Nelson | Metabolic Imaging of Patients with Prostate Cancer Using Hyperpolarized [1-13C]Pyruvate[END_REF] C NMR spectrum of a green tomato fruit pericarp extract. (b) Thermal spectrum obtained without hyperpolarization on an identical extract. (c) Single-scan[START_REF] Nelson | Metabolic Imaging of Patients with Prostate Cancer Using Hyperpolarized [1-13C]Pyruvate[END_REF] C NMR spectrum of a 20 mg extract. (c) Repeatability and sensitivity of D-DNP[START_REF] Nelson | Metabolic Imaging of Patients with Prostate Cancer Using Hyperpolarized [1-13C]Pyruvate[END_REF] C NMR evaluated on 8 successive experiments performed on identical tomato extracts. The average precision, expressed in terms of repeatability, is 6.4% for all buckets containing signals above the limit of detection (LOD), and 3.6% when only the 16 buckets with signals above the limit of quantification (LOQ) are taken into account. The dashed orange bars correspond to the average SNR of the corresponding buckets, showing that the repeatability is proportional to the inverse of the SNR. The buckets are numbered from 1 to 26, indicated by lines on top of the spectra. Those in bold indicate buckets containing signals above the LOQ. Reproduced with permission from Reference[START_REF] Bornet | Highly Repeatable Dissolution Dynamic Nuclear Polarization for Heteronuclear NMR Metabolomics[END_REF] .

  Average precision for buckets with SNR > LOQAverage precision for buckets with SNR >

Figure 6 .

 6 Figure 6. Description of the d-DNP SPEN DOSY experiment. a) Timing of the polarization, dissolution and acquisition steps, with the evolution of the temperature and magnetic field. b) Spin-echo SPEN DOSY pulse sequence. c) Double spin-echo SPEN DOSY pulse sequence. d) Double diffusion encoding SPEN DOSY pulse sequence. Crusher gradients are shown in grey. The selected coherence transfer pathway is shown in red. Reproduced with permission from reference 60 . e) DOSY spectrum for the double-diffusion-encoding SPEN DOSY pulse sequence, obtained in a single D-DNP experiment.

Figure 7 .

 7 Figure 7. Setup for transfer of a DNP hyperpolarized solid sample to an NMR spectrometer as proposed by Meier and co-workers. After DNP (left) the solid sample is pushed by pressurized helium through a tube surrounded by a solenoid that maintains a non-zero magnetic field during the transfer within ca. 100 ms to a detection spectrometer (right), where it is dissolved prior to injection into an NMR tube. Reproduced with permission from reference 34 .

Acknowledgments

The authors acknowledge support of the European Research Council under the European Union's Horizon 2020 research and innovation program (ERC Grant Agreements n°714519/HP4all and n°801936/HYPRO-TIN). Support from the French National Research Agency (Grant ANR-17-ERC2-0011) is also acknowledged. Support from the Corsaire metabolomics core facility is also acknowledged.