Midhun Puthumana Melepattu

Clément De Loubens

Steady streaming flow induced by active biological microstructures; application to small intestine villi

Physiological transport of fluid at small scales is often achieved by microscopic active finger-like structures. It is recognized that they have to move in a non-symmetric fashion in order to break the symmetry of creeping flow and to induce a net movement of the fluid. However, in the limit of low, but non-vanishing, Reynolds number, irreversible flow on long time scales could also be generated by symmetric oscillations of these microstructures.

Inspired by small intestine villi, we reported three dimensional direct numerical simulations of the irreversible part of the flow, namely steady streaming flow (SSF), generated by an array of oscillating finger-like structures. In order to capture these second order flow phenomena, the algorithm was based on a combination of lattice-Boltzmann methods with two relaxation times and the smoothed profile method.

SSF was confined inside a steady viscous boundary above the villi. Two steady vortices at the tip of the villi characterized this flow, which induced mass transfers between the bulk and the periphery. Strikingly, the spatial extension of these vortices was not solely governed by the Stokes boundary layer but also by the lateral confinement between the villi. Moreover, secondary vortices outside the steady boundary layer were also observed. These findings were rationalized in a state diagram showing three regimes of SSF. Lastly, orders of magnitude showed that SSF should contribute to the transport of particles, such as bacteria or nano-particles, on a layer of a few hundred micrometers above the villi and on time scales of few minutes.

I. INTRODUCTION

Transport of fluids at small scale in biological organisms is achieved by active boundaries or active microstructures. The main constraint is coping with the strong dominance of viscous force over inertia which means that any reversible movement of these boundaries or structures does not induce a net movement of the fluid. [START_REF] Purcell | Life at low reynolds number[END_REF][START_REF] Dabiri | Landmarks and frontiers in biological fluid dynamics[END_REF] In the lymphatic vessels, microscopic valves prevent the reflux of lymph during the contraction of lymphangions. [START_REF] Margaris | Modelling the lymphatic system: challenges and opportunities[END_REF] In the airways, the cerebral ventricles or the female reproductive tract, propulsion is achieved by carpets of ciliated cells, which are microscopic, active and flexible finger-like structures of a few dozen micrometers in length. [START_REF] Marshall | Cilia orientation and the fluid mechanics of development[END_REF] Net movement of the fluid in one direction is made possible with the non-reciprocal beating of these cilia and their coordination. [START_REF] Brennen | Fluid mechanics of propulsion by cilia and flagella[END_REF][START_REF] Dauptain | Hydrodynamics of ciliary propulsion[END_REF][START_REF] Siyahhan | Flow induced by ependymal cilia dominates near-wall cerebrospinal fluid dynamics in the lateral ventricles[END_REF][START_REF] Smith | Symmetry-breaking cilia-driven flow in embryogenesis[END_REF][START_REF] Loiseau | Active mucus-cilia hydrodynamic coupling drives self-organization of human bronchial epithelium[END_REF] In the gastrointestinal tract, flow and mixing is secured at macroscopic scale by smooth muscle motility which generates standing and propagating contractions (e.g. segmentation and peristaltis). [START_REF] Schulze | Imaging and modelling of digestion in the stomach and the duodenum[END_REF][START_REF] Lentle | A review of mixing and propulsion of chyme in the small intestine: fresh insights from new methods[END_REF] Like other organs, small intestine mucosa is also covered by fingershaped or leaf-shaped microstructure of a few hundred micrometers in length called villi (Fig. 1-a). Whereas it has long been considered that the presence of villi should passively increase the absorption of nutrients by increasing the exchange surface between the mucosa and the lumen, [START_REF] Strocchi | Role of villous surface area in absorption science versus religion[END_REF] several studies have pointed out an active enhancement of absorption by these structures. [START_REF] Westergaard | Measurement of resistance of barriers to solute transport in vivo in rat jejunum[END_REF][START_REF] Mailman | Villous motility and unstirred water layers in canine intestine[END_REF][START_REF] Levitt | Human jejunal unstirred layer: evidence for extremely efficient luminal stirring[END_REF] At first sight, this enhancement could be explained by the obsera) clement.de-loubens@univ-grenoble-alpes.fr vations of Gruby and Delafond in 1843, [START_REF] Gruby | Resultats des recherches faites sur l'anatomie et les fonctions des villosites intestinales, l'absorption, la preparation et la composition organique du chyle dans les animaux[END_REF] who reported spontaneous activity of villi in living animals. Uncoordinated piston-like and pendular movements of villi were described one century later in ex-vivo preparations. [START_REF] Hambleton | Note upon the movements of the intestinal villi[END_REF][START_REF] Kokas | Intestinal villous motility and its regulation[END_REF][START_REF] Joyner | Effect of various gastrointestinal hormones and vasoactive substances on villous motility[END_REF][START_REF] Womack | Quantitative as-sessment of villous motility[END_REF] More recently, characterization of the mechanical behaviour of isolated villi under flow showed that villi can be considered as relatively rigid structures that cannot be deformed by physiological flow [START_REF] Lim | Determination of villous rigidity in the distal ileum of the possum (trichosurus vulpecula)[END_REF] and their movement is driven by standing or propagating activity of the mucosa. [START_REF] Lentle | Mucosal microfolds augment mixing at the wall of the distal ileum of the brushtail possum[END_REF] It is very unlikely that net fluid transport in the small intestine at microscopic scale is induced by a nonsymmetric motion of villi motion, contrary to flexible ciliated cells. Consequently, in creeping flow conditions, the only source of irreversibility in mass transfers generated by symmetric activity of the villi is diffusion. [START_REF] Lentle | Mucosal microfolds augment mixing at the wall of the distal ileum of the brushtail possum[END_REF][START_REF] Lim | Flow and mixing by small intestine villi[END_REF][START_REF] Zhang | How motility can enhance mass transfer and absorption in the duodenum: Taking the structure of the villi into account[END_REF] However, it is worth noting that there is a difference of several orders of magnitudes between the time scale of smooth muscle motility (∼ 1 s) and the resident time of the fluid in the small intestine (∼ 10 3 s). [START_REF] Lentle | The physical processes of digestion[END_REF] These considerations lead us to the hypothesis that cyclic and symmetric movement of the villi could trigger second order flow phenomena, at low, but non vanishing, Reynolds number, and consequently irreversible transport phenomena on long time scales.

Indeed, periodic forcing flow at moderate Reynolds number induced a non-zero time average flow, the socalled steady-streaming flow (SSF). [START_REF] Riley | Steady Streaming[END_REF] This flow phenomena can be triggered by an acoustic wave, 27 a periodic pressure gradient, [START_REF] Holtsmark | Boundary layer flow near a cylindrical obstacle in an oscillating, incompressible fluid[END_REF] or the oscillation of a rigid body. [START_REF] Tatsuno | Circulatory streaming around an oscillating circular cylinder at low reynolds numbers[END_REF] SSF results from the time-irreversible convective term in Navier-Stokes equations and attracts lots of attention to overcome limitations of low Reynolds number flows for active mixing, particle sorting in microfluidics devices [START_REF] Costalonga | Low frequency vibration induced streaming in a hele-shaw cell[END_REF][START_REF] Mackley | Mixing and dispersion in a baffled tube for steady laminar and pulsatile flow[END_REF][START_REF] Dincau | Pulsatile flow in microfluidic systems[END_REF] or trapping particles with hy- Other and that spaces is uld limit . [START_REF] Westergaard | Measurement of resistance of barriers to solute transport in vivo in rat jejunum[END_REF][START_REF] Levitt | Human jejunal unstirred layer: evidence for extremely efficient luminal stirring[END_REF] The everted segment was cannulated at the oral and aboral ends, and installed in the organ bath at the same length as it was in vivo and with the mesenteric attachment located at the upper edge of the video image. The organ bath contained 170 mL of HBS solution with the following composition in millimoles: NaCl 124.0, KCl 5.4, MgSO4 0.8, NaH2PO4 1.0, NaHCO3 14.3, Hepes 10.0, CaCl2 1.8, and glucose 5.0 and with a pH of 7.35. The solution was warmed to 37 °C, continuously carboxygenated (95% O2, 5% CO2), and recirculated at 60 mL/min. The lumen of the gut segment was perfused with HBS at a rate of l-2 mL/min and the perfusion pressure was maintained at 0-2 cm of water by appropriate adjustment of the height of the outflow at the distal end of the preparation.

To determine the effect of eversion on motility, the excised gut segments were either mounted directly in the organ bath or everted before mounting. In some cases, segments were removed from the bath after image capture, and again everted and remounted in the bath for further image capture. Excised segments of both everted and non-everted ileum were installed in the organ bath with length equal to that determined in vivo. Subsequently, the effect of the lengthening or shortening of a given segment on microfold formation was determined by changing the position of the distal cannula. A further series of experiments was conducted on unstained everted segments to determine whether the application of the methylene blue dye had influenced the formation of microfolds.

Image acquisition and spatiotemporal mapping

The movements of the mucosa and associated villi covering the external surface of the segment of ileum were recorded with a camera (Basler, scA1000-20fc, Ahrensburg, Germany) and zoom lens (Cosmicar 12.5-75 mm) mounted 30 cm above the organ bath so as to give a magnified view of a short section of the ileum. A second camera (The Imaging Source DMK41AF02, Taipei, Taiwan) was mounted 40 cm to the side of the tank so as to give a view of the whole segment of ileum. Monochrome images were captured from both cameras at a rate of five frames per second and stored as The smoothed profile of a villi in the (x-z) plane. The lines are the lattice grid and the contour is the villi domain which is described by Eq.11 with dv = 20∆x and ξ = ∆x. drodynamical tweezers. [START_REF] Karimi | Hydrodynamic mechanisms of cell and particle trapping in microfluidics[END_REF] In the biological world, selfpropulsion of micro-swimmers at moderate Reynolds number [START_REF] Dombrowski | Transition in swimming direction in a model self-propelled inertial swimmer[END_REF] and mixing in micro-cavities in the respiratory system (acinar) [START_REF] Kumar | Steady streaming: A key mixing mechanism in low-reynolds-number acinar flows[END_REF] have been attributed to SSF. Periodic forcing induces the emergence of an unsteady viscous boundary layer near the boundary in which the vorticity is non-zero, the so-called Stokes layer δ St . Consequently, the main non-dimensionless number that characterizes SSF is the modified Reynolds number (or Womersley number), Re m = d ωρ/µ, which represents the ratio between the characteristic length of the flow d and the thickness of the Stokes layer δ St = µ/ωρ where µ is the fluid viscosity, ω the pulsation of the forcing, and ρ the fluid density. Concerning small intestine villi, our hypothesis is supported at first sight by the fact that the Stokes layer is of the same order of magnitude as the dimensions of the villi; Re m ∼ 0.1 -1, by taking the villi diameter d v as the characteristic length (Table I).

Our objective is to simulate steady streaming flow induced by small intestine villi in a prototypical situation and these effects on fluid transport on long time scales. We considered a 3D infinite array of oscillating villi in a semi-infinite space. For this purpose, we developed a flow solver that combined a lattice-Boltzmann model with two-relaxation times and the smoothed profile method in order to capture this second order flow phenomena. Firstly, we validated the model with a benchmark. Secondly, we studied the influence of the different dimensionless parameters on the thickness of the unsteady viscous boundary layer. Thirdly, we showed that steadystreaming flow patterns are strongly dependent on the lateral confinement between the villi. Lastly, we dis-cussed the consequences of SSF phenomena at scale of villi on mass transfers and transport of particles in the small intestine of mammals.

II. MODEL AND METHODS

The three-dimensional geometry under consideration was an infinite array of small intestine villi with a fingerlike structure by using periodic boundary conditions in x and y directions, Fig. 1-a, b. We considered a semiinfinite space as the length of the villi (∼ 500 µm) is small compared to the diameter of the small intestine (∼ 1-5 cm). In regard to experimental evidence, we considered the villi as a rigid structure. [START_REF] Lim | Determination of villous rigidity in the distal ileum of the possum (trichosurus vulpecula)[END_REF] metrical values of villi dimensions in several species. [START_REF] Lim | Determination of villous rigidity in the distal ileum of the possum (trichosurus vulpecula)[END_REF][START_REF] Hosoyamada | Structural and mechanical architecture of the intestinal villi and crypts in the rat intestine: integrative reevaluation from ultrastructural analysis[END_REF] We note l v and d v , the length and diameter of villi, respectively. ρ and µ are the density of the dynamic viscosity of the fluid. The distance between two adjacent villi is l i . Due to the action of longitudinal smooth muscles, [START_REF] Lentle | A comparison of the organization of longitudinal and circular contractions during pendular and segmental activity in the duodenum of the rat and guinea pig[END_REF] we considered an oscillating translation of the villi in the x-direction. The velocity of translation of the villi is given by a sinusoidal function of frequency f and amplitude U 0 = 2πf a, where a is the amplitude of the displacement. The velocity was scaled by 2πf a. We used the thickness of the Stokes layer δ St = µ/2πf ρ as the typical length scale and δ St /U 0 as the typical time scale. Consequently, the velocity of translation of the villi ŨV is given in dimensionless form by

ŨV ( t) = cos d v a 1 Re m t e x (1)
.

The dimensionless Navier-Stokes equations for incompressible laminar flows are given by

∂ ũi ∂ xi = 0 (2) ∂ ũi ∂ t + ũj ∂ ũi ∂ xj = - ∂ p ∂ xi + d v a 1 Re 2 m ∂ 2 ũi ∂ xj ∂ xj ( 3
)
where i, j (=1,2,3) are the indices of the system of coordinates. ũi , t, xi , and p are the dimensionless velocity, time, coordinate, and pressure, respectively. Therefore, four independent variables defined our problem: the modified Reynolds number Re m = d v 2πf ρ/µ, the reduced amplitude a/d v , and the geometric ratios d v /l i and

d v /l v .
Direct simulation of steady streaming flows requires a high accuracy. For this purpose, flow was solved by a combination of D3Q19 Two-Relaxation-Time (TRT) lattice-Boltzmann (LB) methods and the smoothed profile method to take into account the rigid body motion of the villi. Moreover, a multi-grid algorithm was used to simulate a semi-infinite space with a higher resolution in the viscous boundary layer induced by the villi movement.

A. TRT LBM scheme

The flow was simulated by the D3Q19 incompressible TRT Bhatnagar-Gross-Krook LB methods. [START_REF] Ginzburg | Two-relaxationtime lattice boltzmann scheme: About parametrization, velocity, pressure and mixed boundary conditions[END_REF][START_REF] Rui | Incompressible multi-relaxation-time lattice boltzmann model in 3-d space[END_REF] The nineteen discrete velocities are defined by e α = (0, 0, 0) , α = 0 e α = (±c, 0, 0) , (0, ±c, 0) , (0, 0, ±c) , α = 1 -6 e α = (±c, ±c, 0) , (±c, 0, ±c) , (0, ±c, ±c) , α = 7 -18 where c = ∆x/∆t, ∆x and ∆t are the lattice grid spacing and the lattice time step respectively. The evolution equation of the model is divided into two steps, the propagation,

f α (x + e α ∆t, t + ∆t) = fα (4)
and the collision,

fα (x, t) = 1 τ + f + α (x, t) -f +,eq α (x, t) + 1 τ - f - α (x, t) -f -,eq α (x, t) + b α (x, t) (5)
f + α = 1 2 (f α + f ᾱ) , f - α = 1 2 (f α -f ᾱ) (6) f +,eq α = 1 2 (f eq α + f eq ᾱ ) , f -,eq α = 1 2 (f eq α -f eq ᾱ ) (7)
where f α is the density distribution function, f eq α is the equilibrium distribution function, symbols '+' and '-' refer to the symmetric and anti-symmetric part of both functions, ᾱ is the opposite direction to α (i.e. e α = -e ᾱ), τ + and τ -are the two relaxation parameters, f is the density distribution function after collision and before propagation and b is a forcing term. f eq α is defined by

f eq 0 = 1 -(1 -ω 0 ) p c 2 s + s 0 (u) (8)
f eq α = ω α p c 2 s + s α (u) , α = 1 -18 ( 9
)
where u is the velocity, p is the pressure, s α (u) = ω α 3e α .u + 4.5 (e α .u) 2 -1.5u 2 , with the weight coefficients ω 0 =1/3, ω 1-6 =1/18, ω 7-18 =1/36 and c s = c/ √ 3 is the speed of sound. The macroscopic flow velocity and pressure are computed from the distribution functions,

u = 18 α=1 e α f α , p = c 2 s 1 -ω 0 18 α=1 e α f α + s 0 (u) (10)
The dynamic lattice viscosity is given by η = c 2 s (τ + -1/2) ∆t. The major interest of the TRT model compared to the Single Relaxation Time (SRT) model is to tune the lattice viscosity by changing τ + without loss of accuracy when the relaxation parameter is larger than 1. [START_REF] Ginzburg | Two-relaxationtime lattice boltzmann scheme: About parametrization, velocity, pressure and mixed boundary conditions[END_REF] The second relaxation parameter is defined by τ -= Λ τ+-0.5 + 0.5, where Λ is the magic collision parameter and taken to 1/4 in order to optimize the accuracy of the numerical scheme. [START_REF] Humières | Viscosity independent numerical errors for lattice boltzmann models: From recurrence equations to "magic" collision numbers[END_REF] The practical implication of the TRT model for simulating steady streaming is being able to choose the physical grid resolution independently of the physical time steps, without any loss of accuracy, in order to accelerate the convergence of the simulation.

Whereas periodic boundary conditions were applied in x and y directions, no-slip boundary conditions were enforced at the top and bottom of the computational domain, i.e. u(z = 0) = U v (t) and u(z = Z max ) = 0. Preliminary tests were carried out in order to find a sufficenlty large value of Z max that did not influence the results.

B. Smoothed profile method

Moving boundary conditions were enforced using the smoothed profile method (SPM), which was developed to consider multi-body hydrodynamic interactions of solid particles. [START_REF] Nakayama | Simulation method to resolve hydrodynamic interactions in colloidal dispersions[END_REF] It has been recently combined with LBM to investigate the rheology of concentrated suspensions of rigid particles. [START_REF] Jafari | Lattice-boltzmann method combined with smoothed-profile method for particulate suspensions[END_REF] The principle is to couple the rigid body dynamics and the flow dynamics through a smoothed profile of the rigid body. This approach makes it possible to use the same lattice grid for both flow and rigid body, and the operations are local, which made the method highly efficient and easily used in parallel computing. Furthermore, describing the boundary between the fluid and the rigid body by a continuous and smoothed interface reduces the numerical errors associated with the interpolation-extrapolation methods generally used for curved and moving boundary conditions in LBM solvers. [START_REF] Bouzidi | Momentum transfer of a boltzmann-lattice fluid with boundaries[END_REF][START_REF] Kao | An investigation into curved and moving boundary treatments in the lattice boltzmann method[END_REF] The profile function Φ V of the villi was simply built as the stack of disks of diameter d v , thickness ∆x and total length l v . The profile Φ D of each disk is given by

Φ D (x) = 1 2 1 + tanh d/2-| x -X c | ξ ( 11
)
where x is the position of lattice nodes, X c the center of the disk and ξ the interface thickness. The tip of the villi was modeled by a semi-spherical cap. In the fluid region, Φ V = 0 while Φ v = 1 in solid villi region, and it continuously changes near the interfacial region, Fig. 1-c. In this study, ξ = 1∆x as it is commonly used. [START_REF] Nakayama | Simulation method to resolve hydrodynamic interactions in colloidal dispersions[END_REF][START_REF] Jafari | Lattice-boltzmann method combined with smoothed-profile method for particulate suspensions[END_REF] No-slip boundary conditions were enforced by computing the fluid-solid interaction force at each lattice x by

f V (x, t) = Φ V (x, t) [U V (t) -u(x, t)] /∆t (12)
with u the fluid velocity computed in Eq. 10 and U V the translational velocity of the villi. The latter is given by a sinusoidal function of frequency f and amplitude U 0 = 2πf a, where a is the amplitude of the displacement

U V (t) = U 0 cos (2πf t) e x (13)
The hydrodynamic force at the lattice node x is given by

f H (x, t) = -f V (x, t) (14)
and added to the collision step (Eq. 6) via the forcing term b α = -3ω α f H .e α , to enforce no-slip boundary conditions.

C. Multi-grid algorithm

The communication and reconstruction of information between the two sets of grids (Fig. 1-a) were done with the coupling algorithms of Dupuis and Chopard. [START_REF] Dupuis | Theory and applications of an alternative lattice boltzmann grid refinement algorithm[END_REF] The interest of these algorithms is to be accurate for all values of the relaxation time τ + . In their algorithm, Dupuis and Chopard choose to keep the same velocities u on different lattices and so the ratio ∆x/∆t for the two grids, which implies that ∆t changes from one grid level to the other. On the other hand, this choice requires modifying the relaxation time τ + in order to keep the viscosity constant across the grids. Hence, the relationship between the relaxation time of the coarse and fine grids is,

τ f + = ∆x c ∆x f τ c + - 1 2 + 1 2 (15)
where subscripts 'c' and 'f ' refer to the coarse and fine grids respectively. At the interface between the two grids, information has to be exchanged between fine and coarse grids at the streaming step (Eq.4). The transformation between fine and coarse grids is given by

f c α = f f,eq α + f f α -f f,eq α nτ c + τ f + ( 16
)
f f α = f c,eq α + f c α -f c,eq α τ f + nτ c + ( 17
)
where n = ∆x c /∆x f and f α denotes the spatially and temporally interpolated value of f on the coarse grid.

The reader can refer to Refs. [START_REF] Lim | Flow and mixing by small intestine villi[END_REF][START_REF] Dupuis | Theory and applications of an alternative lattice boltzmann grid refinement algorithm[END_REF] for validation of this specific algorithm.

D. Steady streaming flow resolution

The Eulerian steady streaming velocity field u s (x) is the non-reversible part of the velocity field u ( x). It is so defined as the mean temporal value of the velocity field in the pseudo-steady state over one cycle of activity, i.e.

u s (x) = 1 T T 0 u(x, t)dt (18)
with T = 1/f . The pseudo-steady state of the flow was achieved by convergence of the L2-norm of | u s (x, t + T ) -u s (x, t) | (< 10 -4 ). Typically, the small lattice grid consisted of a mesh of at least 30 × 30 × 100 nodes and the size ratio n between the coarse and fine grids was at least 3. One cycle of activity was divided into at least 10 3 time steps. The Lagrangian streamlines of the SSF were computed by integrating over time, the position of markers randomly dispersed in the computational domain, i.e. x(t + ∆t) = x(t) + u(t)∆t, and were plotted at the end of each cycle of oscillation.

III. RESULTS

A. Steady streaming flow in an oscillating centered annuli

The streaming flow in an infinitely long centered annuli [START_REF] Holtsmark | Boundary layer flow near a cylindrical obstacle in an oscillating, incompressible fluid[END_REF][START_REF] Tatsuno | Circulatory streaming around an oscillating circular cylinder at low reynolds numbers[END_REF][START_REF] Bertelsen | Nonlinear streaming effects associated with oscillating cylinders[END_REF][START_REF] Ilin | Steady viscous flows in an annulus between two cylinders produced by vibrations of the inner cylinder[END_REF] was simulated as a benchmark to validate our SPM-TRT-LBM numerical algorithm for Re m of the order of unity, Fig. 2. The external cylinder of radius R out was fixed, whereas the inner cylinder of radius R in was oscillating in the (x-y) plane. We used periodic boundary conditions in the z direction. We fixed Re m , a/R in and R out /R in to 0.98, 0.322 and 7.69 in order to reproduce the experimental results of Tatsuno. [START_REF] Tatsuno | Circulatory streaming around an oscillating circular cylinder at low reynolds numbers[END_REF] The solution dependency with the size of the mesh and the temporal resolution was studied with R out = 154 ∆x and T = 4.9 10 2 or 14 10 3 ∆t. The relative error decreased with the number of time steps without any divergence in both cases, Fig 2-a. The slope indicated a second order convergence with time, as expected for the LBM solver. [START_REF] Ginzburg | Two-relaxationtime lattice boltzmann scheme: About parametrization, velocity, pressure and mixed boundary conditions[END_REF][START_REF] Rui | Incompressible multi-relaxation-time lattice boltzmann model in 3-d space[END_REF][START_REF] Humières | Viscosity independent numerical errors for lattice boltzmann models: From recurrence equations to "magic" collision numbers[END_REF] The experimental Lagrangian SSF streamlines were obtained by observing the displacement of par-ticles with a stroboscopic light, [START_REF] Tatsuno | Circulatory streaming around an oscillating circular cylinder at low reynolds numbers[END_REF]

B. Unsteady flow induced by oscillating villi

The instantaneous flow patterns generated by the translation of an infinite array of villi in a semi-infinite space was localized in an unsteady boundary layer δ AC , Fig. 3, as expected for pulsatile flow at non-vanishing Reynolds number. [START_REF] Loudon | The use of the dimensionless womersley number to characterize the unsteady nature of internal flow[END_REF] Inside this boundary layer, the flow was characterized by an unsteady vortex at the tip of the villi in the (x-z) plane, whose direction of rotation was reversed every half periods. Vortices were also localised in the intervillus space in the (x-y) plane.

In order to measure the thickness of the unsteady boundary layer, we defined the mean longitudinal velocity u x y as the mean of u x along the y direction in the mid-plane of the flow. Fig. 4-a shows the evolution of u x y /U 0 as a function of z/l v across the fine and the coarse grids. The tip of the villi was localised at z/l v = 1, the upper boundary at z/l v = 7 and the transition between the both grids at z/l v = 1.8. The transition between both grids was smooth and continuous and wellcaptured by the multi-grid algorithm. [START_REF] Dupuis | Theory and applications of an alternative lattice boltzmann grid refinement algorithm[END_REF] δ AC 1/2 was defined such as

u x y (z -l i = δ AC 1/2 , t = T ) = U 0 /2 (19)
As expected, δ AC 1/2 scaled with the Stokes layer δ St and did not depend on the reduced amplitude a/d v , Fig. 4-b. Consequently, the flow was more and more confined in a thin layer of fluid adjacent to the villi tips for increasing values of Re m = d v /δ St .

C. Steady streaming flow induced by oscillating villi

The 3D patterns of SSF were similar for Re m ranging from 0.1 to 3.5 (Fig. 5). Two symmetric vortices were present at the tip of the villi in the plane of translation (x,z). These vortices were confined in a steady boundary layer of thickness δ DC . Surprisingly, we noticed that δ DC was independent on the unsteady Stokes layer δ St . Above these boundary layers, the remaining region was globally irrotational. According to Re m , the magnitude of the streaming flow was from 1 to 2 orders of magnitude smaller than the amplitude of velocity of villi translation U 0 . In the intervillus space, SSF was characterized by four vortical structures in the plane perpendicular to the villi (x-y plane) that fully occupied each quadrant.

The finding that the steady vortices were present at the tip of the villi was of particular interest, as they created fluid transfers between the lumen and the tip of the villi over a distance which corresponds to δ DC . The flux density ϕ associated to this pheomenon is given by averaging the absolute value of the streaming velocity in the z direction over the plane (x-y), i.e.

ϕ(z) = 1 S S |u s,z |dxdy (20)
where S is the surface of the computational domain in the (x-y) plane. Figures 6-a andc show the profile ϕ(z)/U 0 along z for various Re m and reduced amplitude a/d v , respectively. ϕ/U 0 was negligible in the intervillus space (z/l v < 0.8) and was maximal above the tip of the villi (z/l v =1.1). The maximum of the flux ϕ max increased linearly with Re m , for values lower than 1.6 and then started to saturate, Fig. 6-b. ϕ max also increased linearly with a/d v up to 0.5. Above 0.5, the increase of the flux density was more moderate, Fig. 6-d. Again, whereas the amplitude of ϕ depended on Re m and a/d v , it was surprising to observe that SSF propagated in the z direction over a distance (up to z/l v =1.5) which did not depend on Re m and the Stokes layer δ St . Typically δ DC /l v was of 0.5 in the range of parameters investigated in Fig. 6.

D. Role of lateral confinement on steady streaming flow

The role of the lateral confinement of the villi on SSF was studied by varying the inter-villus space l i , for different Re m and a fixed amplitude a/d v = 0.5. ϕ max /U 0 showed a maximum for a given value of l i /d v which depended on Re m (Fig. 7-a). Above this optimum, ϕ max /U 0 decreased and tended towards a constant value. This value depended also on Re m . This set of results was rationalized by rescaling ϕ max by U 0 Re m and the intervillus space l i by the Stokes layer δ St . Whatever the value of Re m was, the optimum was obtained when l i 3δ St . At low Re m (< 1), the maximum of ϕ max / U 0 Re m was constant ( 1.2 10 -2 ). At larger Re m , this value decreased. We defined the thickness of the steady boundary layer

δ DC 1/2 by ϕ(z -l v = δ DC 1/2 ) = ϕ max /2 (21)
Fig. 7-c shows that δ DC 1/2 /l v increased with l i /d v . It means that the lateral confinement acted as a cut-off of the SSF above the villi. At low Re m , the steady boundary layer reached a steady value at high l i /d v , whereas it continued to increase for Re m larger than 1.5. However, this increase was not representative of the flow patterns, as explained above. Observations of the flow patterns according to the confinement allowed us to understand the mechanism at play. Fig. 8 shows flow patterns at Re m = 1.5 in the cross-section of the villi in the (x,z) plane (top row) and also at the mid-height of the villi in the (x,y) plane (bottom row). Just above the optimal value of the intervillus space (l i /δ St =4.5, Fig. 8-a, b), the four vortices in the intervillus space took up the whole space. The development of the viscous boundary layer was limited by the lateral confinement, whereas at larger intervillus space (l i /δ St =10.5, Fig. 8-d), the four vortices were localized in the vicinity of the villi, and four outer vortices of lower amplitude emerged in the remaining space. The same observation was also done in the mid-plane of the villi (Fig. 8-c) where the development of the vortices at the tip of the villi was localised in the viscous boundary layer, and outer vortices emerged far from the villi. This is a consequence of the continuity of stresses between the viscous boundary layer and the remaining region, which induces an outer (Rayleigh) streaming flow. The existence of these outer vortices made artificially the value of δ DC 1/2 (Eq. 21) larger than the thickness of the steady boundary layer. It explained why the apparent thickness of the steady boundary layer, increased for Re m larger than 1.5, in Fig. 8-c, whereas observations of the flow patterns showed that this thickness did not increased when the outer streaming was present, Fig. 7-a, c. Note that outer streaming was not observed for Re m < 1 and should depend on the location of the upper boundary (i.e. Z max ).

IV. DISCUSSION

Inspired by small intestine villi, we numerically studied the 3D steady streaming flow forced by the reciprocal translation of an infinite array of finger-like structures (Fig. 1). We showed that such active biological microstructures are able to induce irreversible flow patterns at low, but non-vanishing Reynolds number, despite the absence symmetric forcing. Roughly, the magnitude of SSF at the tip of these microstructures was found to be almost inversely proportional to the Stokes boundary layer (Fig. 6). Consequently, the relative influence of SSF on transport and mixing cannot be generalized directly for other biological systems.

The flow patterns generated by this reciprocal forcing were mainly characterized by two symmetric vortices at the tip of the villi (Fig. 5). It was in line with the steady flow structures, which are forced by the vibration of a beam in its longitudinal direction. [START_REF] Costalonga | Low frequency vibration induced streaming in a hele-shaw cell[END_REF] These vortices could be responsible for mass transfers between the lumen and the tip of the villi over a distance which corresponds to the thickness of the steady boundary layer δ DC . To evaluate this transfer, we defined the flux density in the direction longitudinal to the villi ϕ, Eq. 20.

We also observed four vortices in the intervillus space (in the (x-y) plane), which are expected when a cylinder oscillates (Fig. 2). [START_REF] Tatsuno | Circulatory streaming around an oscillating circular cylinder at low reynolds numbers[END_REF][START_REF] Bertelsen | Nonlinear streaming effects associated with oscillating cylinders[END_REF][START_REF] Lutz | Microscopic steady streaming eddies created around short cylinders in a channel: Flow visualization and stokes layer scaling[END_REF] Then, the effects of three main dimensionless parameters on δ DC and ϕ were investigated: the ratio between the intervillus space l i and the Stokes layer δ St , the reduced amplitude of translation a/d v , and the ratio between the diameter of the villi d v and δ St (= Re m ) .

The state diagram shown in Fig. 9 summarises our findings in the Re m -l i /δ St space parameters for a fixed reduced amplitude a/d v = 0.5. The colour code corresponds to the magnitude of ϕ max /U 0 Re m . Three different patterns of SSF were observed that we referred to as 'confined streaming', 'free streaming' and 'outer streaming'. In the 'confined streaming' regime, the thickness of the steady boundary layer above the villi δ DC was limited by the lateral confinement when the intervillus space was sufficiently small to prevent the development of the unsteady boundary layer in the intervillus space (i.e. l i < 3δ St , Fig. 7-b). The SSF was optimal when the intervillus space corresponded to the unconfined steady boundary layer (Fig. 8-b, c). Above this optimal value (l i > 3δ St ), two situations had to be distinguished. At low Re m , the SSF was limited to the vicinity of the villi, which is the 'free streaming' regime. The transition between 'confined' and 'free streaming' was defined at the optimum of SSF. At high Re m and high l i /δ St , the stress induced in the steady boundary layer was sufficient to promote secondary SSF in the bulk flow (Fig. 8-c, d), which is called the Rayleigh streaming. [START_REF] Tatsuno | Circulatory streaming around an oscillating circular cylinder at low reynolds numbers[END_REF] This kind of non-monotonic effect of the confinement on SSF characteristics was also reported in a bi-dimensionnal oscillating centered annuli. [START_REF] Bertelsen | Nonlinear streaming effects associated with oscillating cylinders[END_REF] However, it worth noting that, in the 'confined regime', the confinement in the lateral direction acted as a cut-off distance for SSF not only in the intervillus space, but also above the villi.

Having characterized SSF in a simplified geometry of small intestine villi, let us discuss their effects on mass I), the maximal flux density ϕ max is of the order of 10 µm/s. For nutrients with high rates of diffusion (D ∼ 10 -9 m 2 /s, e.g. glucose), the associated Péclet number P e = ϕ max d v /D is lower than the unity, whereas for particles of a few dozen of nanometers (D ∼ 10 -12 m 2 /s), P e is of the order of 10 3 . Consequently, streaming flow phenomenon should not accelerate molecular mass transfers, but should be an important phenomena for the transport in the vicinity of the villi of nano-or micro-objects such as biliary micelles, protein aggregates, drug delivery particles or bacteria.

To support this analysis, we computed the transport of mass-less particles (i.e. the Lagrangian streamlines) at Re m = 0.5 for 200 s (Fig. 10). Downward spiral movements of particles, towards the edge of the villi, were observed. Particles travelled faster at the top of the villi than in the intervillus space. The particles near the tip of the villi completed a full circular loop over a distance of a few hundred of µm; i.e. they traveled from the top to the bottom of the steady boundary layer. It is interesting to note that this time scale is long compared to the frequency of oscillation, but short in regard to the resident time of fluids in the small intestine. Therefore, SSF could be a key mechanism to transport particles near the mucosa of the small intestine. A more detailed description and modelling of this mechanism could be achieved through ex-vivo experiments at micro- [START_REF] Lim | Determination of villous rigidity in the distal ileum of the possum (trichosurus vulpecula)[END_REF][START_REF] Kuriu | Microfluidic device using mouse small intestinal tissue for the observation of fluidic behavior in the lumen[END_REF] and macro-scales. [START_REF] De Loubens | Characterisation of mixing in the proximal duodenum of the rat during longitudinal contractions and comparison with a fluid mechanical model based on spatiotemporal motility data[END_REF][START_REF] Agbesi | Flow and mixing induced by single, colinear, and colliding contractile waves in the intestine[END_REF] Moreover, numerical simulations could be done to study the coupling with flow conditions at macroscopic scales due to the spatio-temporal organization of motility patterns. [START_REF] Zhang | How motility can enhance mass transfer and absorption in the duodenum: Taking the structure of the villi into account[END_REF][START_REF] De Loubens | Fluid mechanical consequences of pendular activity, segmentation and pyloric outflow in the proximal duodenum of the rat and the guinea pig[END_REF][START_REF] Agbesi | Flow and mixing induced by single, colinear, and colliding contractile waves in the intestine[END_REF] In conclusion, the mechanism of steady streaming flow should contribute to the enhancement of transport of nano-or micro-particles in the vicinity of small intestine villi. Our study contributes to a better understanding of the physical conditions faced by nano drug delivery systems at the vicinity of the mucosa. [START_REF] Ensign | Oral drug delivery with polymeric nanoparticles: the gastrointestinal mucus barriers[END_REF] Moreover, in regard to the growing body of evidence that bacterial evolution and the immune response in the gastrointestinal tract are highly dependent on the competition between flow clearance and localized mixing conditions, [START_REF] Cremer | Effect of flow and peristaltic mixing on bacterial growth in a gut-like channel[END_REF][START_REF] Labarthe | A mathematical model to investigate the key drivers of the biogeography of the colon microbiota[END_REF][START_REF] Hoces | Growing, evolving and sticking in a flowing environment: understanding iga interactions with bacteria in the gut[END_REF][START_REF] Waclawiková | Gut microbiota-motility interregulation: insights from in vivo, ex vivo and in silico studies[END_REF][START_REF] Labavić | Hydrodynamic flow and concentration gradients in the gut enhance neutral bacterial diversity[END_REF] our results suggested that the presence of localised mixing conditions at small scales could influence the spatial organisation of microbiota and the immune response in the small intestine.

5 Continue

 5 50.5 51.5 52.5 53.5 54.5 55.5 56.5 57.5 58.5 59.5 60.5 61.5 62.5 63.5 64.5 65.5 66.5 67.5 68.5 69.5 70.5 71.5 72.5 73.5 74.5 75.5 76.5 77.5 78.5 79.5 80.5 81.5 82.5 83.5 84.5 85.5 86.5 87.5 88.5 89.5 90.5 91.5 92.5 93.5 94.5 95.5 96.5 97.5 98.5 99.5 100.5 101.5 102.5 103.5 104.5 105.5 106.5 107.5 108.5 109.5 110.5 111.5 112.5 113.5 114.5 115.5 116.5 117.5 118.5 119.5 120.5 121.5 122.5 123.5 124.5 125.5 126.5 127.5 128.5 129.5 130.5 131.5 132.5 133.5 134.5 135.5 136.5 137.5 138.5 139.5 140.5 141.5 142.5 143.5 144.5 145.5 146.5 147.5 148.5 149.5 150.5 151.5 152.5 153.5 154.5 155.5 156.5 157.5 158.5 159.5 160.5 161.5 162.5 163.5 164.5 165.5 166.5 167.5 168.5 169.5 170.5 171.5 172.5 173.5 174.5 175.5 176.5 177.5 178.5 179.5 180.5 181.5 182.5 183.5 184.5 185.5 186.5 187.5 188.5 189.5 190.5 191.5 192.5 193.5 194.5 195.5 196.5 197.5 198.5 199.

Figure 1 FIG. 1 .

 11 Figure 1 Staining of villous tips following application and elution of methylene blue.

FIG. 2 .

 2 FIG. 2. Simulation of steady streaming flow in an oscillating centered annuli and comparison with experiments. (a) The relative error for different temporal resolutions as a function of the number of cycles. (b) Experimental steady Lagrangian streamlines obtained by Tatsuno 29 . The arrows show the direction of oscillation of the inner cylinder. (c) Steady Eulerian streamlines simulated by our SPM-TRT-LBM algorithm for the same conditions as (a). (d) Corresponding steady Lagrangian streamlines. For all the captions, Rem = 0.979, a/Rin = 0.322 and Rout/Rin = 7.69.

FIG. 3 .FIG. 4 .

 34 FIG. 3. Instantaneous flow at different time steps (a) t=0, (b) t=T/8 (c) t=T/4 and in three different planes. The color map shows the magnitude of the dimensionless velocity | u | /U0. Rem = 1, a/dv = 0.5, lv/dv = 5.5, li/dv = 1.

FIG. 5 .

 5 FIG. 5. Steady streaming flow patterns induced by the oscillation of a villi in the x direction for (a) Rem = 0.1, (b) Rem = 1 and (c) Rem = 3.5. The color map shows the magnitude of the dimensionless steady streaming velocity | us | /U0. a/dv = 0.5, lv/dv = 5.5 and li/dv = 1.

Fig. 2 -

 2 b. With this set of parameters, one inner circulation occupied each quadrant. Fig. 2-c and d respectively show the Eulerian and Lagrangian steady streamlines simulated with our SPM-TRT-LBM algorithm. Both patterns of streamlines were similar and in very good agreement with the experiments of Tatsuno.29

FIG. 6 .

 6 FIG. 6. Flux density ϕ induced by SSF in the longitudinal direction to the villi (i.e. z direction, Eq. 20). (a) ϕ profile for a fixed amplitude (a/dv =0.5) and different Rem. (b) Maximal value of ϕ as a function of Rem. (c) ϕ profile for Rem = 1 and different amplitudes. (d) Maximal value of ϕ as a function of a/dv. lv/dv = 5.5 and li/dv = 1.

FIG. 7 .FIG. 8 .FIG. 9 .

 789 FIG. 7. Role of the lateral confinement of the villi on SSF. (a) Maximal flux density ϕmax as a function of the intervillus space li/dv for different Rem. (b) ϕmax was rescaled by U0Rem and the intervillus space li by the Stokes layer δ St . (c) Steady boundary layer δ DC 1/2 as a function of li/dv. a/dv = 0.5, lv/dv =5.5.

FIG. 10 .

 10 FIG. 10. Steady Lagrangian streamlines observed in (a) 3D, (b) x -z plane, and (c) y -z plane for Rem = 0.5, a/dv = 0.5 and li/dv=2. The different colors were used to individualise the particles.

  10.7106 11.7106 12.7106 13.7106 14.7106 15.7106 16.7106 17.7106 18.7106 19.7106 20.7106 21.7106 22.7106 23.7106 24.7106 25.7106 26.7106 27.7106 28.7106 29.7106 30.7106 31.7106 32.7106 33.7106 34.7106 35.7106 36.7106 37.7106 38.7106 39.7106 40.7106 41.7106 42.7106 43.7106 44.7106 45.7106 46.7106 47.7106 48.7106 49.7106 50.7106 51.7106 52.7106 53.7106 54.7106

TABLE I .

 I Typical values of parameters characterizing villi geometry and the motility of small intestine in mammals, values from Refs[START_REF] Lentle | Mucosal microfolds augment mixing at the wall of the distal ileum of the brushtail possum[END_REF][START_REF] Lim | Determination of villous rigidity in the distal ileum of the possum (trichosurus vulpecula)[END_REF][START_REF] Lentle | A comparison of the organization of longitudinal and circular contractions during pendular and segmental activity in the duodenum of the rat and guinea pig[END_REF][START_REF] De Loubens | Fluid mechanical consequences of pendular activity, segmentation and pyloric outflow in the proximal duodenum of the rat and the guinea pig[END_REF]

		Diameter of the villi	dv		200 µm
		Length of the villi	lv		500 µm
		Inter-villi space	li		50-250 µm
		Amplitude of translation	a		150 µm
	.	Frequency Amplitude of velocity	f U0 = 2πf a 0.66 mm/s 0.7 Hz
		Fluid density	ρ		10 3 kg/m 3
		Fluid viscosity	µ		0.7 mPa.s
		Stokes layer	δ St =	µ 2πf ρ	400 µm
		Modified Reynolds number Rem = dv/δ St	0.5

ACKNOWLEDGMENTS

LRP is part of the LabEx Tec21 (ANR-11-LABX-0030) and of the PolyNat Carnot Institute (ANR-11-CARN-007-01). The authors thank Agence Nationale de la Recherche for its financial support of the project Trans-portGut, ANR-21-CE45-0015.


Martin Picard

Ilan Azuelos

Boris Jung

Christian Giordano

Stefan Matecki

Sabah Hussain

Kathryn White

Tong Li

Feng Liang

Andrea Benedetti

Benoit J Gentil

Yan Burelle

Basil J Petrof
email: basil.petrof@mcgill.ca

Mechanical ventilation triggers abnormal mitochondrial dynamics and morphology in the diaphragm

Keywords: fragmentation, intermyofibrillar mitochondria, subsarcolemmal mitochondria, electron microscopy, ventilator-induced diaphragmatic dysfunction

The diaphragm is a unique skeletal muscle designed to be rhythmically active throughout life, such that its sustained inactivation by the medical intervention of mechanical ventilation (MV) represents an unanticipated physiological state in evolutionary terms. Within a short period after initiating MV, the diaphragm develops muscle atrophy, damage, and diminished strength, and many of these features appear to arise from mitochondrial dysfunction. Notably, in response to metabolic perturbations, mitochondria fuse, divide, and interact with neighboring organelles to remodel their shape and functional properties-a process collectively known as mitochondrial dynamics. Using a quantitative electron microscopy approach, here we show that diaphragm contractile inactivity induced by 6 h of MV in mice leads to fragmentation of intermyofibrillar (IMF) but not subsarcolemmal (SS) mitochondria. Furthermore, physical interactions between adjacent organellar membranes were less abundant in IMF mitochondria during MV. The profusion proteins Mfn2 and OPA1 were unchanged, whereas abundance and activation status of the profission protein Drp1 were increased in the diaphragm following MV. Overall, our results suggest that mitochondrial morphological abnormalities characterized by excessive fission-fragmentation represent early events during MV, which could potentially contribute to the rapid onset of mitochondrial dysfunction, maladaptive signaling, and associated contractile dysfunction of the diaphragm. mitochondrial dynamics; mitochondrial

 [START_REF] Vassilakopoulos | Ventilator-induced diaphragmatic dysfunction[END_REF]and has the potential to impede the ability to remove a patient from a ventilator, thereby contributing to greater medical complications and higher health care costs. The molecular events characterizing VIDD include oxidative stress [START_REF] Kavazis | Mechanical ventilation induces diaphragmatic mitochondrial dysfunction and increased oxidant production[END_REF][START_REF] Mcclung | Redox regulation of diaphragm proteolysis during mechanical ventilation[END_REF][START_REF] Picard | Mitochondrial dysfunction and lipid accumulation in the human diaphragm during mechanical ventilation[END_REF][START_REF] Powers | Mitochondria-targeted antioxidants protect against mechanical ventilation-induced diaphragm weakness[END_REF], mitochondrial energy deficiency [START_REF] Kavazis | Mechanical ventilation induces diaphragmatic mitochondrial dysfunction and increased oxidant production[END_REF][START_REF] Picard | Mitochondrial dysfunction and lipid accumulation in the human diaphragm during mechanical ventilation[END_REF], activation of autophagy [START_REF] Hussain | Mechanical ventilation-induced diaphragm disuse in humans triggers autophagy[END_REF], apoptosis [START_REF] Mcclung | Caspase-3 regulation of diaphragm myonuclear domain during mechanical ventilation-induced atrophy[END_REF][START_REF] Tang | Intrinsic apoptosis in mechanically ventilated human diaphragm: linkage to a novel Fos/FoxO1/ Stat3-Bim axis[END_REF], and increased activation of proatrophy signaling pathways [START_REF] Levine | Increased proteolysis, myosin depletion and atrophic AKT-FOXO signaling in human diaphragm disuse[END_REF][START_REF] Levine | Rapid disuse atrophy of diaphragm fibers in mechanically ventilated humans[END_REF]. Importantly, all of these cellular processes can be either directly or indirectly induced by mitochondrial dysfunction, which occurs in the inactive diaphragm within a short period of time (a few hours in animal models, a few days in humans) after the initiation of MV [START_REF] Kavazis | Mechanical ventilation induces diaphragmatic mitochondrial dysfunction and increased oxidant production[END_REF][START_REF] Picard | Mitochondrial dysfunction and lipid accumulation in the human diaphragm during mechanical ventilation[END_REF]. Therefore, rapidly acquired mitochondrial dysfunction during MV may represent a key early cellular trigger for the development of VIDD.

Skeletal muscle fibers contain two pools of mitochondria: intermyofibrillar (IMF) and subsarcolemmal (SS) mitochondria. IMF mitochondria normally exist as tubular and branched organelles (i.e., mitochondrial reticulum) surrounding myofibrils in tridimensional space, whereas SS mitochondria are more spheroid-shaped and are located between the plasma membrane and myofibrils [START_REF] Bakeeva | Mitochondrial framework (reticulum mitochondriale) in rat diaphragm muscle[END_REF][START_REF] Picard | Mitochondrial morphology, topology, and membrane interactions in skeletal muscle: a quantitative three-dimensional electron microscopy study[END_REF]. Importantly, IMF and SS mitochondria exhibit different functional characteristics with respect to oxidative capacity, reactive oxygen species (ROS) generation, and sensitivity to the proapoptotic event of mitochondrial permeability transition pore opening [START_REF] Cogswell | Properties of skeletal muscle mitochondria isolated from subsarcolemmal and intermyofibrillar regions[END_REF][START_REF] Palmer | Biochemical differences between subsarcolemmal and interfibrillar mitochondria from rat cardiac muscle: effects of procedural manipulations[END_REF], which could have implications in disuse-associated diaphragmatic dysfunction.

Mitochondria have the ability to undergo remodeling through fusion, fission, and interactions with neighboring mitochondria as well as with other organelles, a process collectively referred to as mitochondrial dynamics [START_REF] Chan | Fusion and fission: interlinked processes critical for mitochondrial health[END_REF][START_REF] Van Der Bliek | Mechanisms of mitochondrial fission and fusion[END_REF]. In cultured cells, effector proteins of mitochondrial dynamics induce changes in mitochondrial shape within seconds to minutes, which has consequences for mitochondrial function [reviewed in [START_REF] Picard | Mitochondrial morphology transitions and functions: implications for retrograde signaling?[END_REF]]. For example, loss of function of the mitochondrial profusion proteins mitofusin 2 (Mfn2) and optic atrophy 1 (OPA1) favors the accumulation of mitochondrial DNA damage [START_REF] Chen | Mitochondrial fusion is required for mtDNA stability in skeletal muscle and tolerance of mtDNA mutations[END_REF][START_REF] Ono | Human cells are protected from mitochondrial dysfunction by complementation of DNA products in fused mitochondria[END_REF] and decreased mitochondrial bioenergetic efficiency with impaired energy production capacity [START_REF] Benard | Multi-site control and regulation of mitochondrial energy production[END_REF][START_REF] Chen | Disruption of fusion results in mitochondrial heterogeneity and dysfunction[END_REF]. These effects appear to be at least partly related to the fact that mitochondrial fusion enables functional complementation via sharing of proteins, RNA, and DNA [START_REF] Chen | Mitochondrial fusion is required for mtDNA stability in skeletal muscle and tolerance of mtDNA mutations[END_REF][START_REF] Ono | Human cells are protected from mitochondrial dysfunction by complementation of DNA products in fused mitochondria[END_REF]. On the other hand, mitochondrial fragmentation triggered by excessive activation of the profission protein dynamin-related protein 1 (Drp1) can lead to greater ROS production, loss of ATP production, and greater mitochondrial membrane depolarization [START_REF] Jheng | Mitochondrial fission contributes to mitochondrial dysfunction and insulin resistance in skeletal muscle[END_REF][START_REF] Lee | Roles of the mammalian mitochondrial fission and fusion mediators Fis1, Drp1, and Opa1 in apoptosis[END_REF][START_REF] Ong | Inhibiting mitochondrial fission protects the heart against ischemia/ reperfusion injury[END_REF][START_REF] Yu | Mitochondrial fission mediates high glucose-induced cell death through elevated production of reactive oxygen species[END_REF]. Furthermore, dysregulation of mitochondrial dynamics and the resulting mitochondrial dysfunction can promote exaggerated apoptotic signaling [START_REF] Lee | Roles of the mammalian mitochondrial fission and fusion mediators Fis1, Drp1, and Opa1 in apoptosis[END_REF][START_REF] Ong | Inhibiting mitochondrial fission protects the heart against ischemia/ reperfusion injury[END_REF][START_REF] Wasilewski | The changing shape of mitochondrial apoptosis[END_REF] and activation of the muscle atrophy program [START_REF] Romanello | Mitochondrial fission and remodelling contributes to muscle atrophy[END_REF].

Given that the functional consequences of exaggerated mitochondrial fission-fragmentation overlap closely with the main cellular mechanisms implicated in the development of VIDD, we hypothesized that mitochondria could undergo adverse morphological remodeling in the diaphragm during MV.

In the present study, we employed a quantitative transmission electron microscopy (TEM) approach to determine the effects of MV on mitochondrial shape and membrane interactions [START_REF] Picard | Mitochondrial morphology, topology, and membrane interactions in skeletal muscle: a quantitative three-dimensional electron microscopy study[END_REF] in the IMF and SS mitochondrial populations of the diaphragm. We also evaluated the effect of MV on canonical profusion (Mfn2, OPA1) and profission (Drp1) mitochondrial proteins known to mediate mitochondrial remodeling and interorganelle interactions. Our findings suggest that MV rapidly leads to an excess of fission-fragmentation events in IMF (but not SS) mitochondria resulting in a loss of their characteristic morphological specialization features, which could potentially contribute to the pathogenesis of VIDD. Mechanical ventilation protocol. Mice were subjected to 6 h of MV using the same protocol that had been shown to induce impaired diaphragmatic function, as previously described in detail [START_REF] Mrozek | Rapid onset of specific diaphragm weakness in a healthy murine model of ventilator-induced diaphragmatic dysfunction[END_REF]. Briefly, mice were anesthetized by intraperitoneal (i.p.) injection of xylazine and pentobarbital sodium (50 mg/kg body wt) and then orotracheally intubated with a 22-gauge angiocatheter. No neuromuscular blocking agents were used. General care included continuous maintenance of body temperature using a homeothermic blanket control unit (Harvard Apparatus, Saint-Laurent, QC, Canada), and hourly i.p. injections of 0.05 to 0.10 ml of Ringer lactate solution to maintain hemodynamic stability and compensate for insensible losses. MV was performed with a small-animal ventilator (Minivent; Harvard Apparatus) using the following ventilator settings: fraction of inspired oxygen of 0.21 (room air), controlled volume mode with tidal volume of 10 l/mg body wt, respiratory rate of 150 -170 breaths/min, and positive endexpiratory pressure level of 3-4 cmH 2O achieved by placing the expiratory port under a water seal. MV parameters and anesthesia were adjusted to prevent spontaneous breathing efforts, which were assessed by regular observations of thoracoabdominal motion and the bubbling pattern of the underwater seal. Control mice did not undergo mechanical ventilation. To replicate the fact that mice undergoing MV for 6 h were not fed during this period, control mice were fasted for the equivalent time with access to water. All mice were euthanized by i.p. injection of pentobarbital sodium (50 mg/kg body wt) and cervical dislocation at the same time of day (between 2:00 and 4:00 P.M.).

METHODS

Animals

Transmission electron microscopy. For TEM analysis, diaphragm muscle strips (ϳ 5 mm wide, ϳ 15 mm long) were fixed in a 2% glutaraldehyde solution in 0.1 M cacodylate buffer (pH 7.4) and processed exactly as described in [START_REF] Picard | Mitochondrial morphology, topology, and membrane interactions in skeletal muscle: a quantitative three-dimensional electron microscopy study[END_REF]. Samples were postfixed in 1% osmium tetroxide and dehydrated with acetone before impregnation in resin. Smaller segments of diaphragms were then embedded either in cross-section (i.e., transverse) or longitudinal orientation in 100% resin. To verify orientation and section quality, 1-m-thick sections were cut and stained with 1% toluidine blue in 1% borax. Ultrathin sections of 70 nm were subsequently cut using a diamond knife on a Leica EM UC7 ultramicrotome, stretched with chroloform, and mounted on Pioloform-filmed copper grids prior to staining with 2% aqueous uranyl acetate and lead citrate. Ultrathin sections were examined on a Phillips CM 100 Compustage (FEI) transmission electron microscope and digital micrographs were captured with a charge-coupled device camera (Advanced Microscopy Techniques, Woburn, MA). Tissues from four to five mice per group were analyzed in two separate batches.

Morphological analysis. For each animal, randomly selected mitochondria-rich oxidative muscle fibers were analyzed in both transverse and longitudinal sections as previously described in detail [START_REF] Picard | Mitochondrial morphology, topology, and membrane interactions in skeletal muscle: a quantitative three-dimensional electron microscopy study[END_REF]. Briefly, to analyze IMF mitochondrial morphology, muscles were sectioned in transverse (cross-section) orientation. To ensure optimal transverse orientation at the subcellular level, muscle fibers must be sectioned in a near-parallel orientation to the Z-line. This was consistently achieved by selecting for analysis myofibers presenting at least one but no more than two Z-lines separated by at least 10 -15 m. Obliquely sectioned myofibers with Z-lines appearing closer than 10 m were not selected for analysis. A total of 1,011 (control) and 1,011 (MV) IMF mitochondria from 22-23 myofibers were thus analyzed by an observer who was blind to group identity. SS mitochondrial morphology was determined at ϫ 19,000 magnification in the longitudinal orientation (n ϭ 3 mice per group), for which 708 (control) and 537 (MV) SS mitochondria were similarly analyzed.

Mitochondrial shape descriptors and size measurements were determined using ImageJ software (version 1.42q; National Institutes of Health, Bethesda, MD) as previously described [START_REF] Picard | Mitochondrial morphology, topology, and membrane interactions in skeletal muscle: a quantitative three-dimensional electron microscopy study[END_REF] by manually tracing the perimeter of IMF and SS mitochondria with clearly discernible outlines on TEM micrographs, as shown in Fig. 1E. Aspect ratio was computed as [(major axis)/(minor axis)] and reflects the length-to-width ratio; form factor [(perimeter 2 )/(4 surface area)] reflects morphological complexity in terms of waviness and branching; roundness [4(surface area)/( major axis 2 )] is a two-dimensional index of sphericity; Feret's maximum and minimum diameters reflect the longest and shortest distances between outer boundaries of a mitochondrion [START_REF] Koopman | Simultaneous quantitative measurement and automated analysis of mitochondrial morphology, mass, potential, and motility in living human skin fibroblasts[END_REF]. To produce frequency distributions of these morphological parameters, each mitochondrion was assigned to one of 20 bins.

To quantify interactions among IMF and SS mitochondria, micrographs of muscle from five mice per group photographed in longitudinal orientation were used at magnifications of ϫ 13,500 for IMF and ϫ 19,000 for SS. In the IMF compartment, a total of 689 (control) and 648 (MV) Z-lines possessing mitochondria on both sides, either as pairs of discrete organelles, as a continuous mitochondrion, or as interacting organelles joined by an electron-dense intermitochondrial junction (IMJ) [START_REF] Amchenkova | Coupling membranes as energy-transmitting cables. I. Filamentous mitochondria in fibroblasts and mitochondrial clusters in cardiomyocytes[END_REF][START_REF] Picard | Trans-mitochondrial coordination of cristae at regulated membrane junctions[END_REF] were evaluated. The proportion of Z-lines spanned by continuous or interacting mitochondria is reported as a percentage of the total number of Z-lines analyzed. In addition, the proportion of electron-dense physical contact sites between adjacent mitochondria was determined as described previously [START_REF] Picard | Mitochondrial morphology, topology, and membrane interactions in skeletal muscle: a quantitative three-dimensional electron microscopy study[END_REF] in 543 (control) and 726 (MV) pairs of IMF mitochondria, and 1,206 (control) and 921 (MV) pairs of SS mitochondria.

Western blot analysis. For protein analyses, the diaphragm muscle was harvested and snap-frozen in liquid nitrogen. Muscle lysates were mixed with sample buffer and boiled for 5 min before gel loading. The dilutions of primary and secondary antibodies were made according to the manufacturers' instructions. Quantification of specific protein bands was performed using the Odyssey Infrared Imaging System (LI-COR Biosciences, Lincoln, NE) using Ponceau red staining to adjust for any differences in total protein loading. The following proteins were detected: total Drp1 (611112, BD Biosciences), phosphorylated forms of Drp1 at serine 616 (pDrp1-616; 3455, Cell Signaling) and serine 637 (pDrp1-637; 6319, Cell Signaling), Mfn2 (M6319, Sigma), and OPA1 (MA5-16149, Thermo-Scientific).

Statistical analyses. Comparisons of morphological shape and size parameters between control and MV mitochondrial populations were made using a repeated-measures ANOVA. Distributions of these parameters were nonnormal, and hence, normalizing transformations were performed using either Johnson or Box-Cox methods, selected on the basis of which method yielded the best residual plot distribution for the data. The significance of differences in mitochondrial population proportions falling above or below a predefined level was assessed using the z-test for proportions. Differences in mitochondrial interaction parameters and Western blot analysis quantifications between control and MV groups were evaluated by an unpaired, twotailed Student's t-test assuming unequal variances, or the Mann-Whitney test in the case of nonparametric data (evaluated by the Anderson-Darling normality test). All statistical analyses were performed using Minitab 17 (Minitab) or Prism 6 (Graphpad) software with the alpha level set at 0.05.

RESULTS

IMF mitochondrial morphology.

A representative example of IMF mitochondria in transverse section from a control diaphragm is shown in Fig. 1A. As can be seen, normal IMF mitochondria in the diaphragm are for the most part relatively elongated and wavy serpentine structures. In contrast, IMF mitochondria in the MV group diaphragm appear to be shorter with less branching and hence a less morphologically complex structure (Fig. 1B). Using the combined total IMF mitochondria from control (Fig. 1C) and MV (Fig. 1D) groups, dot plots of aspect ratio vs. form factor were generated and subdivided into four quadrants on the basis of 25th percentile values obtained for these two parameters in the control group. The IMF mitochondria falling in the lower left-hand quadrant of the dot plots (i.e., with Ͻ 25th percentile values for both aspect ratio and form factor) were observed with greater frequency in the MV group (56%) compared with the control group (20%). Illustrative images of the individual marked mitochondria indicated by arrows in Fig. 1, C and D are shown in Fig. 1E.

To quantify these observations in greater detail, frequency distribution analyses of the total IMF mitochondrial populations in control and MV groups were individually determined for each of the following morphological parameters: aspect ratio (Fig. 2A), form factor (Fig. 2B), roundness (Fig. 2C), Feret's maximal (Fig. 2D) and minimal (Fig. 2E) diameters, and total perimeter (Fig. 2F). Using the median value obtained in the control group as a reference threshold for each parameter (hence by design 50% of the control population), greater percentages of IMF mitochondria in the MV group were observed with low values for aspect ratio, form factor, Feret's maximum diameter, and total perimeter. In addition, a slightly greater percentage of IMF mitochondria in the MV group demonstrated higher values for Feret's minimum diameter, which is in keeping with the elevated roundness values in this group. Table 1 shows mean and median values for these measurements in the control and MV groups. As indicated in Table 1, differences in IMF mitochondrial morphology between the control and MV groups were highly statistically significant as determined by repeated-measures ANOVA. Therefore, these data indicate that MV was associated with rapid remodeling of IMF mitochondria in the diaphragm, leading to a shift toward shorter, rounder, and less morphologically complex organelles within 6 h of initiating MV.

SS mitochondrial morphology. The same analyses were applied to SS mitochondria. Under baseline control conditions, SS mitochondria in the diaphragm are more spheroid and less morphologically complex than IMF mitochondria (Fig. 3A), which is also reflected by their smaller 25th percentile values for aspect ratio and form factor (Fig. 3C). The 25th percentile values from the control group were used to subdivide the SS mitochondria populations from control (Fig. 3C) and MV (Fig. 3D) groups into four quadrants as we did for IMF mitochondria in Fig. 1. However, in marked contrast to the results of this analysis in IMF mitochondria, the proportion of SS mitochondria falling into the lower left-hand quadrant was identical (17%) in the control and MV groups.

Frequency distribution analyses in control and MV groups were next determined in the total SS mitochondrial population using the median value obtained in the control group as a reference threshold, as was performed for IMF mitochondria in Fig. 2. For aspect ratio and Feret's maximum diameter, there were slightly greater percentages of mitochondria with high values in the MV group compared with controls, whereas the opposite was true for roundness (Fig. 4). As shown in Table 2, the frequency distribution pattern was also associated with larger average values for Feret's maximum diameter (P ϭ 0.03) and perimeter (P ϭ 0.05) in MV vs. control SS mitochondria as determined by repeated-measures ANOVA. Therefore, morphological changes induced by MV in SS mitochondria were mild, and the overall pattern of changes was not consistent with the shift toward shorter and rounder mitochondria observed in the IMF population.

Mitochondrial interactions. IMF mitochondria are often observed in pairs flanking Z-lines in the longitudinal orientation, and less frequently as continuous organelles that cross the Z-line (Fig. 5, A andB). Mitochondria-mitochondria interactions can also be visualized as electron-dense IMJs between adjacent mitochondrial membranes (Fig. 5, B andC) [START_REF] Amchenkova | Coupling membranes as energy-transmitting cables. I. Filamentous mitochondria in fibroblasts and mitochondrial clusters in cardiomyocytes[END_REF][START_REF] Picard | Trans-mitochondrial coordination of cristae at regulated membrane junctions[END_REF]. The use of MV was associated with reductions in mitochondria crossing Z-lines in the IMF population (Fig. 5D). In addition, MV tended to decrease the proportion of IMJs between IMF mitochondria (P ϭ 0.06), whereas IMJs between SS mitochondria (which were less abundant at baseline) did not show evidence of being affected by MV (Fig. 5E).

Proteins of mitochondrial dynamics. Western blot analysis of whole diaphragm tissue was performed to investigate the potential roles of mitochondrial profusion and profission proteins in mediating mitochondrial shape changes and mitochondrial membrane interactions induced by MV. There were no significant changes in the outer mitochondrial membrane profusion protein Mfn2 (Fig. 6A) or inner mitochondrial membrane profusion and organizing protein OPA1 (Fig. 6B) in the diaphragm following MV. However, the total amount of the mitochondrial fission protein Drp1 in diaphragm muscle was increased by MV (Fig. 6C). Phosphorylation of Drp1 at serines 616 (pDrp1-S616) and 637 (pDrp1-S637) are believed to activate and inhibit, respectively, the fission process initiated by Drp1 [START_REF] Van Der Bliek | Mechanisms of mitochondrial fission and fusion[END_REF]. The level of pDrp1-S616 in the diaphragm was increased by MV (Fig. 6D), whereas pDrp1-S637 remained unchanged (Fig. 6E). Furthermore, in MV group diaphragms, a significant increase in the proportion of very small mitochondria (less than or equal to the lower 5th percentile) was observed in the IMF population, whereas this was not the case for SS mitochondria (Fig. 6, F andG). Taken together, these findings support the presence of increased fission and associated fragmentation of mitochondria in the IMF population of the diaphragm during MV.

DISCUSSION

Mitochondria form a dynamic network that must be continuously adapted and tailored to the specific physiological requirements of different tissues. Such dynamic remodeling of the mitochondrial network requires the combined actions of fusion and fission, as well as interactions with other organelles and cytoskeletal components. These changes are mediated by the Mfn1/2 and OPA1 proteins, which promote fusion of the outer and inner mitochondrial membranes, respectively, whereas phosphorylation-dependent activation of the cytoplasmic dynamin-related protein Drp1 is largely responsible for mitochondrial fission [START_REF] Chan | Fusion and fission: interlinked processes critical for mitochondrial health[END_REF][START_REF] Van Der Bliek | Mechanisms of mitochondrial fission and fusion[END_REF]. In addition, Mfn2 plays a role in the regulation of mitochondrial tethering to other organelles, such as the endoplasmic reticulum [START_REF] De Brito | Mitofusin 2 tethers endoplasmic reticulum to mitochondria[END_REF].

In the present study, we employed quantitative electron microscopy to assess mitochondrial morphological remodeling in the diaphragm following application of a wellestablished model of VIDD, consisting of 6 h of controlled MV in mice [START_REF] Mrozek | Rapid onset of specific diaphragm weakness in a healthy murine model of ventilator-induced diaphragmatic dysfunction[END_REF]. We separately analyzed the IMF and SS mitochondrial populations, which are known to exhibit different functional properties and responses to various physiological perturbations [START_REF] Adhihetty | Differential susceptibility of subsarcolemmal and intermyofibrillar mitochondria to apoptotic stimuli[END_REF][START_REF] Crescenzo | Subsarcolemmal and intermyofibrillar mitochondrial responses to shortterm high-fat feeding in rat skeletal muscle[END_REF][START_REF] Krieger | Populations of rat skeletal muscle mitochondria after exercise and immobilization[END_REF][START_REF] Nielsen | Subcellular localization-dependent decrements in skeletal muscle glycogen and mitochondria content following short-term disuse in young and old men[END_REF][START_REF] Picard | Acute exercise remodels mitochondrial membrane interactions in mouse skeletal muscle[END_REF]. Our major findings are that in response to MV, the IMF (but not the SS) mitochondrial population in the diaphragm undergoes major shape changes (becoming significantly shorter, rounder, and less morphologically complex) and also contains a higher proportion of very small mitochondria, consistent with mitochondrial fragmentation. Furthermore, simultaneously higher levels of activated Drp1 (pDrp1-S616) protein in the diaphragm without any changes in either Mfn2 or OPA1 provide additional biochemical evidence for a net shift in mitochondrial dynamics toward induction of the mitochondrial fission-fragmentation pathway during MV.

There is substantial evidence that mitochondrial health and normal skeletal muscle function depend on continually main-taining a finely tuned balance between fusion and fission events [START_REF] Chan | Fusion and fission: interlinked processes critical for mitochondrial health[END_REF][START_REF] Van Der Bliek | Mechanisms of mitochondrial fission and fusion[END_REF]. Disruption of this equilibrium can lead to decreased mitochondrial respiratory capacity [START_REF] Chen | Disruption of fusion results in mitochondrial heterogeneity and dysfunction[END_REF][START_REF] Jheng | Mitochondrial fission contributes to mitochondrial dysfunction and insulin resistance in skeletal muscle[END_REF][START_REF] Yu | Mitochondrial fission mediates high glucose-induced cell death through elevated production of reactive oxygen species[END_REF], greater susceptibility to apoptosis [START_REF] Lee | Roles of the mammalian mitochondrial fission and fusion mediators Fis1, Drp1, and Opa1 in apoptosis[END_REF][START_REF] Ong | Inhibiting mitochondrial fission protects the heart against ischemia/ reperfusion injury[END_REF], and failure to appropriately eliminate or recycle damaged mitochondria [START_REF] Twig | Fission and selective fusion govern mitochondrial segregation and elimination by autophagy[END_REF]. In rat skeletal muscle cells, silencing of Mfn2 and OPA1 attenuated insulinstimulated Akt phosphorylation and cellular respiratory rate [START_REF] Del Campo | Mitochondrial fragmentation impairs insulin-dependent glucose uptake by modulating Akt activity through mitochondrial Ca 2ϩ uptake[END_REF]. Along the same lines, decreased Mfn1/2 and increased Drp1 were associated with impaired mitochondrial respiration and reduced ATP levels in the skeletal muscles of mice with high-fat-diet-induced obesity [START_REF] Liu | Impaired mitochondrial dynamics and bioenergetics in diabetic skeletal muscle[END_REF]. The latter findings are consistent with reports of decreased Mfn2 and smaller mitochondria in skeletal muscles of obese and diabetic patients [START_REF] Bach | Expression of Mfn2, the Charcot-Marie-Tooth neuropathy type 2A gene, in human skeletal muscle: effects of type 2 diabetes, obesity, weight loss, and the regulatory role of tumor necrosis factor alpha and interleukin-6[END_REF][START_REF] Hernández-Alvarez | Subjects with early-onset type 2 diabetes show defective activation of the skeletal muscle PGC-1{alpha}/Mitofusin-2 regulatory pathway in response to physical activity[END_REF]. Excessive mitochondrial fission has also been linked to mitochondrial dysfunction and insulin resistance in mouse skeletal muscle [START_REF] Jheng | Mitochondrial fission contributes to mitochondrial dysfunction and insulin resistance in skeletal muscle[END_REF], and to greater mitochondrial ROS release and less ability to resist mitochondrial permeability transition pore opening in other cell types [START_REF] Picard | Mitochondrial morphology transitions and functions: implications for retrograde signaling?[END_REF][START_REF] Yu | Mitochondrial fission mediates high glucose-induced cell death through elevated production of reactive oxygen species[END_REF]. Moreover, there is evidence that exaggerated mitochondrial fission-fragmentation is a stimulus for activation of muscle atrophy pathways [START_REF] Romanello | Mitochondrial fission and remodelling contributes to muscle atrophy[END_REF].

Mitochondrial fusion and fission occur within seconds to minutes in various types of cultured cells in vitro, and a rapid time course of mitochondrial dynamics has also recently been demonstrated in adult skeletal muscle fibers [START_REF] Eisner | Mitochondrial fusion is frequent in skeletal muscle and supports excitation-contraction coupling[END_REF][START_REF] Liu | Impaired mitochondrial dynamics and bioenergetics in diabetic skeletal muscle[END_REF]. However, very little work has been published regarding changes in mitochondrial dynamics induced by skeletal muscle disuse in vivo. In rodents, denervation [START_REF] Iqbal | Expression of mitochondrial fission and fusion regulatory proteins in skeletal muscle during chronic use and disuse[END_REF][START_REF] Wagatsuma | Expression of nuclear-encoded genes involved in mitochondrial biogenesis and dynamics in experimentally denervated muscle[END_REF] and hind limb unloading [START_REF] Cannavino | The role of alterations in mitochondrial dynamics and PGC-1alpha over-expression in fast muscle atrophy following hindlimb unloading[END_REF][START_REF] Wagatsuma | Mitochondrial adaptations in skeletal muscle to hindlimb unloading[END_REF] have been reported to downregulate either OPA1, or Mfn2, or both. The present investigation is to our knowledge the first in any skeletal muscle disuse model to demonstrate through a quantitative morphometric analysis that skeletal muscle inactivity produces signs of exaggerated mitochondrial fission-fragmentation in vivo.

Beyond fusion and fission events, dynamic remodeling of the mitochondrial network is also influenced by mitochondrial interactions with other cellular organelles. In the present study, we observed evidence of reduced mitochondrial interactions across Z-lines following diaphragm inactivity induced by MV, and electron-dense IMJs [START_REF] Amchenkova | Coupling membranes as energy-transmitting cables. I. Filamentous mitochondria in fibroblasts and mitochondrial clusters in cardiomyocytes[END_REF][START_REF] Picard | Trans-mitochondrial coordination of cristae at regulated membrane junctions[END_REF] between adjacent mitochon-dria also tended to be less frequent in MV group diaphragms. Interestingly, voluntary running was recently shown to significantly increase the prevalence of IMJs between neighboring mitochondria in mouse soleus muscle [START_REF] Picard | Acute exercise remodels mitochondrial membrane interactions in mouse skeletal muscle[END_REF]. In addition to the potential effect on mitochondrial shape, a reduction in such interorganellar interactions would be expected to disrupt functional cross-talk between mitochondria and other cellular constituents. For example, there is evidence that contacts between mitochondria and the sarcoplasmic reticulum are critically involved in normal Ca 2ϩ handling [START_REF] Eisner | Interactions between sarco-endoplasmic reticulum and mitochondria in cardiac and skeletal musclepivotal roles in Ca(2)(ϩ ) and reactive oxygen species signaling[END_REF], and it was recently reported that Mfn1 depletion interferes with ryanodine receptor-mediated excitation-contraction coupling [START_REF] Eisner | Mitochondrial fusion is frequent in skeletal muscle and supports excitation-contraction coupling[END_REF]. It is conceivable that mitochondria-mitochondria interactions and the transmitochondrial coordination of mitochondrial ultrastructure [START_REF] Picard | Trans-mitochondrial coordination of cristae at regulated membrane junctions[END_REF] can similarly play a role in electrochemical coupling between neighboring mitochondria (2). On the basis of their different localization and functional properties, it has been hypothesized that IMF mitochondria play the dominant role in supplying ATP for muscle contraction, whereas SS mitochondria are likely to be more involved in sarcolemmal membrane-associated functions [START_REF] Lawrie | A role for calcium influx in the regulation of mitochondrial calcium in endothelial cells[END_REF]. Previous studies have established that IMF mitochondria, which constitute ϳ 80% of mitochondria in skeletal muscle, possess a higher oxidative capacity than SS mitochondria [START_REF] Cogswell | Properties of skeletal muscle mitochondria isolated from subsarcolemmal and intermyofibrillar regions[END_REF][START_REF] Palmer | Biochemical differences between subsarcolemmal and interfibrillar mitochondria from rat cardiac muscle: effects of procedural manipulations[END_REF]. Few studies have examined whether skeletal muscle disuse differentially affects IMF and SS mitochondria, and these prior investigations have provided conflicting results with regard to which mitochondrial population is more vulnerable to disuse effects [START_REF] Ferretti | The interplay of central and peripheral factors in limiting maximal O2 consumption in man after prolonged bed rest[END_REF][START_REF] Krieger | Populations of rat skeletal muscle mitochondria after exercise and immobilization[END_REF][START_REF] Nielsen | Subcellular localization-dependent decrements in skeletal muscle glycogen and mitochondria content following short-term disuse in young and old men[END_REF]. In our study, major morphological alterations occurred in IMF mitochondria, whereas the SS population exhibited relatively few and minor changes in response to MV. It is interesting to note that the general direction of changes observed in IMF mitochondria was toward the more spheroid and morphologically simple characteristics of the SS mitochondrial population. This finding suggests that diaphragm inactivity blunts the specialized morphological features associated with IMF mitochondria, thus making the two mitochondrial subpopulations more homogeneous. The reason for a greater susceptibility of the IMF population to MV is unclear, but could be related to its naturally more complex and wide range of morphology [START_REF] Picard | Mitochondrial morphology, topology, and membrane interactions in skeletal muscle: a quantitative three-dimensional electron microscopy study[END_REF], its larger role in ATP-driven muscle contraction, and the fact that IMF mitochondria are more sensitive to ROS-induced proapoptotic protein release [START_REF] Adhihetty | Differential susceptibility of subsarcolemmal and intermyofibrillar mitochondria to apoptotic stimuli[END_REF].

An important question raised by our study is how the mitochondrial morphological abnormalities we have documented in the mechanically ventilated diaphragm might be causally related to mitochondrial and contractile dysfunction in the muscle. A cardinal feature of VIDD pathogenesis is increased oxidative stress derived in large part from mitochondria [START_REF] Kavazis | Mechanical ventilation induces diaphragmatic mitochondrial dysfunction and increased oxidant production[END_REF][START_REF] Mcclung | Redox regulation of diaphragm proteolysis during mechanical ventilation[END_REF][START_REF] Picard | Mitochondrial dysfunction and lipid accumulation in the human diaphragm during mechanical ventilation[END_REF][START_REF] Powers | Mitochondria-targeted antioxidants protect against mechanical ventilation-induced diaphragm weakness[END_REF]. Cell culture studies have demonstrated that mitochondrial fission-fragmentation can trigger increased mitochondrial ROS emission [START_REF] Yu | Mitochondrial fission mediates high glucose-induced cell death through elevated production of reactive oxygen species[END_REF], and greater oxidative stress can also provoke mitochondrial fragmentation [START_REF] Fan | H2O2-induced mitochondrial fragmentation in C2C12 myocytes[END_REF], suggesting the potential for a deleterious feed-forward loop. In addition, either inhibition of mitochondrial fission or promotion of mitochondrial fusion can blunt the increased ROS production triggered by metabolic overload with high glucose and lipid exposure [START_REF] Jheng | Mitochondrial fission contributes to mitochondrial dysfunction and insulin resistance in skeletal muscle[END_REF][START_REF] Yu | Mitochondrial fission mediates high glucose-induced cell death through elevated production of reactive oxygen species[END_REF]. This is of interest because hyperglycemia has been linked to diaphragmatic oxidative stress and respiratory muscle dysfunction in animals [START_REF] Callahan | Hyperglycemia-induced diaphragm weakness is mediated by oxidative stress[END_REF] and humans during MV [START_REF] Hermans | Impact of intensive insulin therapy on neuromuscular complications and ventilator dependency in the medical intensive care unit[END_REF]. We have also previously reported evidence of metabolic substrate overload in diaphragm muscle fibers of mechanically ventilated patients and found that hyperlipidemia exacerbates oxidative stress in parallel with contractile dysfunction [START_REF] Picard | Mitochondrial dysfunction and lipid accumulation in the human diaphragm during mechanical ventilation[END_REF]. Nevertheless, it is important to recognize that although a mechanistic link between mitochondrial fragmentation and VIDD is biologically plausible and consistent with the findings of our study, this hypothesis remains to be formally tested. This will likely require the use of genetically modified mice either deficient or overexpressing the major proteins of mitochondrial dynamics to perform a simultaneous analysis of mitochondrial dynamics, mitochondrial ROS production, and diaphragm contractility outcomes. In addition, it will be of interest to ascertain how mitochondrial dynamics are affected after more prolonged periods of MV, when diaphragmatic muscle atrophy becomes a prominent feature.

In summary, this study has demonstrated for the first time that an early abnormality of mitochondrial structure during MV consists of the loss of regionally specialized morphological characteristics within the IMF mitochondrial population, which lies in closest contact with the contractile apparatus and constitutes the bulk of skeletal muscle mitochondria. The physical alterations found in IMF mitochondria during MV suggest a major dysequilibrium of mitochondrial dynamics in favor of exaggerated fission-fragmentation. Most of the cellular events demonstrated to be causally involved in the development of diaphragmatic weakness during MV can be mechanistically linked to mitochondrial dysfunction. Given this fact together with accumulating evidence of an intimate relationship between mitochondrial morphology transitions and canonical aspects of the organelle's function [START_REF] Picard | Mitochondrial morphology transitions and functions: implications for retrograde signaling?[END_REF], it is possible that dysregulated mitochondrial dynamics play a significant role in the pathogenesis of VIDD. This remains to be determined by future studies, and it will also be of interest to ascertain whether mitochondrial dynamics are affected by other known modifiers of VIDD such as metabolic substrate supply [START_REF] Picard | Mitochondrial dysfunction and lipid accumulation in the human diaphragm during mechanical ventilation[END_REF], ROS scavengers [START_REF] Powers | Mitochondria-targeted antioxidants protect against mechanical ventilation-induced diaphragm weakness[END_REF], and the use of partial support modes of MV [START_REF] Futier | Pressure support ventilation attenuates ventilator-induced protein modifications in the diaphragm[END_REF].

Fig. 1 .

 1 Fig. 1. Mechanical ventilation alters intermyofibrillar (IMF) mitochondrial morphology. Representative electron micrographs from control (A) and samples that underwent mechanical ventilation (MV) (B) with mitochondria pseudocolored in green (scale bars ϭ 2 m). Graphical representation of mitochondrial form factor (shape complexity) and aspect ratio (length to width ratio) from control (C) and MV (D) groups indicates less morphological complexity of MV mitochondria (n ϭ 1,011 traced mitochondria for both groups). Percentages indicate proportions of mitochondria within each quadrant, defined by the 25th percentile of control mitochondria; the shaded quadrants contain mitochondria for which both parameters fall either below (left lower quadrant) or above (right upper quadrant) this threshold. E: representative morphology of mitochondrial subpopulations corresponding to the numbered data points in C and D.

Fig. 2 .

 2 Fig. 2. MV fragments in IMF mitochondria. A-F: frequency distributions of the major IMF mitochondrial shape and size descriptors in diaphragms of control mice and those that underwent MV. Vertical dashed lines indicate the median value for each descriptor in the control group. Arrows adjacent to vertical dashed lines indicate the direction of change in each descriptor following MV, and pie charts show proportions of mitochondria falling to the arrow side of the dashed line in each experimental group. ***P Ͻ 0.001 by z-test.

Fig. 3 .

 3 Fig. 3. MV does not fragment subsarcolemmal (SS) mitochondria. Representative electron micrographs from control (A) and MV (B) samples. The sarcolemma is marked by a dashed line, and cytoplasmic space of the myofiber is pseudocolored in blue. Scale bars ϭ 1 m. Myofibr indicates myofibrils. Graphical representation of mitochondrial form factor and aspect ratio in control (C) and MV (D) groups (n ϭ 708 and 539 mitochondria for control and MV groups, respectively), with percentages indicating proportions of mitochondria within each quadrant defined by the 25th percentile of control mitochondria as described in Fig. 1.

Fig. 4 .

 4 Fig. 4. MV has minimal effects on SS mitochondrial morphology. A-F: frequency distributions of the major SS mitochondrial shape and size descriptors in control and MV diaphragm. Vertical dashed lines represent median values in the control group from which proportions (shown in pie charts) were calculated as described in Fig. 2. *P Ͻ 0.05 by z-test. N.S., nonsignificant.

Fig. 5 .

 5 Fig. 5. MV reduces IMF mitochondrial membrane interactions. A and B: transmission electron microscopy images of diaphragm myofibers in longitudinal orientation showing several examples of mitochondria spanning Z-lines (double arrowheads). Electron-dense intermitochondrial junctions (IMJs) between adjacent IMF (B) and SS (C) mitochondria are also shown (arrows). D: proportion of IMF mitochondria interacting across Z-lines in control and MV diaphragms. E: proportion of mitochondrial IMJs in IMF and SS mitochondria in control and MV diaphragms. Scale bars ϭ 500 nm.

Fig. 6 .

 6 Fig. 6. Effect of MV on mitochondrial profission and profusion proteins. Abundance of profusion proteins mitofusin 2 (Mfn2, A) and optic atrophy 1 (OPA1, B). C: abundance of profission dynamin-related protein 1 (DRP1) and its phosphorylated forms p-DRP1 Ser616 (D) and p-DRP1 Ser637 (E); groups were compared by t-test. F: proportion of very small mitochondria in IMF and SS compartments (based on 5th percentile value for control IMF mitochondria); groups were compared by z-test. G: representative image showing very small mitochondrion (arrow) in the diaphragm of a mouse that underwent MV. Scale bar ϭ 200 nm.

  . Male C57BL/6N mice 8 -10 wk of age (Charles River Laboratories, Saint-Constant, QC) were used for our experiments. All mice were housed under a standard 12:12-h light-dark cycle with food and water available ad libitum for 72 h before the experiments. The study was approved by the McGill University Health Centre institutional ethics board in accordance with guidelines of the Canadian Council on Animal Care.

Table 1 .

 1 Morphological parameters for intermyofibrillar mitochondria in control and MV diaphragms

	Parameter	Diaphragm	Mean Ϯ SE	Median, IQ	P*
	Aspect ratio	Control	2.64 Ϯ 0.05	2.19, 1.52
		MV	1.79 Ϯ 0.03	1.48, 0.67	Ͻ 0.001
	Form factor	Control	1.88 Ϯ 0.03	1.49, 0.91
		MV	1.37 Ϯ 0.02	1.15, 0.28	Ͻ 0.001
	Roundness, 0-1	Control	0.48 Ϯ 0.01	0.46, 0.30
		MV	0.65 Ϯ 0.01	0.68, 0.27	Ͻ 0.001
	Feret's maximum	Control	1.02 Ϯ 0.02	0.89, 0.62
	diameter, m	MV	0.83 Ϯ 0.02	0.74, 0.52	Ͻ 0.001
	Feret's minimum	Control	0.25 Ϯ 0.004	0.21, 0.14
	diameter, m	MV	0.26 Ϯ 0.004	0.24, 0.17	0.01
	Perimeter, m	Control	2.55 Ϯ 0.05	2.20, 1.50
		MV	2.19 Ϯ 0.04	1.97, 1.34	Ͻ 0.001
	MV, mechanically ventilated; SE, standard error; IQ, interquartile range.
	*Comparisons between control and MV by repeated-measures ANOVA.

Table 2 .

 2 Morphological parameters for subsarcolemmal mitochondria in control and MV diaphragms

	Parameter	Diaphragm	Mean Ϯ SE	Median, IQ	P*
	Aspect ratio	Control	1.55 Ϯ 0.02	1.36, 0.50
		MV	1.57 Ϯ 0.02	1.44, 0.56	0.12
	Form factor	Control	1.19 Ϯ 0.01	1.11, 0.16
		MV	1.20 Ϯ 0.01	1.11, 0.22	0.68
	Roundness, 0-1	Control	0.70 Ϯ 0.01	0.73, 0.24
		MV	0.69 Ϯ 0.01	0.70, 0.25	0.13
	Feret's maximum	Control	0.66 Ϯ 0.01	0.62, 0.34
	diameter, m	MV	0.72 Ϯ 0.02	0.67, 0.50	0.03
	Feret's minimum	Control	0.56 Ϯ 0.008	0.55, 0.30
	diameter, m	MV	0.60 Ϯ 0.013	0.55, 0.39	0.11
	Perimeter, m	Control	1.78 Ϯ 0.03	1.72, 0.90
		MV	1.93 Ϯ 0.04	1.79, 1.32	0.05

MV, mechanically ventilated; SE, standard error; IQ, interquartile range. *Comparisons between control and MV by repeated-measures ANOVA.

GRANTS