Nicolas Pernet

Sylvie Cauvin

Frédéric Thomas

Chokri Mraidha

Michel Sall

Philippe Robin

UML Modeling of a Real-Time Embedded Industrial System: an Engine Testbed

Keywords: Eclipse, Platform Independent Model (PIM), Platform Description Model (PDM), Platform Specific Model (PSM), UML modeling, real-time embedded, RTAI

The paper presents a work performed in the Software Factory / OpenDevFactory project which is part of the French System@tic cluster. The OpenDevFactory project focuses on the modeling of complex systems using a wide variety of tools and technologies and the Eclipse framework as an integration platform.

The paper presents the work performed in an industrial use case proposed by French IFP research institute which, among other disciplines, is a specialist of internal combustion engine modeling, design and testing. The modeled system is a realtime distributed control system for engine testbeds.

Real-time and embedded systems dedicated UML modeling components developed within the OpenDevFactory project are used and combined to describe the deployment of the testbed control applications onto the underlying execution infrastructure based on RTAI real-time operating system. Modeling components are relevant to the modeling of the real-time and communication requirements of applications, the modeling of faulttolerant requirements and the modeling of the underlying technical architecture. The deployment is performed down to the actual code using automatic code generation.

The paper presents the modeling process used in the industrial use case and its usability and will conclude on the portability and productivity enhancements achieved with this modeling process.

Introduction

Model-based engineering currently offers new solutions to deal with real-time systems development. The recently adopted OMG MARTE 1 (Modeling Analysis of Real-time and Embedded systems) standard [START_REF] Omg | A UML Profile for MARTE[END_REF] brings improvements in three directions: enrichment / refinement of system 1 http://www.omgmarte.org/ functionalities, reduction of time-to-market and production costs, and compliance with non-functional requirements. Based on MARTE standard, CEA LIST developed the two components called CT-RTE and CT-PDM for the Eclipse framework. Another component named CG-LA was provided as an Action Language editor. At last, by combining these components with the new UML modeler named Papyrus 2 , CEA LIST offers a comprehensive integrated platform for the modeling, analysis and synthesis of real-time and embedded systems.

IFP proposed an industrial use case which consists in the modeling of a real-time test-bed supervisor and used the new integrated platform proposed by CEA LIST for this purpose. In order to assess a complete model-to-code process, the project decided to target an implementation of the supervisor on the RTAI real-time operating system. In order to achieve the required model-to-code transformation, TRIALOG used the CT-PDM component to describe the RTAI software platform and developed an automatic code generation solution. This work was performed in the context of the Usine Logicielle project of the System@tic Paris Région Cluster. Figure 1 presents the different components used for the use case and the foundation of each of them.

Presentation of engine testbed use case

IFP, along with D2T company, has developed a unique solution for test-bed automation, engine calibration test implementation and model integration into the test-bed (simulation). The solution is based on a real-time control system working with RTX realtime kernel. Figure 2 shows a screenshot of the commercial version of the software. UML [START_REF] Omg | Unified Modeling Language: Superstructure[END_REF] is a general purpose modeling language that provides concepts for behavioral modeling, some concepts for concurrency modeling (e.g. CallConcurrencyKind in Communications, concurrent states in StateMachines), and some basic concepts on time modeling. However, in order to guarantee that UML is a general purpose language, those concepts are not defined precisely enough to capture the specificities of a given domain (e.g. the real-time domain). To handle domain specificities, UML provides a specialization mechanism called profiles. Profiles provide the capability to tailor the UML metamodel for different domains. This is achieved by extending the UML metamodel elements in order to adapt them for the targeted domain. CCSL is a declarative language used to specify constraints between clocks. The specified constraints may then be validated on models. In short, MARTE concepts used in CT-RTE may be used to qualify UML structural and behavioral application models of real-time and embedded systems. Those qualified models include the complete semantics related to the characteristics of real-time systems and are therefore ready to support either a system analysis (e.g. a schedulability analysis, a performance analysis) or a system synthesis (e.g. a code generation).

Assessment of modeling components

CT-RTE component

Description of component

Modeling requirements

IFP real-time supervisor relies on a mix of off-line and on-line scheduling and consequently deals with various time representations and real-time constraints. From a modeling point of view, it is important to represent the timing behaviors. In addition, the future versions of the supervisor will have to exploit the capabilities of multi-core architectures. Consequently, IFP is looking for modeling solutions which could provide a complete design framework to cope with these new challenges. The main need is to represent nonfunctional properties such as timing constraints. Then the possibility to use standardized patterns is also required in order to make the collaboration and exchange between different partners easier during the development. The utilization of a standardized design approach should also offer new opportunities in term of analysis tools. Finally, IFP pays attention to the high level of expressiveness of the descriptions achieved. Consequently CT-RTE has to offer comprehensive capabilities for the description of non-functional properties but at the same time it has to produce easy-to-understand models.

Assessment criteria

Following the IFP modeling requirements presented above, CT-RTE component was evaluated according to four criteria. Criterion #1 is relevant to the descriptive capabilities offered by the component. Can we just use standardized patterns of nonfunctional properties or is a strong language (with no limitation of modeling possibilities) available to specify non-functional properties ? Criterion #2 is the user-friendliness of the language ("easy-to-use" aspect). Is it a new language, a new methodology or philosophy or on the contrary is it intuitive ? Criterion #3 completes criterion #2 since it concerns the "easy-to-read" aspect. We want to specify more complete models, we do not want them to be more complex. The last criterion #4 is relevant to the availability of new tools that might be available for model analysis and transformation.

Results of assessment

During the modeling process performed by IFP, CT-RTE was used in different ways at different abstraction levels. Actually, CT-RTE component introduces some general concepts which are out of the scope of MARTE which is focused on the modeling of real-time systems. Such general concepts are for instance the following stereotypes: << tupleType >> which supports the definition of composed types, <<choiceType>> which supports the instantiation of an object which may belong to different classes and <<collectionType>> which supports the description of sets. CT-RTE component contains also more specific concepts. For example, it contains a MARTE library which defines various patterns allowing designers to represent periodic and aperiodic entities. Different time units are available too. At last, VSL language offers a real freedom of description for defining new specific values of nonfunctional properties.

Summarising, CT-RTE provides (i) general concepts which could belong to a more general standard, (ii) specific and ready-to-use concepts which improve the modelling of real-time systems and (iii) an open standard for value description which allows designers to specify their own non-functional properties. Criterion #1 which is relevant to the variety of description possibilities is therefore fully satisfied. The models using CT-RTE are clear and easy to understand, and consequently CT-RTE satisfies criterion #3. Nevertheless, even if the MARTE library is easy to use, the other stereotypes may require more documentation to be fully used. We expect a "how to" documentation to be issued in a not too far future and therefore criterion #2 will be met. Finally, we investigated the availability of external tools. Since MARTE adoption as an OMG standard is recent (June 2007), few MARTEcompliant tools are available yet. However the fact it is standardised will facilitate the arrival of tools. In the OpenDevFactory project for instance, Thales TRT showed how to generate a file compatible for RapidRMA 3 tool which supports the verification of schedulability properties. Evaluation criterion #4 should also be met in the future.

CT-PDM component

Description of component CT-PDM stands for Technical Component for

Platform Description Modeling. CT-PDM covers software and hardware platform modeling. This section gives a brief presentation of the concepts and principles used for modeling these two kinds of platforms.

The MDA guide [START_REF] Omg | MDA Guide" (version 1.0.1)[END_REF] provides the following generic definition of the platform concept: "A platform is a set of subsystems and technologies that provide a coherent set of functionalities through interfaces and specified usage patterns, which any application supported by that platform can use without concern for the details of how the functionality provided by the platform is implemented". Although this is a very broad and high-level definition which leaves a large scope for interpretation, it shows clearly that the MDA guide considers a platform as a support for the execution of software applications. This is consistent with the intuitive definition of "platform" used in the industry which refers to machines or systems such as frameworks, middleware, virtual machines and RTOS, which are built to support an execution process.

In [START_REF] Sangiovanni-Vincentelli | Platform-based design and software design methodology for embedded systems[END_REF], A. Sangiovanni -Vincentelli states that resources and services are provided by application programming interfaces (APIs). APIs should provide a complete and accurate description of the platform, so that the execution of any application consistent with these interfaces is guaranteed on the platform. A model of a platform is thus a model of the platform APIs. Hence, a platform metamodel is nothing but a language to describe the APIs. A language dedicated to the modeling of Real-Time and Embedded (RTE) multitasking platforms was proposed : this is the UML Software Resource Modeling profile (SRM). SRM has been implemented as an extension to the Unified Modeling Language (UML) (e.g. a UML profile). SRM profile is now a part of the new UML profile for MARTE. It is not a new set of multitasking APIs. It is rather a language to describe multi-tasking APIs (existing or under definition). SRM language has been built from the results of a detailed analysis of main multitasking API standards [START_REF] Thomas | Software Real-Time Resource Modeling[END_REF] and of several industrial standards. Three families of concepts were identified: -Concurrent (i.e. parallel) execution contexts such as an interrupt context and a task context. -Interactions between concurrent contexts for either communication or synchronization purposes (e.g. mailbox and semaphore mechanisms). -Hardware and software resource brokering concepts, such as driver or memory management. For this purpose, SRM profile is based on the "Resource Service" pattern. That pattern supports the description of resources having properties and providing services. Some properties and services might play roles which are modeled as resource attributes. Figure 3 illustrates how such a pattern is represented in SRM profile package. A schedulable resource in SRM is the modeling of a context for executing concurrent sequences of actions (i.e. a task). A schedulable resource has some attributes. Some of these attributes may play the role of the priority. A schedulable resource provides services also. Some services may be used by the resource itself to activate it. It would be too lengthy to describe all SRM profile details. Therefore the interested reader will find more information in [START_REF] Thomas | Software Real-Time Resource Modeling[END_REF]. The way SRM profile is used in the modeling process consists in three basic steps. First step is to model the multitasking APIs under consideration as a UML model library. Figure 3 below shows the first step of the (partial) modeling of the OSEK/VDX platform. Then in the second step, the designer applies SRM profile to clarify the taxonomy of modeling elements. For instance when modeling the OSEK/VDX platform, the OSEK/VDX BasicTask is considered as a SRM software schedulable resource whose attributes and operations are referenced in the stereotype properties. Finally in the third step, the classifier is instantiated for describing a multitask design (e.g. a task t1 is created in the application model). The resulting multitasking design is the platform instance model. HRM is composed of two views: a logical view that classifies the hardware resources depending on their functional properties, and a physical view that concentrates on their physical nature. Both are specializations of a more general model. The logical and physical views are complementary. They provide two different abstractions for the hardware and they could be simply merged. Each view is, in turn, composed of many models, as shown in Figure 5.

Stereotypes introduced within HRM profile are organized under a tree of successive inheritance paths from generic to more specific stereotypes ; no stereotype is an orphan. This is the reason why HRM profile is able to describe low-level details.

Optional tagged values and composition mechanisms are strengthening this ability as well. Another feature of HRM profile is that it supports the description of most hardware concepts thanks to a wide range of stereotypes and to its layered architecture. If no specific stereotype corresponds to a particular hardware component, a generic stereotype may match instead. This is appropriate to support new hardware components and new technologies. Reader should refer to [START_REF] Omg | A UML Profile for MARTE[END_REF][6] for a more detailed description of HRM.

Modeling requirements

IFP requirements for CT-PDM components were relevant to the modeling of the software and hardware platforms on one hand and the modeling of the implementation on the other hand. In addition to the assessment of CT-PDM modeling capabilities, IFP was also interested in CT-PDM capabilities relevant to the testing of the implementation and the support for multiple platform development.

Assessment criteria

IFP wanted to assess first whether HRM and SRM profiles provide an easy way to represent the engine test-bed specific architecture. An easy way means both the ease of utilisation and the availability of entities allowing designers to describe precisely the platform under consideration. Then IFP wanted to use also CT-PDM to describe the implementation onto RTAI software platform and on the actual hardware platform. It was important for IFP that this part of the model be expressive and easy to understand. Finally IFP wanted to assess how easy or difficult it was to go further into the modelling process towards code generation and multiple platform development.

Results of assessment

First, both SRM profile and HRM profile are very complete with respect to modeling entities. No lack was identified when modeling RTAI thanks to SRM stereotypes that map well every single concept of real-time operating systems. HRM profile proposes a large set of hardware concepts and could be employed in other domains than the industrial control system under consideration in the project. Future work at IFP will apply HRM profile to scientific computing for the description of repetitive structures (Repetitive Structure Modeling, annex E of the MARTE standard). Actually IFP used a combination of SRM profile (CT-PDM) and Allocation profile (CT-RTE) and obtained interesting results by using the two concepts in a complementary way. For instance, SRM profile allows a designer to connect a task entity to an object of the functional description and to specify the called class operations. The Allocation profile allows a designer to stereotype the "grain" object, i.e. the entity he/she has to allocate in the functional description as well as in the software resources (task, timer, etc.) and to define the destination of the allocation (processor, memory, etc.). Figure 6 shows an example of such an implementation. Three levels of description can be distinguished, from top to bottom : functional description entities, software resources and hardware resources. Stereotyped dependencies allow designers to describe operation calls and resource allocation.

In brief, SRM and HRM profiles are efficient to describe software and hardware platforms. CT-PDM and CT-RTE components include interesting concepts for the implementation description, although a more comprehensive documentation would be appreciated. At last, for the use case under consideration, TRIALOG performed some work on the development of a RTAI-oriented code generator which analyzes the implementation model and generates the corresponding allocation. Since MARTE is now a standard, the number of available real-time operating system description will certainly grow up. The creation of a central repository containing these descriptions would help. Consequently, an interesting work to be done in the future would consist in defining a template for the code generator.

The template would avoid re-developing a code generator from scratch each time a real-time operating system is added to the repository.

IFP considers also that a potential advantage of CT-PDM is to make multiple platform development easier. Starting from a unique implementation model, the software code could generated automatically for RTAI, RTX and VxWorks operating systems. Some work is still needed in this direction however. Interactions are used to capture protocols of message exchange between instances composing the system. Activities are built using Actions. Actions are the basic entities for behavioral modeling in UML. The UML specification provides a concrete syntax associated to the abstract syntax for all the behavioral packages except for the Action package for which UML specifies only the abstract syntax of Actions. Without a concrete syntax however, the Action package cannot be used for modeling purpose, Hence it is not possible to construct UML models that are completely specified in UML. Usually UML-based design approaches rely on programming languages such as C++ or Java to specify the behavioral algorithmic aspects [START_REF] Taha | An Open Framework for Hardware Detailed Modeling[END_REF]. This results in a mixing of the higher levels of abstraction and the semantics provided by UML with the lower levels of abstraction and the semantics provided by the programming languages. Such a mix may lead to inconsistencies in the resulting model. To cope with this problem, the Object Management Group (OMG) issued a RfP (Request for Proposal) that aims at standardizing a text-based concrete syntax for UML Actions abstract syntax [START_REF] Douglass | Real Time UML -Advances in the UML for Real Time Systems[END_REF]. CG-LA provides an action language named Accord-AL [START_REF] Omg | Concrete Syntax for a UML Action Request For Proposal[END_REF] that gives a concrete syntax for UML Actions abstract syntax. This language is defined by a oneto-one mapping between its elements and the elements of the UML Actions abstract syntax. Accord-AL language gives to UML the capability to use UML Actions for the algorithmic aspects of behavioral modeling. The concrete syntax allows designers to model 100% of their application behavior in UML, and thus avoids the mixing of different semantics and abstraction levels in the same model. Since the concrete syntax is not standardized yet, no existing UML tool supports it for the time being. This is why CG-LA provides such a support for Accord-AL through an advanced editing tool. The editor supports the description of operation bodies using the Accord-AL language. The editor provides syntax highlighting and completion functionalities that helps the model designer describing behaviors with Accord-AL language. The specified behavior is then translated in UML2 actions. By doing so, we obtain a platform and language independent UML2 model that can be used for application execution or analysis purposes through simulation or code generation processes. Modeling requirements IFP was interested to test an alternative approach to activity diagram and direct programming language description. IFP wanted to use an action language instead to describe the class operations during the modeling process.

Assessment criteria IFP investigated the possibilities and limitations of the action language semantics and compared the utilization of the action language in place of activity diagrams. Since CG-LA is a textual editor, IFP paid as much attention to the user-friendliness (ergonomics) of the editor as to the descriptive power of the Action language.

Results of assessment CG-LA was used to describe more than thirteen operations of the real-time supervisor model. IFP tried to use it each time C++ was not necessary. For several operations, IFP specify activity diagrams too.

The textual editor provided with the action language (see Figure 8) is considered pleasant. It offers syntax highlighting and textual completion on language keywords. Since it is not totally coupled with the Papyrus modeler yet, the completion does not include the names of instances and classes. The Action Language semantics is object-oriented and close to UML2 concepts. Consequently, the utilization of the Action Language is very intuitive. Moreover, the component includes a documentation for each keyword with an equivalent example in activity diagrams. Nevertheless, IFP assessment is that the semantics of the Action Language could be improved. For example, the semantics does not include any iterator. This is somewhat surprising because an action language is used in particular to explore models (classes, associations, etc.) and a keyword like "for each" could be helpful to apply the same action to every object of an association link. The comparison with activity diagrams was very informative. Although they are well adapted to describe an object flow or a sequential action, activity diagrams become complex as soon as control structures (loop, if then else statements, etc.) are present. The approach followed usually by designers in such a case consists in dropping the modeling abstraction and using directly the programming language. An action language offers a real alternative close to the activity diagram philosophy but with the advantage of imperative textual language in term of control structure description.

In our case, the final implementation programming language is known and determined, but we need to underline that an Action Language improves the reusability of the model. Moreover, the use of CG-LA component and the associated Action Language is not limited to the modelling of real-time systems and they could be employed in every UML2 project.

Autocoding from UML models

As shown on the Figure 4 above, the engineering process used in the project included the code generation from the UML model. The code generation proceeds as follows. In addition to the scripts developed for generating the skeleton of the application (headers and source files), a script based on the Acceleo tool4 generates a C++ RTAI file for the initialization of the application. This script reads the PSM model and for all real-time objects such as the tasks, timers and resources used by the application the script generates the code for the declaration, creation and deletion of the real-time objects. For example, for a task, the script uses information like the stack size, the task priority, the task entry point and whether the task is periodic or not for creating the corresponding task object within RTAI and for launching the task (or not) at initialization time.

Conclusion

Recently adopted, the OMG MARTE standard offers a new modeling solution for the modeling of real-time systems. In the OpenDevFactory project, IFP proposed a use case to assess the following three modeling components: CG-LA, CT-RTE and CG-PDM. The use case was relevant to the modeling of a real-time supervisor of engine test-bed which was complex enough to raise different modeling issues and consequently to explore different modeling solutions.

It appeared that the modeling components (profiles) dedicated to the modeling of software and hardware platforms (CT-PDM) and to the modeling of non functional properties (CT-RTE) seem exhaustive and offer an unlimited number of modeling solutions. These profiles are available with libraries of predefined entities that can be used as such for what could be named a standard modeling process. An interested observation is that HRM profile and CG-LA editor are not limited to the modeling of real-time systems. Finally, the Papyrus modeler, in the Eclipse-based integration platform was pleasant to use. Some more work needs to be done in two directions. First, it is necessary to define a global modeling methodology that would describe the successive steps of the modeling process and include documentation and examples. The interaction between tools needs also to be improved in order to fully exploit the MARTE standard. Second, CT-PDM opens the way for multiple platform development and code generation. It is therefore now necessary to build and collect the descriptions of various operating systems based on SRM profile and to streamline the code generation process by providing some sort of a generic code generator using a CT-PDM model as input.

Figure 1 :

 1 Figure 1: Use case principles and components foundations

Figure 2 :

 2 Figure 2: Real-time supervisor screenshot In the OpenDevFactory project, IFP aimed at testing a new modeling process based on components dedicated to real-time systems. First, CT-RTE was used to specify non-functional properties such as real-time constraints or time behavior. Second, CG-LA offered a new solution to describe operations and algorithms, without choosing either a specific programming language or activity diagrams. Third, CT-PDM allowed IFP designers to specify the final implementation of the system. IFP chose to investigate an implementation based on the RTAI platform.

Figure 3 :Figure 4 :

 34 Figure 3: The "Resource Service" patternDuring the project, SRM profile was used by TRIALOG to model the RTAI operating system. The objective of the work was to create a UML model library that captures the RTAI concepts and that could be used by designers to describe how the functional part of various applications is implemented on a RTAI platform. We expect that in the future designers will have access to libraries allowing them to choose between different real-time operating systems such as Xenomai, VxWorks, RTX, RTAI, RT-Linux, etc. The development of the model libraries began by studying RTAI operating system APIs which are C-language oriented. However concepts like profiles, models or stereotypes are closer to Java. Therefore the first step of the model

Figure 5 :

 5 Figure 5: Hardware Resource Modeling models

Figure 6 :

 6 Figure 6: Example of implementation description with CT-PDM and CT-RTE Concerning the implementation description, IFP considers it would be preferable to group all the implementation concepts into a unique profile. Actually IFP used a combination of SRM profile (CT-PDM) and Allocation profile (CT-RTE) and obtained interesting results by using the two concepts in a

3. 3

 3 CG-LA component Description of component CG-LA stands for Generic Component for Action Language modeling. The component aims at providing a way to model 100% of the application behavior in UML. As shown on Figure 7, UML offers several packages for behavior modeling. Use Cases specify requirements of the system, in other words they specify what the system must do. State Machines are generally used to specify behavioral control aspects of applications.

Figure 7 :

 7 Figure 7: UML2 Packages for Behavior Modeling

Figure 8 :

 8 Figure 8: CG-LA-Action Language editor

  The UML profile for Modeling and Analysis of Real-Time and Embedded systems (MARTE) is a specialization of UML that provides concepts dedicated to the real-time domain. CT-RTE component is based on the UML profile for MARTE. CT-RTE aims at providing a way to define and model the real-time characteristics of real-time and embedded systems, such as non-functional properties (NFPs MARTE sub-profile), time structure (Time MARTE sub-profile) (e.g. not-timed / asynchronous, synchronous, multi-clock). CT-RTE component allows designers to specify real-time quantitative features (e.g. deadline, energy consumption, memory footprint, etc), as well as qualitative features (e.g. concurrency modeling).

	CT-RTE relies on MARTE language and provides
	the appropriate editors that support MARTE model
	specification. These are a Value Specification
	Language (VSL) editor and a Clock Constraint
	Specification Language (CCSL) editor.
	VSL is used to specify the values of constraints,
	properties and stereotype attributes particularly
	related to non-functional aspects. Actually, this
	expression language can be used by profile users in
	tagged values, body of constraints, and in any UML
	element associated with value specifications. VSL
	supports the following requirements:
	-How to specify parameters / variables,
	constants, and expressions in textual form.
	-How to define relationships between various
	parameters or constant values with the
	support of arithmetic, logical, relational, and
	conditional expressions.
	-How to define different time values and
	assertions in UML.
	-How to specify composite values such as
	collection, interval, and tuple values.
	CT-RTE provides an advanced VSL editor with
	completion that assists the user for the specification
	of real-time and embedded expressions in models.

http://www.papyrusuml.org

http://www.tripac.com/

Acceleo is a tool of the French OBEO company which translates an UML model to text.

Glossary

UML:

Unified


Nicolas Gargam

Luc Darrasse

Jean-Sebastien Raynaud

Jean-Christoph Ginefri

Philippe Robert

Marie Poirier-Quinot

; Luc

An experimental system

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design! and! microfabrication! process! [START_REF] Serfaty | Multi?turn! split?conductor! transmission?line! resonators.! Magnetic! resonance! in! medicine! :! official! journal! of! the! Society! of! Magnetic! Resonance! in! Medicine! /! Society! of[END_REF].! It! was! composed! of! 10! circular! concentric! copper! tracks! deposited! of! both! sides! of! a! sapphire! substrate.! The! MTLR! was! placed! below! the! µ?slide,! 180!µm! away! from! the! cell! monolayer! (Figure!1!a.!b.)! and! was! inductively! coupled! (14)! to! the! receiver! electronics! using! a! 6!mm! single?turn! copper! loop,! parallel! tuned! at! f 0! =!100.53!MHz.! Orthogonality! between! the! transmit! and! receive!coils!axis!leaded!to!a!attenuated!transmission!coefficient!S 21 !between!the!two! coils!of!about!-!40!dB!at!the!Larmor!frequency.!! MRI#sequence:!A!T 1 ?weighted!3D?FLASH!(Fast!Low!Angle!SHot)!sequence!was! used!with!a!field!of!view!of!0.6!×!1.9!×!0.8!cm 3 ,!a!resolution!of!12.4!µm!in!the!readout! direction,!perpendicular!to!the!cell!layer,!and!an!in?plane!resolution!of!160!×!160!µm ² .! To!reach!such!high!resolution!in!the!readout!direction,!echo!asymmetry!was!adjusted! to! 5%,! meaning! that! only!55%! of! the! k?space! was! acquired.! Acquisition! parameters! were:!TR!(Time!Repetition)/TE!!(Time!Echo)!of!74.

!bulk!culture!medium's!relaxation!rate!R 1m ,!diffusion!coefficient!D m ,!and!assuming! the!cell!monolayer!was!entirely!contained!in!the!first!voxel,!the!local!relaxation!rate!is! then!expected!to!vary!as!:! ! ! !,!"#$! ! !! = ! !,! !! + ! !,!"#$! ! !! -! !,! !! ! ! ! ! ! .! !,! !! ! Eq.!!1.! Considering! a! Spoiled! Gradient! Recalled! Echo! sequence,! with! TR!=!75!ms, R 1c (

  7/3.7!ms,!total!sampling!bandwidth! of! 12.5!kHz,! 2! averages,! 100! dummy! scans! to! reach! the! steady! state,! and! acquisition! time! of! 8!min.! Radiofrequency! spoiling! was! performed! with! a! 117°! phase! increment! between! successive! excitations! to! reduce! residual! transverse! magnetization! effects.! The!alignment!of!the!microfluidic!channel!onto!the!horizontal!image!axis!was!carefully! adjusted!using!scout!scans!at!the!beginning!of!the!protocol.! Data#Processing# A! cylindrical! region! of! interest! (ROI)! of! 5!mm! diameter! was! centered! to! the! sensitivity! pattern! of! the! reception! coil.! One?dimensional! signal! profiles! were! then! ! 9! extracted!with!a!projection!signal!intensity!of!the!ROI!along!the!2!directions,!y!and!z,! parallel! to! the! cell! layer! (5! and! 50!mm).! The! homodyne! method! (15)! was! applied! to! ensure! low! distortion! of! the! reconstructed! profiles! despite! the! highly! asymmetric! k? space! coverage.! To! avoid! truncation! artifacts,! a! linear! phase! ramp! correction! was! applied! to! the! k?space! with! the! appropriate! sub?voxel! shift! before! the! homodyne! reconstruction.! The! R 1 ! measurements! were! performed! on! the! first! non?zero! voxel! along!the!x?axis,!assuming!this!to!be!the!voxel!containing!the!cells.!! The! signal?to?noise! (SNR)! measurements! were! extracted! from! magnitude! images! using! the! average! signal! intensity! over! the! ROI! and! the! standard! deviation! outside!of!the!channel.! The! systematic! evaluation! of! the! performance! of! the! R 1 ! measurements! was! based! on! Cramer?Rao! Bound! according! to! the! SNR! and! the! flip! angle! of! the! experiments!(16).! The! relaxation! rate! was! also! simulated! considering! the! theoretical! model! developed!by!Strijkers!et!al.!(17),!based!on!the!Bloch!equations!including!exchanges!of! water! molecules! among! 3! different! compartments! (vesicles,! cytoplasm! and! the! extracellular! medium).! Their! model! allows! the! quantification! of! the! decreased! efficiency!due!to!the!CA!internalization,!depending!on!the!location!of!the!paramagnetic! chelates.! The! shape! of! the! cells! highly! influences! the! values! of! the! water! molecule! exchange! constants! between! two! compartments.! In! the! present! study,! cells! are! adherent!on!a!surface!and!were!assumed!an!oblate!semi?spheroid!cell!shape,!following! ! 10! a! previous! work! by! Lee! et! al.! (18).! This! modified! model! was! applied! using! the! parameters!of!Table!1!to!simulate!R 1,c! ([Gd])!measurements,!assuming!equal!relaxation! rates!between!the!vesicle,!cytosol,!and!extracellular!compartments!in!the!absence!of! CA.!The!number!of!vesicles,!their!radii,!and!their!permeability!were!of!the!same!order! as!those!reported!in!the!literature!(19?21).! ! Diffusion## Based! on! the! integration! of! the! Bloch?Torrey! equation,! this! system! could! be! represented! by! a! mean! local! relaxation! time! assuming! a! mono?exponential! position? dependent! decay! (Mean! Relaxation! Time! Approximation! (22)).! Due! to! the! planar! configuration! of! the! cell! monolayer! (over! y! and! z! axes),! the! apparent! relaxation! rate! R 1,local (x), induced!by!the!paramagnetic!CA, is!expected!to!vary!along!the!x?direction.! Considering!a!time!integration!of!the!Bloch?Torrey!equation,!from!0!to!infinity,!taking! the

  Figure!3?b! shows! the! R 1,c ([Gd])! values,! R 1 ! measurements! for! different! Gd!

Figure! 4 !Figure! 1 :Figure! 2 :Figure! 3 :Figure! 4 :

 41234 Figure! 4.a! presents! the! signal! variation! along! the! x?axis,! i.e.,! the! receiver! coil!


Olivier M Girard
email: olivier.girard@univ-amu.fr

Ludovic De Rochefort

Marie Poirier-Quinot

Luc Darrasse

Robert F Mattrey

Molecular imaging techniques-new frontiers Chapter 9: Quantification strategies for MRI

Quantification strategies have been a long standing challenge since the early days of MR molecular and cellular imaging. Quantitative imaging is desirable in the framework of comparative or follow-up studies in order to establish objective evidences of a specific target expression pertaining to a specific disease. Numerous strategies of increasing complexity have been proposed to address this need. In this chapter, we briefly review common strategies related to quantitative molecular imaging for MRI and we discuss their respective outcomes. We focus on relaxation Contrast Agents (CAs) that generate MR contrast by affecting the proton relaxation times, and which are the most common kind of CAs used in MRI. Particular attention is paid on cutting edge applications enabling local CA quantification as well as distinction of the bound/activated sub-population of the CA.

Introduction

Quantification strategies have been a long standing challenge since the early days of MR molecular and cellular imaging. Quantitative imaging may be required to establish the in vivo proofof-principle of a new compound efficiency, and it is desirable in the framework of comparative or follow-up studies performed on multiple patients. Typical molecular imaging studies, for instance, consist in comparing the bio-distribution of a targeted contrast agent (CA) with its non-targeted counterpart. Such assessment has to be repeated on several patients in order to overcome the inherent biological variability and to extract statistically significant results, ultimately establishing objective evidences of a specific target expression pertaining to a specific disease. Hence, numerous quantitative strategies of increasing complexity have been proposed to address this need and perform such studies. In this chapter, we briefly review common strategies related to quantitative molecular imaging for MRI and we discuss their respective outcomes. Particular attention is paid on the most cutting edge applications enabling local CA quantification as well as distinction of the bound/activated sub-population of the CA.

Simple quantification strategies consist is measuring the fractional signal change (i.e. % signal enhancement/drop) due to the presence of the CA, on a given MR image. The total area (or volume) of signal enhancement may be easily calculated as well to deliver some quantitative index of the CA distribution. This can be done either using a well chosen reference intensity tissue or by using registered pre-and post-injection images. Although popular, these strategies are not really quantitative but should rather be considered as pseudo-quantitative, since they do not provide quantitative information on the CA or the target distribution themselves, but instead dilute the relevant local information in a high-level global parameter. In addition, such measurements are prone to multiple biases, especially the choice of the MR sequence parameters used to acquire the weighted image, which makes multi-center and cross-vendor studies difficult to perform. Conversely, more complex data processing procedures may be used to estimate parametric maps (e.g. relaxation time maps) which provide, at least in theory, sequence-independent parameters that can be compared from site to site. The underlying interpretation in terms of CA concentration may not be univocal, but at least the data are truly quantitative and can be compared from one study to another.

Actual CA quantification is certainly the ultimate goal of quantitative imaging protocol applied to CA detection. Indeed, knowledge of the CA concentration is a prerequisite to derive the number of targeted receptors or labeled cells as well as the quantity of carried drug when using theranostic agents for instance, which is ultimately the relevant information typically expected from molecular imaging studies. Robust CA quantification is still very challenging for targeted CA such as those used in molecular imaging applications, mostly because the CA coexists in multiple states (i.e. free and targeted form) at the same time in the sample and these states do typically have different MR contrast efficiency. Current advanced methods hold promise for absolute CA quantification, including the specific assessment of the targeted population of a compound only.

In the following we focus on relaxation CAs, as opposed to chemical shift reagents (e.g. CEST imaging agents) or multinuclear reagent (e.g. 19 F probes), i.e. we focus on CAs that generate MR contrast by affecting the proton relaxation times, which are the most common kind of CA used in MRI.

MR is an indirect detection modality

As opposed to nuclear medicine modalities, usual CAs cannot be observed directly using MRI because they do not provide intrinsic MR signal and this adds an extra level of complexity to the detected signal (see Chapter 3 for details on direct detection using X-nuclei, i.e. non 1 H). Instead, CA detection is based on their interaction with surrounding protons through several mechanisms affecting relaxation rates and resonance frequency. This indirect nature of CA detection makes it prone to multiple biases that need to be accounted for to quantify the amount of CA directly by imaging.

MRI detects CA through their effect on mobile water protons. Relaxation MR contrast agents shorten proton relaxation times through magnetic interaction with neighboring protons and subsequent exchange of these protons to the bulk water, which amplifies and propagates the CA effect. In general, the MRI signal is proportional to the local proton density and is weighted by some function of the longitudinal (T1) and transverse (T2/T2*) relaxation times of the tissues -the actual weighting formulae depends on the actual pulse sequence that is used to capture the image. The effect of MR CA is usually summarized in term of their efficiency to speed up proton relaxation processes -defined as relaxivity, according to the following formulae: Ri = Ri0 + ri [CA] , with i = 1, 2 or 2* , Eq. 1

where Ri = 1/Ti is the relaxation rate observed in presence of CA, Ri0 is the baseline tissue relaxation rate, ri is the CA relaxivity and [CA] its concentration. This relation may apply to both relaxation mechanisms, i.e. longitudinal T1 and transverse, T2 and T2*. By acquiring appropriate weighted images of a given sample it is thus possible to visualize CA by MRI, although the measured MR signal is a complex non-linear function of the CA content.

While usual MRI contrast agents affect both proton relaxation times (longitudinal and transverse), they are typically classified according to their dominant mechanism:

1/ Paramagnetic compounds such as Gadolinium (Gd) chelates [START_REF] Lauffer | Paramagnetic Metal-Complexes as Water Proton Relaxation Agents for Nmr Imaging -Theory and Design[END_REF] have a r1/r2 ratio close to 1, thus they mainly affect T1 (because R10< R20 for most tissues) and hence provide positive contrast on T1 weighted images.

2/ Superparamagnetic compounds such as iron oxide nanoparticles [START_REF] Laurent | Magnetic iron oxide nanoparticles: Synthesis, stabilization, vectorization, physicochemical characterizations, and biological applications[END_REF] (IONPs) have a low r1/r2 ratio (i.e. << 1), thus they usually have dominant T2 effect, leading to signal voids (negative contrast) on T2or T2*-weighted scans.

Although this simplified classification does not account for all encountered effects and observed contrast types it certainly corresponds to the most popular use for either type of compounds. As alternative examples, Gd-based CAs are routinely used for bolus tracking studies to measure perfusion (DSC-MRI for dynamic susceptibility contrast); a technique that relies on the negative T2* effect arising around vessels containing high concentrations of Gd. Conversely, recent advances in MR pulse sequence methodology have enabled probing the T1-effect of IONPs using utrashort echo time (UTE) scans, hence providing positive contrast detection of such compounds (see Girard et al. [START_REF] Girard | Optimization of Iron Oxide Nanoparticle Detection Using Ultrashort Echo Time Pulse Sequences: Comparison of T1, T2*, and Synergistic T1-T2* Contrast Mechanisms[END_REF] for a general theory of CA-induced MR contrast and a detailed comparison of the T1 and T2 effects of IONPs).

Parametric map estimation

To address CA quantification challenge, multiple weighted images can be used to extract parametric maps which are quantitative maps of a parameter of interest such as T1 or T2 (i.e. images that scale directly proportional with the corresponding parameter). These maps are usually obtained from several MR images acquired with varying imaging parameter, and computed using least-square data fitting algorithms based on analytical MR signal description. For instance, multiple-echo spinecho or gradient-echo sequences allow for T2 and T2* quantification, respectively, using an exponential decay model. Similarly, inversion recovery prepared sequences acquired using various inversion times allow for T1 quantification, using an exponential recovery model.

Relaxation time quantification has been a very popular way to extract information about CA content. Indeed, using a relaxation time map and Eq.1 it is possible to derive a CA concentration map, assuming that the baseline tissue relaxation time is known or has been measured prior to CA injection, and assuming a constant value for the corresponding relaxivity as well. As we will see later, this last assumption is a critical issue related to CA quantification. Relaxation time quantification has been applied for years in the MR community to study CA, and it is actually the method of choice to measure CA relaxivity, as Eq.1 may also be used to infer relaxivity using in vitro samples of known CA concentration.

Despite its apparent simplicity, relaxation mapping methods have been the focal point of many researchers for years until now, as it is still challenging to get robust and accurate relaxation time measurements in a short scan time. Multiple confounding factors may affect the measured signal and refined signal models have to be considered. RF magnetic field inhomogeneities, for instance, need to be corrected to get reliable T1 estimates [START_REF] Yarnykh | Actual flip-angle imaging in the pulsed steady state: A method for rapid threedimensional mapping of the transmitted radiofrequency field[END_REF]. In the context of T2* quantification, which is the most sensitive parameter to IONPs [START_REF] Bowen | Application of the static dephasing regime theory to superparamagnetic iron-oxide loaded cells[END_REF], significant work has been done to account for macroscopic B0 inhomogeneities that arises close to air/tissue interfaces, and this has made possible reliable in vivo T2* measurements [START_REF] Dahnke | Limits of detection of SPIO at 3.0 T using T-2* relaxometry[END_REF].

CA relaxivity modulation scenarios

An important challenge for CA quantification based on relaxation mapping results from the indirect nature of CA detection. Unfortunately, CA relaxivity is not constant in many practical conditions, which breaks down the validity of Eq.1. Indeed, because the relaxivity depends on magnetic interactions of the CA with neighboring protons as well as water exchange and diffusion around the magnetic core, it is affected by the microscopic distribution of the compound as well as the microstructure of the tissue of interest, which obviously influence the magnetic interaction strength and the water mobility [START_REF] Donahue | Water diffusion and exchange as they influence contrast enhancement[END_REF][START_REF] Weisskoff | Microscopic Susceptibility Variation and Transverse Relaxation -Theory and Experiment[END_REF][START_REF] Yablonskiy | Theory of NMR signal behavior in magnetically inhomogeneous tissues: the static dephasing regime[END_REF]. Thus, CA relaxivity may vary spatially and temporarily during a single experiment, as the CA experiences various micro-environments from the injection site to the targeted receptor. This is especially true in the framework of molecular imaging CAs which are designed to interact with other molecules [START_REF] Querol | Amplification strategies in MR imaging: Activation and accumulation of sensing contrast agents (SCAs)[END_REF][START_REF] Perez | Magnetic relaxation switches capable of sensing molecular interactions[END_REF] and for which amplification strategies have been intended, such as the accumulation of CA inside cells. In this later case, the modification of the CA local distribution is obtained intentionally to enhance the MR signal and hence facilitate the detection of small doses of the targeted receptors or cells (see Chapter 3 for general rules of detection sensitivity). However, this complicates tremendously CA quantification based on relaxation time measurements because a given relaxation time variation may be attributed either to a concentration change or to a change of contrast efficiency (i.e. relaxivity, see Eq.1).

In a global molecular imaging perspective, such MR contrast switching capabilities are actually fortunate because they have allowed CAs to probe tissue microenvironment (e.g. OFF or silent state for the native CA state, and ON or active state upon receptor binding). Thus it has been a driving force in developing responsive agents that have enabled detection of specific targeted receptor or enzymes (e.g. see following references [START_REF] Querol | Amplification strategies in MR imaging: Activation and accumulation of sensing contrast agents (SCAs)[END_REF][START_REF] Tu | Activatable T (1) and T (2) Magnetic Resonance Imaging Contrast Agents[END_REF] for various responsive CA designs and principles). Illustrations of CA relaxivity modulation scenarios due to receptor binding or cell labeling are presented in Fig 1 . A well known effect related to paramagnetic CA is the modulation of the tumbling rate of the complex following binding with a high molecular weight target, which strongly affects the r1 relaxivity profile (Fig. 1 a). Such effect can be exploited to generate highly specific image contrast related to the bound form of the CA only, and is known as delta relaxation enhanced MR (dreMR [START_REF] Hoelscher | Quantification and localization of contrast agents using delta relaxation enhanced magnetic resonance at 1.5 T[END_REF]). The dreMR technique is a promising candidate for quantification of paramagnetic CA based on T1 relaxation measurements since it totally suppresses the non-specific (i.e. unbound) components of the CA. Hence with this technique, no more MR signal comes from the free CA component and only targeted CAs, of known relaxivity (assuming no other mechanism is modulating relaxivity), contribute to the MR signal [START_REF] Hoelscher | Quantification and localization of contrast agents using delta relaxation enhanced magnetic resonance at 1.5 T[END_REF]. Note however that such an approach requires some dedicated piece of hardware and is still in an early research phase (see Chapter 3 for more details).

Another well documented T1 modulation effect is related to the slowdown of the water exchange regime that may follow CA internalization into cellular compartments (Fig. 1 b): the time needed for the water molecules to cross cellular membranes and propagate the relaxation enhancement effect to the bulk water is lengthened and this results in saturation or "quenching" of the T1 contrast [START_REF] Terreno | Effect of the intracellular localization of a Gd-based imaging probe on the relaxation enhancement of water protons[END_REF][START_REF] Kok | Cellular compartmentalization of internalized paramagnetic liposomes strongly influences both T1 and T2 relaxivity[END_REF][START_REF] Levy | How cellular processing of superparamagnetic nanoparticles affects their magnetic behavior and NMR relaxivity[END_REF]. Although, this latter effect may be understood based on complex multiple compartments and exchange ways modeling, it is rather difficult to predict the actual relaxivity value following targeting and subsequent cell internalization, hence hindering quantification.

For cellular imaging using IONPs, a third relaxation modulation effect is related to the T2 and T2* susceptibility contrasts mechanism. As opposed to the T1 effect which relies on close water access to the magnetic core of the CA, the susceptibility contrast is a long distance mechanism affecting both T2 and T2*, and which is mediated by the strong magnetic field inhomogeneities induced by the IONPs (Fig. 1 c). The characteristic size of the magnetic field inhomogeneities is a critical factor here and thus accumulation of multiple IONPs into clusters in the cellular space has a strong effect on induced MR contrast. For free IONPs, the random motion of water molecule leads to an irreversible loss of phase coherence because each single proton experience random magnetic field variations. In this case T2 and T2* relaxivities have somewhat similar intensity. In contrast, for large IONP clusters the characteristic size of the field heterogeneities becomes larger than the random walk of the water molecules during the time scale of the MR experiment. Hence the induced spin dephasing is reversible using a spin echo and the associated T2 effect is strongly reduced. Conversely, the T2* effect reaches its maximum intensity as described by the static dephasing regime theory (SDR) [START_REF] Bowen | Application of the static dephasing regime theory to superparamagnetic iron-oxide loaded cells[END_REF][START_REF] Yablonskiy | Theory of NMR signal behavior in magnetically inhomogeneous tissues: the static dephasing regime[END_REF]. In this context R2', defined as R2*-R2 (usually reported as related to "large scale" magnetic field inhomogeneities) is mostly sensitive to large IONP clusters, i.e. IONP labeled cells.

Multiparametric imaging

Based on this concept, Kuhlpeter et al. [START_REF] Kuhlpeter | R2 and R2*mapping for sensing cell-bound superparamagnetic nanoparticles: In vitro and murine in vivo testing[END_REF], have shown that cell-internalized IONPs can be differentiated from freely distributed IONPs using joint T2-and T2*-mapping, demonstrating the benefit of multiparametric relaxation mapping. This was confirmed recently by Girard et al. [START_REF] Girard | Toward absolute quantification of iron oxide nanoparticles as well as cell internalized fraction using multiparametric MRI[END_REF] using another IONP type and cell line, and pushed further to assess the full quantification potential of such a multiparametric approach. In this study, all four contrast mechanisms (T1, T2, T2* and T2') as well as magnetic susceptibility were studied in vitro using cell culture samples (cf. Fig 2). In addition IONP content was quantified on the same samples using inductively coupled plasma -mass spectroscopy, and considered as the gold standard. From these measurements it was shown that quantitative relaxation data yield quantitative estimates of the IONP internalized fraction providing that the local particle concentration is know. In addition the T2' contrast mechanism was found very consistent with the SDR theory (i.e. it was predictable), allowing for cell-internalized fraction estimation without the need for preliminary calibration of the internalized relaxivity curve. Last but not least, this study demonstrated that magnetic susceptibility, as measured through IONP induced MR frequency shift, is a potential candidate for absolute CA concentration estimation since it does not depend on whether the IONPs are free or internalized into cells (Fig 3). An important limitation of this study however was that the susceptibility was not measured by imaging means (MR spectroscopy was used instead), and a well defined shape of the sample was necessary to extract susceptibility estimates from measured data. Hence direct translation of the proposed methodology to in vivo application is not possible. To overcome this limitation, alternative susceptibility quantification approaches are necessary.

Quantitative Susceptibility Mapping (QSM)

Recently, development of complex post-processing algorithms has made possible to quantify the magnetic susceptibility of tissues directly by imaging means using MRI. In contrast with its predecessor susceptibility weighted imaging (SWI) [START_REF] Haacke | Susceptibility weighted imaging (SWI)[END_REF], which was only qualitative, a new family of techniques has emerged, called quantitative susceptibility mapping (QSM) [START_REF] De Rochefort | Quantitative Susceptibility Map Reconstruction from MR Phase Data Using Bayesian Regularization: Validation and Application to Brain Imaging[END_REF][START_REF] Schweser | Quantitative imaging of intrinsic magnetic tissue properties using MRI signal phase: An approach to in vivo brain iron metabolism?[END_REF], which delivers quantitative measurements of the magnetic susceptibility distribution. In addition to CA quantification, several other research areas may benefit from QSM since it is particularly promising for venous blood oxygen saturation level, endogenous iron as well as local myelin content estimation, and hence should yield to multiple potential clinical applications.

The QSM technique relies on the phase information of the MR signal that was often disregarded so far. Local phase data is directly proportional to the MR frequency shift, and hence can be used to detect local field inhomogeneities induced by magnetic material such as IONPs, which modulate the proton resonance frequency in their neighborhood. In short, a magnetic source distribution consistent with the observed field inhomogeneities is reconstructed by solving an inverse problem with similar concepts that found in magneto-encephalography (MEG). An important complexity, however, lies in the ill-posed inverse problem. Tremendous efforts have been carried out recently to develop dedicated algorithms able to regularize the solution by adding priors into the reconstruction, and this has been addressed in many different ways by several groups [START_REF] De Rochefort | Quantitative Susceptibility Map Reconstruction from MR Phase Data Using Bayesian Regularization: Validation and Application to Brain Imaging[END_REF][START_REF] Schweser | Quantitative imaging of intrinsic magnetic tissue properties using MRI signal phase: An approach to in vivo brain iron metabolism?[END_REF][START_REF] Mills | Automated detection and characterization of SPIOlabeled cells and capsules using magnetic field perturbations[END_REF][START_REF] Langley | Quantification of SPIO Nanoparticles in vivo Using the Finite Perturber Method[END_REF][START_REF] Haacke | Susceptibility Mapping as a Means to Visualize Veins and Quantify Oxygen Saturation[END_REF]. Other important challenges need to be addressed along this complex post-processing chain, especially robust phase unwrapping as well as background field variation removal, which are prerequisite steps to obtain high quality susceptibility maps.

In the context of IONPs quantification, QSM-like methods have been successfully applied in a couple recent studies [START_REF] Mills | Automated detection and characterization of SPIOlabeled cells and capsules using magnetic field perturbations[END_REF][START_REF] Langley | Quantification of SPIO Nanoparticles in vivo Using the Finite Perturber Method[END_REF], although no actual susceptibility maps were generated (or equivalent parameter such as magnetic moment map). Figure 4 illustrates the potential of QSM method to quantify IONP in a preliminary cellular imaging experiment; an actual magnetic moment map is displayed on Fig. 4. c) where the image intensity is directly proportional to IONP content. Besides, QSM has been proven efficient for quantification of Gd-based agents [START_REF] De Rochefort | Quantitative MR susceptibility mapping using piece-wise constant regularized inversion of the magnetic field[END_REF] as well. However, because of multiple confounding factors, and various different approaches presented in the literature to address them, robustness and sensitivity of the QSM technique is still an open question. In the near future it is important to reach consensus regarding which particular QSM reconstruction algorithm and associated parameters have to be used to obtain reliable results. This would definitely promote wider acceptance of QSM as a routine tool, and ultimately yield to a robust CA quantification method.

Conclusion

Molecular imaging MR contrast agents have been designed to interact with specific molecules and cellular receptors in a way that modifies their relaxation contrast efficiency. This translates into modulation of the usual relaxation mechanisms upon specific binding or activation, which has enabled specific detection of targeted-CA and has made MR a molecular imaging modality. Unfortunately, modulating CA relaxivity complicates CA quantification at the same time, because both free and activated CA pools typically coexist and hence no single relaxivity value can be used to extract CA concentration from relaxation data. Alternatively, magnetic susceptibility measurements have been shown promising for quantifying IONPs in cellular imaging studies, and are suitable for paramagnetic CA quantification as well. Recent advances in modeling and reconstruction algorithms have enabled Quantitative Susceptibility Mapping using the phase data of the complex MR signal. This technique holds great promise for robust absolute CA quantification in the future, which should open new horizons to address current issues in MR molecular imaging. The authors have no relevant affiliations or financial involvement with any organization or entity with a financial interest in or financial conflict with the subject matter or materials discussed in the manuscript.

Legends

No writing assistance was utilized in the production of this manuscript.

Figure 1 :

 1 Figure 1: Relaxivity modulation scenarios following receptor binding and cellular uptake. a) Tumbling rate effect following receptor binding for paramagnetic CA. Relaxation dispersion profile for 0.25 mM of MS-325 (Gd) in pure water and in 0.6 mM HSA. See Girard et al. Proc. of ISMRM 2008, 1656, for more information. b) Relaxivity quenching effect following cell internalization and endosomal encapsulation. Such effect is due to the water exchange slowdown through multiple cellular membranes, and hence may affect all kinds of CA. Adapted with permission from Aime et al., Chem. Res. 2009, 42, 822. Copyright 2009 American Chemical Society. c) Effect of IONP clustering on the T2 and T2* contrast regime. R2' = R2* -R2 is mostly sensitive to IONP clusters such as those encountered into labeled cells.

Figure 2 :

 2 Figure 2: Relaxation rates and corresponding relaxivities for various fractions of free and cellinternalized IONPs. Large relaxivity variations are observed between different groups, evidencing modulation of relaxivity upon cellular internalization. Reprinted with permission from Girard et al., Contrast Media & Molecular Imaging 2012, 7(4), 411. Copyright 2012 John Wiley and Sons.

Figure 3 :

 3 Figure 3: Magnetic susceptibility measurements for various fractions of free and cell-internalized IONPs. The susceptibility per unit concentration is independent of IONP local distribution. Reprinted with permission from Girard et al., Contrast Media & Molecular Imaging 2012, 7(4), 411. Copyright 2012 John Wiley and Sons.

Figure 4 :

 4 Figure 4: Demonstration of Quantitative Susceptibility Mapping on IONP labeled cells. a) Conventional T2* weighted magnitude image where IONPs appear as signal voids. b) Background filtered MR phase image: typical magnetic field dipolar pattern is observed around IONP labeled cells. Such a filtered phase map is a prerequisite for susceptibility extraction, or equivalently magnetic moment. c) Magnetic moment map: the image intensity is directly proportional to the total amount of IONP here. See de Rochefort et al., Proc. of ISMRM 2008, 1691, for full description of the acquisition protocol and post-processing, as well as IONP quantification validation.

Figures Figure 1

 1 FiguresFigure1

Figure 2 Relaxation

 2 Figure 2

Figure 3 Magnetic

 3 Figure 3

Figure 4 Demonstration

 4 Figure 4

Chapter Summary: (5-8 key sentences are pulled out as bullet points to highlight the main points of the chapter.) When using relaxation quantification to perform molecular imaging studies, caution must be paid on the underlying interpretation in terms of CA content.

In general, multiparametric approaches should be preferred over single parameter estimation, as they provide insight into CA microdistribution and activation, e.g. targeting or cell-internalization.

Quantitative Susceptibility Mapping holds great promise for absolute CA quantification, although it is still limited to a few research centers because of complex implementation scheme.

Combining susceptibility and relaxation time mapping should provide new quantitative indexes, allowing for absolute quantification of CA content as well as the activated fraction.

Key terms: (up to 4)

Weighted images: MRI typically exhibits weighted images where the image intensity is a function of a given parameter, such as T1, T2 or the proton density. However weighted images are only qualitative and do not quantify the underlying parameter of interest (i.e. the image intensity is not proportional to the parameter of interest). The scale of a weighted image is unit-less and arbitrary.

Parametric maps: Parametric maps (e.g. T2-map or magnetic susceptibility-map) are quantitative images. Such maps have been typically reconstructed from multiple weighted images using dedicated post-processing algorithms. The scale of a parametric map is directly proportional to the corresponding parameter of interest.

Relaxivity: Relaxivity is defined as the efficiency of a given amount of CA to speed up relaxation processes of surrounding protons. It may relate to either T1 or T2/T2* contrast mechanism. Relaxivity units are mM -1 .s -1 .

Key learning points: (up to 4)

1/Relaxivity depends on the CA microdistribution within a tissue, which hinders CA quantification from relaxation data.

When using relaxation quantification to perform molecular imaging studies, caution must be paid on the underlying interpretation in terms of CA content.

2/Magnetic susceptibility provides an independent measurement of local magnetic content, which is promising for robust CA quantification.

3/Combined susceptibility, T2 and T2* measurements enable absolute quantification of iron oxide nanoparticles as well as cell internalized fraction in cellular imaging studies.