Master of Mechanics
University of Paris-Saclay
Specialty: Biomechanical Engineering
Program Director:
Prof. Abdul Barakat, Ecole Polytechnique
barakat@ladhyx.polytechnique.fr
Tel: +33 (0)1 69 33 52 68
General Presentation
The aim of this second-year (M2) specialty program of the University of Paris-Saclay Master of
Mechanics is to provide students with specialization in the application of mechanics to
biological/biomedical systems. All instruction is in English and is delivered by a group of
distinguished faculty who are internationally recognized in their fields. The program is based at Ecole
Polytechnique, but the faculty come from various partner institutions including Ecole Polytechnique,
Ecole Centrale Paris, Ecole Normale Superieur de Cachan, and the University of Evry val d’Essonne.
Students may apply directly to the program from other academic institutions or may enroll after having
completed the first year (M1) at Ecole Polytechnique or one of the University of Paris-Saclay partner
institutions.
The approach for the program is physics- and engineering-based, so students need to have previous
training in the physical and/or mathematical sciences.
Completion of the program requires 60 ECTS. The program consists of six months of formal
coursework (divided into two 10-week academic quarters) and totaling 30 ECTS followed by a 6month research internship (30 ECTS) in one of the University of Paris-Saclay laboratories.
Language of Instruction
All courses are taught in English. Knowledge of French is helpful but not necessary.
Program Requirements
The Biomechanical Engineering Master program is a one-year program (September to August). The
year is divided into two 10-week academic quarters during which students are required to successfully
complete a total of 30 ECTS of formal coursework. Most courses are 3 ECTS, so 10 courses are
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nominally required (typically 5 courses per academic quarter). The other 30 ECTS come from a 6month research internship.
Courses:
Since most courses applicable to the Biomechanical Engineering program are 3 ECTS each, 10 courses
are typically required. Of these 10 courses, 6 are required of all students. The other 4 courses are
electives and can be chosen from a broad list of courses in mechanics, other engineering fields, physics,
applied mathematics, or biology. The table below provides more information on the courses:
ECTS
Required Courses
Course Title
3
Biomechanics and Bioengineering
3
3
Biomechanical Modeling of Active and
Passive Biological Tissues
Biomimetics and Animal Locomotion
3
Cell Mechanics
3
Control in Biological and Biomechanical
Systems
3
Mechanics of Motility of Living Organisms
Instructor(s)
Instructor Affiliation
B. David
E. Vennat
D. Chapelle
P. Moireau
E. de Langre
S. Michelin
J. Husson
A. Barakat
J. Lerbet
D. Ichalal
L. Nehaoua
J.M. Allain
Ecole Centrale Paris
INRIA
Ecole Polytechnique
Ecole Polytechnique
UEVE
Ecole Polytechnique
Example Elective Courses
3
3
3
3
Biomechanics of Anthropomorphic Systems
Biotechnology
Force Generation in Muscle
Drops, Bubbles and Co.
3
Low Reynolds Number Flows
O. Bruneau
E. Budyn
L. Truskinovsky
D. Quere
C. Baroud
N. Ribe
ENS Cachan
ENS Cachan
Ecole Polytechnique
Ecole Polytechnique
University of Paris
Sud
Research Internship
A 6-month research internship is required. The research is typically conducted within a research
laboratory of one of the University of Paris-Saclay partner institutions. The topic and scope of the
internship needs to be approved by the Program Director.
Employment Opportunities
The Biomechanical Engineering Master program provides excellent preparation for doctoral studies as
well as for careers in the medical device, biotechnology, and pharmaceutical industries. The field of
bioengineering is also perfectly suited to innovation and technology transfer applications, and the
Biomechanical Engineering Master program also prepares students for careers in such fields.
LocationAll teaching will be conducted on the campus of Ecole Polytechnique. Research internships
will typically take place in a research laboratory of one of the University of Paris-Saclay partner
institutions.
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Class Size
An enrollment of 10-20 students is anticipated.
Admission Requirements
The program is open to students with strong training in engineering, physics, or applied mathematics
who are interested in biological/biomedical applications.
Application Procedure
Prospective students should submit their application online through the University of Paris-Saclay
application website. Click on the link below and choose Year of Master: M2, Distinction: Mechanics,
Specialty: Biomechanical Engineering.
Tuition and Fees
Annual registration fee: 237 €
Year M2 tuition fees: 4400 €
Financial Support and Fee Waivers
A number of fellowships that cover tuition, fees, and provide a monthly stipend are available to
outstanding students. The program director will identify potential candidates for these fellowships and
nominate them for consideration.
Tuition and fee waivers are possible under certain conditions.
Additional information on fellowships and fee waivers are available at the following link:
Additional Information
For additional information, please direct all inquiries to the Program Director: Prof. Abdul Barakat barakat@ladhyx.polytechnique.fr.
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Courses details
Biomechanics and Bioengineering
B. David and E. Vennat, Ecole Centrale Paris
Keywords: cellular mechanics; cellular bioengineering
Course Objectives: Introduction to bioengineering and biomechanics.
Course Content:
Role of mechanics in cellular biological structure and function; Bioengineering approaches to
control of cellular function and behavior.
Course References:
1) Cowin, Bone Mechanics Handbook.
2) David B, Bensidhoum M, Potier E, Hannouche D, Logeart D and Petite H. Bone Tissue
Engineering, Chapter 26, Jeremy Mao ed., 2007.
3) David, B., Pierre, J., and Oddou, C. Biomechanical function in regenerative medicine in
Fundamentals of Tissue Engineering and Regenerative Medicine, Ulrich Meyer et al., eds,
Springer, pp. 693-703, 2009.
4) Oddou C, Lemaire T, Pierre J and David B. "Hydrodynamics in Porous Media with
Applications to Tissue Engineering". In CRC Press, Taylor & Francis Group, Porous
Media: Applications in Biological Systems and Biotechnology, Boca Raton, Kambiz
Vafai, 75−119, 2010.
Course Prerequisites: Basic continuum mechanics
Biomechanical Modeling of Active and Passive Biological Tissues
D.Chapelle, P.Moireau
Keywords: tissue mechanics; numerical analysis; modeling; biological tissues; multi-physics.
Course Objectives: 1) To introduce the students to biological tissue mechanics per se.
2) To teach principles of mechanical and biophysical modeling of a complex system (via cardiac
example). 3) To introduce discretization, simulation, and data-driven personalization of models..
Course Content: 1) Mechanical modeling of biological tissues. 2) Cardiac modeling. 3) Multiphysics
coupling. 4) Scientific computing. 5) Towards model personalization.
Credits: 3.0
Detailed Content:
1. Elements of cardiac physiology
a. Cardiac anatomy
b. Cardiac cycle
c. Electrical activation
d. Cardiac function
e. Cardiovascular system components
i. Vascular network
ii. Arterial properties
iii. Valves
iv. Coronary tree
f. Cellular level physiology
2. Cardiac mechanical modeling
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a. Large strain mechanical formulations
b. Hyperelasticity
c. Viscoelasticity
d. Multiscale modeling of myofibres
e. Rheological models
3. Multi-physics coupling
a. Electrophysiology aspects
b. Circulation models
c. Fluid-structure interaction
d. Perfusion modeling
4. Scientific computing
a. Introduction to spatial discretization
b. Guidelines for adequate time-discretization
c. Discretization of coupling
d. Boundary conditions
5. Towards model personalization
a. Data assimilation principles
b. Sequential estimator
i. Optimal filters
ii. Observers
iii. Joint state-parameters estimators
Course References:
1. Bathe, K.J. 1996, Finite Element Procedures, Prentice Hall.
2. Chapelle, D., Le Tallec, P., Moireau, P. and Sorine, M. 2012, An energy-preserving
muscle tissue model: formulation and compatible discretizations, in International Journal
for Multiscale Computational Engineering, 10 (2), pp.189-211.
3. Ciarlet, P. G. 1988, Mathematical Elasticity, Vol. I : Three-Dimensional Elasticity,
Studies in Mathematics and its Applications, North Holland.
4. Le Tallec, P. 1994, Numerical methods for nonlinear three-dimensional elasticity, in
Handbook of Numerical Analysis, vol. 3, edited by P. G. Ciarlet and J.-L. Lions, Elsevier.
5. Fung, Y.C. 1993, Biomechanics: Mechanical Properties of Living Tissues, 2nd Edition..
Course Prerequisites: Continuum mechanics basic courses; introduction to scientific computing
Biomimetics & Animal Locomotion
E. de Langre and S. Michelin, Ecole Polytechnique
Keywords: biomimetics; bio-propulsion; animal locomotion; bio-inspiration; swimming and
flying.
Course Objectives: Show, in particular in the domain of propulsion, how bio-inspiration is
fruitful in the design of mechanical systems. Understanding of the mechanical principles at the
origin of bio-locomotion in fluids.
Course Content: fundamental concepts in biomimetics and bio-inspiration; case studies and
Individual projects; fundamental mechanisms and techniques used in bio-propulsion and how to
apply them to design synthetic swimmers.
Credits: 3.0
Detailed Content
Biomimetics:
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1. The fundamentals of biomimetics
o Historical perspective
o Methodology : function analysis
2. Biomimetics of materials
o … plenty of things to do, but how to chose
o Composite
o Self-healing
3. Biomimetics of surfaces
o Adhesion
o Self-cleaning
4. Biomimetics of structures
o Statics : architecture
o Dynamics : deployable structure
o Structural mechanics with soft material
5. Biomimetics of motion
o Microflyer and micro swimmer
o Land locomotion
6. Project : Explore the practical possibility of bio-inspiration on a specific problem
Animal Locomotion:
1. Introduction to locomotion in fluids
_ Some elements of fluid mechanics, the Navier{Stokes equations, definition/interpretation of
Re,...
_ Posing the swimming problem
2. Locomotion in Stokes flow
_ Reminder on Stokes flow dynamics (fundamental solutions, slender body theory,....)
_ Fundamentals of low-Re swimming : scallop theorem, symmetry-breaking, reciprocal
theorem...
_ Swimming strokes and strategies : prokaryotic vs. eukaryotic flagella motion, ciliates....
_ Classical examples : Taylor's swimming sheet, flagellar propulsion, energetic cost
_ Diffusive behavior of bacteria suspensions (run/tumble of E. Coli), instabilities
_ Outlooks on more advanced research topics (e.g. hydrodynamic interactions, suspension
dynamics,
locomotion in non-Newtonian fluids, finite Re corrections...)
3. Locomotion at high Re
_ Fish swimming/Insect flight/Bird flight : general properties
_ Locomotion in inviscid fluids { analogies with Stokes flows (symmetry breaking)
_ Classical example : Slender body theory and fish locomotion
_ Vortex shedding/dynamics and locomotion
_ Unsteady jet swimming : jellyfish
_ Perspectives : hydrodynamic interactions (fish schooling), fluid-elastic coupling (flexible
insect wings)...
Course References: Biomimetics: Biologically Inspired Technologies, by Yoseph Bar-Cohen,
2005; Mechanics of Swimming and Flying, by S. Childress, 1981.
Course Prerequisites: Basic courses in fluid & solid mechanics
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Cell Mechanics
J. Husson& A. Barakat, Ecole Polytechnique
Keywords: cell mechanics; mechanotransduction; membranes; cytoskeleton; viscoelastic
materials
Course Objectives: Biological basis for cell mechanics. Multiscale description, from molecule
to cell scale. Mechanical aspects of several cell functions: adhesion, migration, force generation,
and mechanotransduction. Role of mechanical forces in pathologies. Introduction to research
subjects in cell mechanics. Description of experimental techniques and models.
Course Content:
1) Structure and mechanics of the cell: molecular scale (molecular motors, adhesion
molecules), the cytoskeleton, the cell membrane, intracellular organelles.
2) Static and dynamic processes in cell mechanics: cell-substrate and cell-cell adhesion,
maintenance of cell shape, force generation, cell migration, mechanosensing.
3) Role of mechanical forces in disease.
4) Experimental methods: motility assays, flow chambers, micropipettes, atomic force
microscopy, optical and magnetic tweezers, others.
5) Models for cell mechanics: continuum elastic and viscoelastic models, multi-phasic
models, models based on tensegrity, polymer-based models of cytoskeletal networks.
Credits: 3.0
Detailed Content:
Biological basis for cellular mechanics - role of mechanics in cell function
- Molecular basis (motors, ratchets, etc.)
- Maintenance of cell shape
- Force generation
- Cell migration
- Mechanosensing
- Role of mechanical forces in disease
Experimental methods for measuring cellular mechanics
- Passive and active rheology
- Motility assays
- Adhesion assays
Static and dynamic cell processes
Structure and mechanics of cell membranes
Structure and mechanics of the cellular cytoskeleton
Structure and mechanics of the cell nucleus
Role of extracellular attachment to cells
Models of cell mechanics
- Continuum elastic or viscoelastic models
- Multiphasic models
- Models based on tensegrity - concept of stress focusing
- Polymer-based models of cytoskeletal networks
Mechanotransduction and cellular integration of mechanical cues
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Course References:
1) Molecular Biology of the Cell. 6th edition. Bruce Alberts, Alexander Johnson, Julian
Lewis, Martin Raff, Keith Roberts, and Peter Walter. New York: Garland Science; 2014.
2) Mechanics of the Cell. 2nd Edition. David Boal. Cambridge University Press; 2012.
3) Fung, Y.C. 1993, Biomechanics: Mechanical Properties of Living Tissues, 2nd Edition.
Course Prerequisites: Basic training in physics, mechanics, and mathematics
Control in Biological and Biomechanical Systems
J. Lerbet, D. Ichalal, & L. Nehaoua, UEVE
Keywords: control theory; biomechanical systems; ODEs; modeling; linear and non-linear
systems
Course Objectives: Introduce students to control theory and its applications to biological and
biomechanical systems.
Course Content:
Initiation to linear and non-linear control theory. Modeling and analysis of biological systems.
Introduction to biological system control.
Credits: 3.0
Course References:
1) Mathematical Biology: I - An introduction. James, D. Murray (2007), Springer.
2) Mathematical Biology: II - Spatial Models and Biomedical. James, D. Murray (2011),
Springer.
3) Mathematical control theory: deterministic finite dimensional systems. Edouardo Sontag
(1998), Springer.
4) Nonlinear systems. Hassan Khalil (2001), Prentice Hall.
Course Prerequisites: Linear Algebra. Theory of stability of ordinary differential
Mechanics of Motility of Living Organisms
JM Allain, Ecole Polytechnique
Keywords: cellular mechanics; cellular bioengineering
Course Objectives: Understanding the biophysical principles of cellular motility and modeling
the processes involved.
Course Content:
1) Biological aspects of cellular motility; 2) Physical modeling of the cell membrane; 3)
Adhesion processes in the cell; 4) Mechanics of the cytoskeleton; 5) Physical principles of
molecular cross-links and motors; 6) Introduction to other motilities.
Credits: 3.0
Course Reference:
Mechanics of Motor Proteins and the Cytoskeleton, J. Howard, Ed. Sinauer.
Course Prerequisites: Basis in continuum mechanics / Basis in statistical physics.
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Biomechanics of Anthropomorphic Systems
O. Bruneau, ENS Cachan
Keywords: anthropomorphic systems; multi-body dynamics; modeling; numerical methods
Course Objectives: Dynamics modeling of anthropomorphic systems.
Course Content:
Advanced methods for multi-body system dynamics flexible elements, resolution of joint torques
and inter-segmental forces based on all of the dynamic terms and external forces applied on the
system. Recursive Newton-Euler method, Lagrangian and Gibbs-Appell formalisms, connection
with the finite element method.
Credits: 3.0
Course Prerequisites: solid mechanics, kinematics, dynamics
Mechanics and Modeling of Human Cells and Tissues
E. Budyn, ENS Cachan
Keywords: human cells; human tissues; embryogenesis
Course Objectives: Familiarity with embryogenesis, different human tissues and their cells, and
examples of their mechanical modeling.
Course Content:
Processes involved in embryogenesis; Human tissues and cells; Mechanical modeling of human
tissues and cells.
Credits: 3.0
Course Prerequisites: none
Active force generation in muscle
L. Truskinovsky
1. Anatomy and physiology of skeletal muscles
2. Mechanical experiments
3. Thermodynamics and efficiency
4. Phenomenological chemo‐mechanical models
5. Power stroke and fast force recovery
6. Molecular motors and Brownian ratchets
7. Cooperative effects in motor assemblies
8. Stochastic models of muscle contractions
9. Smooth muscles and cytoskeleton
10. Contraction and cell motility
11. Active forces and continuum mechanics
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