continuum biomechanics of soft tissue: successes and challenges j. d. humphrey department of...
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Continuum Biomechanics of SoftTissue: Successes and Challenges
J. D. Humphrey
Department of Biomedical Engineering and M.E DeBakey Institute
Texas A&M University, College Station TX 77843-3120 U.S.A.
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Biomechanics - A Long History of Past Successes
Leonardo (1452-1519)
Galileo (1564-1642)
W. Harvey (1578-1657)
R. Descartes (1596-1650)
G. Borelli (1608-1679)
L. Euler (1707-1783)
… and many others
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Biomechanics comes of age ~ 1965
• Renaissance in continuum mechanics (1948-1965)
• Structural biology (1951, 1954)
• Digital computer (late 1950s - mid 1960s)
• Finite element methods (1956)
• Space race (1957-1969)
Note: L. Pauling (1995) attributes the birth of modern biology to the methods of theoretical physics / mathematics
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Constitutive Relations - The Key to Success
“we see that the greatest need lies in the direction of collecting data in multiaxial loading conditions and formulating a theory for the general rheological behavior of living tissues when stresses and strains vary with time in an arbitrary manner.”
Y.C. Fung (1973)
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An Example - Vascular Mechanics
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Early Stress Analyses (~1979)
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Importance of Residual Stress (~1986)
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Importance of Smooth Muscle (~1999)
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From Complexity Comes Simplicity
• Nonlinear Material Properties and Large Strain
• Anisotropy (circumferential muscle, axial collagen)
• Residual Stresses
• Smooth Muscle Activation
• Heterogeneity (functionally graded)
Question – what optimization rules govern the development and adaptation of vessels?
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Future Challenges & Promises
“There are however innumerable other local motions which on account of the minuteness of the moving particles cannot be detected, such as the motions of the particles in hot bodies, fermenting bodies, in putrescent bodies, growing bodies, in the organs of sensation and so forth. If any one shall have the good fortune to discover all these, I might almost say that he will have laid bare the whole nature of bodies so far as the mechanical causes of things are concerned.”
Sir I. Newton (1642-1727)
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ECM
SynthesisCytokines
MMP’s
TIMP’s
Cell
Traction Receptor
Binding
Constitutiv
e
Relations
Cell
Cycle
Cross-linking
GrowthFactors
Integrin
s
MechanicalLoads
Balance
Relations
Cell
Migration
Modeling in Mechanobiology
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Adventitia
Media
Intima
SmoothMuscle Cells
Fibroblasts
Collagen
EndothelialCells
ElasticLamina
LayeringSMC
Elastin
Collagen
EC
BL
RecruitedSMC
EC
BL
DEVELOPMENT
MATURITY
Figure G&R1
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Developmental Biomechanics
“Here and elsewhere we shall not obtain the best insights into things until we actually see them growing from the beginning” Aristotle (384-322 B.C.)
“without the aid of mechanicians, and others skilled in simulation and modelling, developmental biology will remain a prisoner of our inadequate and conflicting physical intuitions and methaphors.” A.K Harris (1994)
See: LA Taber (1995) Appl Mech Rev 48:487-545.
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Growth & Remodeling
Growth - an increase in mass that is achieved locally via an increase in the number (hyperplasia, migration) or size (hypertrophy) of cells and via a synthesis of extracellular matrix that exceeds removal.
Remodeling - a change in structure that is achieved by reorganizing existing constituents (cross-links) or by producing new constituents having a different organization.
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Regulators of Vascular G&R
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Conceptually - G&R
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Constrained mixture stress-response
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Stretches for a constrained mixture
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Kinetics of production and removal
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Solid-Fluid Coupling - Aneurysms
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Linearization – Stability in the Small
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Elastodynamics of Aneurysms
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Phase Plane – Time Plot
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HyperopiaArterio-venousM alformation
CerebralAneurysms
Parkinson'sDisease
TransmyocardialRevascularization
HepatocellularCarcinoma
Atrial Fibrillation
Coronary ArteryDisease
Benign ProstaticHyperplasia
JointLaxity
SkinLesions
M enorrhagia,Endometriosis
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Denaturation of Collagen
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Thermomechanical Testing of Collagenous Membranes
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Heat-induced Changes in Mechanical Properties
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In Summary, the Need…
“The success of reductionist and molecular approaches in modern medical science has led to an explosion of information, but progress in integrating information has lagged… Mathematical models provide a rational approach for integrating this ocean of data, as well as providing deep insight into biological processes.”
1998 BECON Report
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The Promise...
• Molecular & Cellular Biomechanics
• Developmental Biomechanics
• Growth & Remodeling• Injury & Rehab
• Functional Tissue Engineering
• Muscle Mechanics• Solid-Fluid
Interactions• Biothermomechanics
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The Bioengineer’s Bookshelf
• Alberts et al. (2002) Molecular Biology of the Cell. Garland Publishers.
• Fawcett DW (1986) A Textbook of Histology. W.B. Saunders.
• Medical Dictionary (e.g., Dorland’s)
• and a good “system-specific” text on physiology, e.g., Milnor (1990) Cardiovascular Physiology, Oxford.
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Acknowledgments
Funding by the NIH, NSF, Texas-ATP, and Whitaker Foundation
References
•Humphrey JD (2002) Cardiovascular Solid Mechanics: Cells, Tissues, and Organs, Springer-Verlag, NY
•Humphrey JD (2003) Continuum biomechanics of soft biological tissues. Proc R Soc Lond A 459: 3-
46•Humphrey JD (2003) Continuum thermomechanics and
the clinical treatment of disease and injury. Appl Mech Rev 56: 231-260.
•Biomechanics and Modeling in Mechanobiology http://link.springer.de