Continuum Biomechanics of Soft Tissue: Successes and Challenges

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Continuum Biomechanics of SoftTissue Successes
and Challenges
J. D. Humphrey Department of Biomedical
Engineering and M.E DeBakey Institute Texas AM
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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Modeling in Mechanobiology
Cytokines
Cross-linking
Constitutive
Relations
Cell
Migration
Integrins
Mechanical
Loads
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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 48487-545.
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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 GR
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Conceptually - GR
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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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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 Bioengineers 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., Dorlands)
• 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