iMechanica - ES 241 - Comments

thanks Zhigang Suo

Muller Abera — Thu, 08 May 2008 10:33:24 -0400

share what we have

Updates on hydrogels and poroelasticity

Zhigang Suo — Tue, 25 Sep 2007 20:00:56 -0400

Jerry Qi has led a Theme of the Month on the mechanics of hydrogel.
I have posted notes on polyelectrolyte gels.
Several members of my group and I have extended the lecture notes into a paper, which has been submitted to a journal. The preprint of the paper has been posted on iMechanica, and has initiated a thread of good discussion.

Biphasic vs Poroelastic (on behalf of Dr. Van C. Mow)

Ed Guo — Mon, 14 May 2007 13:25:45 -0400

1) Highlights in the historical development of porous media theory:
toward a consistent macroscopic theory. de Boer, Reint, Applied
Mechanics Review, 49:201-262, 1996.

2) Mow VC, Kuei SC, Lai WM, Armstrong CG: Biphasic creep and stress
relaxation of articular cartilage in compression: Theory and Experiment,
J Biomech Engng, Trans ASME, 102:73-84, 1980.

3) Lai WM, Hou JS, Mow VC: A Triphasic theory for the swelling and
deformational behavior of articular cartilage. J Biomech Engng, Trans
ASME, 113:245-258, 1991.

4) Lai WM, Mow VC, Zhu WB: Constitutive modeling of articular cartilage
and biomolecular solutions. J Biomech Engng, Trans ASME,115:474-480, 1993.

5) Gu WY, Lai WM, Mow VC: A mixture theory for charged hydrated soft
tissues containing multi-electrolytes: passive transport and swelling
behavior, J Biomech Engng, Trans ASME, 120:169-180, 1998.

6) Mow VC, Ateshian GA, Lai WM, Gu WY: Effects of fixed charges on the
stress-relaxation behavior of hydrated soft tissues in confined
compression problem. In: Poroelasticity: Maurice Biot Memorial Issue,
edited by AHD Cheng, E Detournay, Y Abousleiman, Pergamon Press,
pp4945-4962, 1998.

7) /Porous Media, /edited by W Ehlers, J Bluhm, 2002, Springer, pp459.

Thanks for the change

Nanshu Lu — Fri, 04 May 2007 13:15:06 -0400

Thank you, Zhigang.

Mechanics: accumulative and infinitely extensible

Zhigang Suo — Fri, 04 May 2007 07:46:15 -0400

Dear Jay: Good to hear from you! Thank you so much for your kindness. I'm sorry that you had to return to Korea early in the semester. I've just given the last lecture of ES 241 Advanced Elasticity yesterday. Most other sit-in people stayed with me till the end.

This is a second-year graduate course in solid mechanics. The students have all taken ES 240 Solid Mechanics, so that I can assume that they have some adult experience of the subject. In addition, we have separate courses on fracture mechanics, plasticity, mechanical behavior of materials, and kinetics. They are all taught at advanced levels.

There is no other constraint on what I have to cover. From very beginning, I knew I would not be able to cover everything that I'd love to cover. Instead of trying to cover everything, I have tried to uncover a few things that are interesting to me and that seem to have lasting value. The notes are rather terse and contain typos and, I'm sure, errors and bad judgments. Often I would go over two pages of the notes in a 90-minute lecture. Many students made perceptive comments in class.

This was the first time that I taught the course. It was both an exhilarating and exhausting experience. I have tried to build ideas from scratch, and tried to trivialize them (i.e., making them transparent in hind sight). I was constantly delighted by the insights and ingenuities of great mechanicians of the past. It was humbling, too. I had to admit in class so many times that I could not have discovered this or that even if I were there!

But that is precisely the beauty of our subject: great depth and breadth. All we are hopeful is to learn great ideas of the past, make a few interesting applications, and add a few new ideas that will make a future professor say, "Ah, that is clever. I wouldn't be able to come up with this even if I were there."

Our subject is accumulative and, I believe, infinitely extensible.

Notes on instabilities

Zhigang Suo — Thu, 03 May 2007 22:10:10 -0400

Dear Henry: Thank you for the tip. I'll follow it up.

I've been working on these notes for the past few weeks. I'm not happy with them yet, but I've run out of time. Today is the last day of the class. I think that I've collected some useful material, and hope these notes will help others learn or teach the subject.

I'll improve the notes when I have time, hopefully before I teach the course next time, possibly two years from now!

Valuable resource

Jae-Hyun Kim — Thu, 03 May 2007 18:31:20 -0400

Dear Zhigang,

I'm very much enjoying your lecture notes. Especially, this note on complex variable methods summarizes key aspects of fracture and elasticity problems. I'm very happy to have a chance to read it. Thank you so much for your enthusiasm and effort.

Jay

Instabilities in Material Behaviors

Henry Tan — Thu, 03 May 2007 18:02:37 -0400

Dear Zhigang,

Two phenomena, catastrophic fracture and catastrophic interface debonding, that I studies may be useful as references for your lecture on instabilities.

Regards,
Henry.

Re: Biphasic and Poroelastic

Zhigang Suo — Thu, 12 Apr 2007 07:16:13 -0400

Dear Ed: Thank you so much for providing this list! For educational purpose, could you please recommend 2 or 3 papers for newcomers to get started to learn the issues and approaches in this area of research?

Biphasic and Poroelastic

Ed Guo — Wed, 11 Apr 2007 15:38:48 -0400

Dear Michelle:

The biphasic theory has been extended in cartilage mechanics to "triphasic" including electric charges.

1: Lux Lu X, Miller C, Chen FH, Edward Guo X, Mow VC.
The generalized triphasic correspondence principle for simultaneous
determination of the mechanical properties and proteoglycan content of articular
cartilage by indentation.
J Biomech. 2007 Jan 11; [Epub ahead of print]
PMID: 17222852 [PubMed - as supplied by publisher]

2: Wan LQ, Miller C, Guo XE, Mow VC.
Fixed electrical charges and mobile ions affect the measurable
mechano-electrochemical properties of charged-hydrated biological tissues: the
articular cartilage paradigm.
Mech Chem Biosyst. 2004 Mar;1(1):81-99.
PMID: 16783948 [PubMed - indexed for MEDLINE]

3: Likhitpanichkul M, Guo XE, Mow VC.
The effect of matrix tension-compression nonlinearity and fixed negative
charges on chondrocyte responses in cartilage.
Mol Cell Biomech. 2005 Dec;2(4):191-204.
PMID: 16705865 [PubMed - indexed for MEDLINE]

4: Huang CY, Stankiewicz A, Ateshian GA, Mow VC.
Anisotropy, inhomogeneity, and tension-compression nonlinearity of human
glenohumeral cartilage in finite deformation.
J Biomech. 2005 Apr;38(4):799-809.
PMID: 15713301 [PubMed - indexed for MEDLINE]

5: Gu WY, Sun DN, Lai WM, Mow VC.
Analysis of the dynamic permeation experiment with implication to cartilaginous
tissue engineering.
J Biomech Eng. 2004 Aug;126(4):485-91.
PMID: 15543866 [PubMed - indexed for MEDLINE]

6: Zheng YP, Shi J, Qin L, Patil SG, Mow VC, Zhou KY.
Dynamic depth-dependent osmotic swelling and solute diffusion in articular
cartilage monitored using real-time ultrasound.
Ultrasound Med Biol. 2004 Jun;30(6):841-9.
PMID: 15219963 [PubMed - indexed for MEDLINE]

7: Sun DD, Guo XE, Likhitpanichkul M, Lai WM, Mow VC.
The influence of the fixed negative charges on mechanical and electrical
behaviors of articular cartilage under unconfined compression.
J Biomech Eng. 2004 Feb;126(1):6-16.
PMID: 15171124 [PubMed - indexed for MEDLINE]

8: Lu XL, Sun DD, Guo XE, Chen FH, Lai WM, Mow VC.
Indentation determined mechanoelectrochemical properties and fixed charge
density of articular cartilage.
Ann Biomed Eng. 2004 Mar;32(3):370-9.
PMID: 15095811 [PubMed - indexed for MEDLINE]

9: Buckwalter JA, Martin JA, Olmstead M, Athanasiou KA, Rosenwasser MP, Mow VC.

Osteochondral repair of primate knee femoral and patellar articular surfaces:
implications for preventing post-traumatic osteoarthritis.
Iowa Orthop J. 2003;23:66-74.
PMID: 14575253 [PubMed - indexed for MEDLINE]

10: Cohen ZA, Mow VC, Henry JH, Levine WN, Ateshian GA.
Templates of the cartilage layers of the patellofemoral joint and their use in
the assessment of osteoarthritic cartilage damage.
Osteoarthritis Cartilage. 2003 Aug;11(8):569-79.
PMID: 12880579 [PubMed - indexed for MEDLINE]

11: Koff MF, Ugwonali OF, Strauch RJ, Rosenwasser MP, Ateshian GA, Mow VC.
Sequential wear patterns of the articular cartilage of the thumb
carpometacarpal joint in osteoarthritis.
J Hand Surg [Am]. 2003 Jul;28(4):597-604.
PMID: 12877846 [PubMed - indexed for MEDLINE]

12: Huang CY, Soltz MA, Kopacz M, Mow VC, Ateshian GA.
Experimental verification of the roles of intrinsic matrix viscoelasticity and
tension-compression nonlinearity in the biphasic response of cartilage.
J Biomech Eng. 2003 Feb;125(1):84-93.
PMID: 12661200 [PubMed - indexed for MEDLINE]

13: Cohen ZA, Henry JH, McCarthy DM, Mow VC, Ateshian GA.
Computer simulations of patellofemoral joint surgery. Patient-specific models
for tuberosity transfer.
Am J Sports Med. 2003 Jan-Feb;31(1):87-98.
PMID: 12531764 [PubMed - indexed for MEDLINE]

14: Mow VC, Guo XE.
Mechano-electrochemical properties of articular cartilage: their
inhomogeneities and anisotropies.
Annu Rev Biomed Eng. 2002;4:175-209. Epub 2002 Mar 22. Review.
PMID: 12117756 [PubMed - indexed for MEDLINE]

15: Lai WM, Sun DD, Ateshian GA, Guo XE, Mow VC.
Electrical signals for chondrocytes in cartilage.
Biorheology. 2002;39(1-2):39-45.
PMID: 12082265 [PubMed - indexed for MEDLINE]

16: Wang CC, Guo XE, Sun D, Mow VC, Ateshian GA, Hung CT.
The functional environment of chondrocytes within cartilage subjected to
compressive loading: a theoretical and experimental approach.
Biorheology. 2002;39(1-2):11-25.
PMID: 12082263 [PubMed - indexed for MEDLINE]

17: Huang CY, Mow VC, Ateshian GA.
The role of flow-independent viscoelasticity in the biphasic tensile and
compressive responses of articular cartilage.
J Biomech Eng. 2001 Oct;123(5):410-7.
PMID: 11601725 [PubMed - indexed for MEDLINE]

18: Cohen ZA, Roglic H, Grelsamer RP, Henry JH, Levine WN, Mow VC, Ateshian GA.

Patellofemoral stresses during open and closed kinetic chain exercises. An
analysis using computer simulation.
Am J Sports Med. 2001 Jul-Aug;29(4):480-7.
PMID: 11476390 [PubMed - indexed for MEDLINE]

19: Wang CC, Hung CT, Mow VC.
An analysis of the effects of depth-dependent aggregate modulus on articular
cartilage stress-relaxation behavior in compression.
J Biomech. 2001 Jan;34(1):75-84.
PMID: 11425083 [PubMed - indexed for MEDLINE]

20: Ahmad CS, Cohen ZA, Levine WN, Ateshian GA, Mow VC.
Biomechanical and topographic considerations for autologous osteochondral
grafting in the knee.
Am J Sports Med. 2001 Mar-Apr;29(2):201-6.
PMID: 11292046 [PubMed - indexed for MEDLINE]

21: Kelkar R, Wang VM, Flatow EL, Newton PM, Ateshian GA, Bigliani LU, Pawluk
RJ, Mow VC.
Glenohumeral mechanics: a study of articular geometry, contact, and kinematics.
J Shoulder Elbow Surg. 2001 Jan-Feb;10(1):73-84.
PMID: 11182740 [PubMed - indexed for MEDLINE]

22: Rivers PA, Rosenwasser MP, Mow VC, Pawluk RJ, Strauch RJ, Sugalski MT,
Ateshian GA.
Osteoarthritic changes in the biochemical composition of thumb carpometacarpal
joint cartilage and correlation with biomechanical properties.
J Hand Surg [Am]. 2000 Sep;25(5):889-98.
PMID: 11040304 [PubMed - indexed for MEDLINE]

23: Lai WM, Mow VC, Sun DD, Ateshian GA.
On the electric potentials inside a charged soft hydrated biological tissue:
streaming potential versus diffusion potential.
J Biomech Eng. 2000 Aug;122(4):336-46.
PMID: 11036556 [PubMed - indexed for MEDLINE]

24: Guilak F, Mow VC.
The mechanical environment of the chondrocyte: a biphasic finite element model
of cell-matrix interactions in articular cartilage.
J Biomech. 2000 Dec;33(12):1663-73.
PMID: 11006391 [PubMed - indexed for MEDLINE]

25: Roh MS, Strauch RJ, Xu L, Rosenwasser MP, Pawluk RJ, Mow VC.
Thenar insertion of abductor pollicis longus accessory tendons and thumb
carpometacarpal osteoarthritis.
J Hand Surg [Am]. 2000 May;25(3):458-63.
PMID: 10811749 [PubMed - indexed for MEDLINE]

26: Gu WY, Mao XG, Foster RJ, Weidenbaum M, Mow VC, Rawlins BA.
The anisotropic hydraulic permeability of human lumbar anulus fibrosus.
Influence of age, degeneration, direction, and water content.
Spine. 1999 Dec 1;24(23):2449-55.
PMID: 10626306 [PubMed - indexed for MEDLINE]

27: Hung CT, Henshaw DR, Wang CC, Mauck RL, Raia F, Palmer G, Chao PH, Mow VC,
Ratcliffe A, Valhmu WB.
Mitogen-activated protein kinase signaling in bovine articular chondrocytes in
response to fluid flow does not require calcium mobilization.
J Biomech. 2000 Jan;33(1):73-80.
PMID: 10609520 [PubMed - indexed for MEDLINE]

28: Gu WY, Mao XG, Rawlins BA, Iatridis JC, Foster RJ, Sun DN, Weidenbaum M,
Mow VC.
Streaming potential of human lumbar anulus fibrosus is anisotropic and affected
by disc degeneration.
J Biomech. 1999 Nov;32(11):1177-82.
PMID: 10541067 [PubMed - indexed for MEDLINE]

29: Iatridis JC, Kumar S, Foster RJ, Weidenbaum M, Mow VC.
Shear mechanical properties of human lumbar annulus fibrosus.
J Orthop Res. 1999 Sep;17(5):732-7.
PMID: 10569484 [PubMed - indexed for MEDLINE]

30: Mow VC, Wang CC.
Some bioengineering considerations for tissue engineering of articular
cartilage.
Clin Orthop Relat Res. 1999 Oct;(367 Suppl):S204-23.
PMID: 10546648 [PubMed - indexed for MEDLINE]

31: Donzelli PS, Spilker RL, Ateshian GA, Mow VC.
Contact analysis of biphasic transversely isotropic cartilage layers and
correlations with tissue failure.
J Biomech. 1999 Oct;32(10):1037-47.
PMID: 10476842 [PubMed - indexed for MEDLINE]

32: Cohen B, Lai WM, Mow VC.
A transversely isotropic biphasic model for unconfined compression of growth
plate and chondroepiphysis.
J Biomech Eng. 1998 Aug;120(4):491-6.
PMID: 10412420 [PubMed - indexed for MEDLINE]

33: Setton LA, Tohyama H, Mow VC.
Swelling and curling behaviors of articular cartilage.
J Biomech Eng. 1998 Jun;120(3):355-61.
PMID: 10412403 [PubMed - indexed for MEDLINE]

34: Mow VC, Wang CC, Hung CT.
The extracellular matrix, interstitial fluid and ions as a mechanical signal
transducer in articular cartilage.
Osteoarthritis Cartilage. 1999 Jan;7(1):41-58. Review.
PMID: 10367014 [PubMed - indexed for MEDLINE]

35: Setton LA, Elliott DM, Mow VC.
Altered mechanics of cartilage with osteoarthritis: human osteoarthritis and an
experimental model of joint degeneration.
Osteoarthritis Cartilage. 1999 Jan;7(1):2-14. Review.
PMID: 10367011 [PubMed - indexed for MEDLINE]

36: Lai WM, Gu WY, Mow VC.
On the conditional equivalence of chemical loading and mechanical loading on
articular cartilage.
J Biomech. 1998 Dec;31(12):1181-5.
PMID: 9882052 [PubMed - indexed for MEDLINE]

37: Cohen NP, Foster RJ, Mow VC.
Composition and dynamics of articular cartilage: structure, function, and
maintaining healthy state.
J Orthop Sports Phys Ther. 1998 Oct;28(4):203-15. Review.
PMID: 9785256 [PubMed - indexed for MEDLINE]

38: Iatridis JC, Setton LA, Foster RJ, Rawlins BA, Weidenbaum M, Mow VC.
Degeneration affects the anisotropic and nonlinear behaviors of human anulus
fibrosus in compression.
J Biomech. 1998 Jun;31(6):535-44.
PMID: 9755038 [PubMed - indexed for MEDLINE]

39: Bachrach NM, Mow VC, Guilak F.
Incompressibility of the solid matrix of articular cartilage under high
hydrostatic pressures.
J Biomech. 1998 May;31(5):445-51.
PMID: 9727342 [PubMed - indexed for MEDLINE]

40: Valhmu WB, Stazzone EJ, Bachrach NM, Saed-Nejad F, Fischer SG, Mow VC,
Ratcliffe A.
Load-controlled compression of articular cartilage induces a transient
stimulation of aggrecan gene expression.
Arch Biochem Biophys. 1998 May 1;353(1):29-36.
PMID: 9578597 [PubMed - indexed for MEDLINE]

41: Xu L, Strauch RJ, Ateshian GA, Pawluk RJ, Mow VC, Rosenwasser MP.
Topography of the osteoarthritic thumb carpometacarpal joint and its variations
with regard to gender, age, site, and osteoarthritic stage.
J Hand Surg [Am]. 1998 May;23(3):454-64.
PMID: 9620186 [PubMed - indexed for MEDLINE]

42: Froimson MI, Ratcliffe A, Gardner TR, Mow VC.
Differences in patellofemoral joint cartilage material properties and their
significance to the etiology of cartilage surface fibrillation.
Osteoarthritis Cartilage. 1997 Nov;5(6):377-86.
PMID: 9536286 [PubMed - indexed for MEDLINE]

43: Ateshian GA, Warden WH, Kim JJ, Grelsamer RP, Mow VC.
Finite deformation biphasic material properties of bovine articular cartilage
from confined compression experiments.
J Biomech. 1997 Nov-Dec;30(11-12):1157-64.
PMID: 9456384 [PubMed - indexed for MEDLINE]

44: Iatridis JC, Setton LA, Weidenbaum M, Mow VC.
The viscoelastic behavior of the non-degenerate human lumbar nucleus pulposus
in shear.
J Biomech. 1997 Oct;30(10):1005-13.
PMID: 9391867 [PubMed - indexed for MEDLINE]

45: Kwak SD, Colman WW, Ateshian GA, Grelsamer RP, Henry JH, Mow VC.
Anatomy of the human patellofemoral joint articular cartilage: surface
curvature analysis.
J Orthop Res. 1997 May;15(3):468-72.
PMID: 9246097 [PubMed - indexed for MEDLINE]

46: Newton PM, Mow VC, Gardner TR, Buckwalter JA, Albright JP.
Winner of the 1996 Cabaud Award. The effect of lifelong exercise on canine
articular cartilage.
Am J Sports Med. 1997 May-Jun;25(3):282-7.
PMID: 9167804 [PubMed - indexed for MEDLINE]

47: Iatridis JC, Setton LA, Weidenbaum M, Mow VC.
Alterations in the mechanical behavior of the human lumbar nucleus pulposus
with degeneration and aging.
J Orthop Res. 1997 Mar;15(2):318-22.
PMID: 9167638 [PubMed - indexed for MEDLINE]

48: Setton LA, Mow VC, Muller FJ, Pita JC, Howell DS.
Mechanical behavior and biochemical composition of canine knee cartilage
following periods of joint disuse and disuse with remobilization.
Osteoarthritis Cartilage. 1997 Jan;5(1):1-16.
PMID: 9010874 [PubMed - indexed for MEDLINE]

49: Gu WY, Lai WM, Mow VC.
A triphasic analysis of negative osmotic flows through charged hydrated soft
tissues.
J Biomech. 1997 Jan;30(1):71-8.
PMID: 8970927 [PubMed - indexed for MEDLINE]

50: Zhu W, Iatridis JC, Hlibczuk V, Ratcliffe A, Mow VC.
Determination of collagen-proteoglycan interactions in vitro.
J Biomech. 1996 Jun;29(6):773-83.
PMID: 9147974 [PubMed - indexed for MEDLINE]

51: Iatridis JC, Weidenbaum M, Setton LA, Mow VC.
Is the nucleus pulposus a solid or a fluid? Mechanical behaviors of the nucleus
pulposus of the human intervertebral disc.
Spine. 1996 May 15;21(10):1174-84. Review.
PMID: 8727192 [PubMed - indexed for MEDLINE]

52: Ebara S, Iatridis JC, Setton LA, Foster RJ, Mow VC, Weidenbaum M.
Tensile properties of nondegenerate human lumbar anulus fibrosus.
Spine. 1996 Feb 15;21(4):452-61.
PMID: 8658249 [PubMed - indexed for MEDLINE]

53: Acaroglu ER, Iatridis JC, Setton LA, Foster RJ, Mow VC, Weidenbaum M.
Degeneration and aging affect the tensile behavior of human lumbar anulus
fibrosus.
Spine. 1995 Dec 15;20(24):2690-701.
PMID: 8747247 [PubMed - indexed for MEDLINE]

54: Bachrach NM, Valhmu WB, Stazzone E, Ratcliffe A, Lai WM, Mow VC.
Changes in proteoglycan synthesis of chondrocytes in articular cartilage are
associated with the time-dependent changes in their mechanical environment.
J Biomech. 1995 Dec;28(12):1561-9.
PMID: 8666595 [PubMed - indexed for MEDLINE]

55: Setton LA, Mow VC, Howell DS.
Mechanical behavior of articular cartilage in shear is altered by transection
of the anterior cruciate ligament.
J Orthop Res. 1995 Jul;13(4):473-82.
PMID: 7674064 [PubMed - indexed for MEDLINE]

56: Ateshian GA, Ark JW, Rosenwasser MP, Pawluk RJ, Soslowsky LJ, Mow VC.
Contact areas in the thumb carpometacarpal joint.
J Orthop Res. 1995 May;13(3):450-8.
PMID: 7602407 [PubMed - indexed for MEDLINE]

57: Guilak F, Ratcliffe A, Mow VC.
Chondrocyte deformation and local tissue strain in articular cartilage: a
confocal microscopy study.
J Orthop Res. 1995 May;13(3):410-21.
PMID: 7602402 [PubMed - indexed for MEDLINE]

58: Grumbles RM, Howell DS, Howard GA, Roos BA, Setton LA, Mow VC, Ratcliffe A,
Muller FJ, Altman RD.
Cartilage metalloproteases in disuse atrophy.
J Rheumatol Suppl. 1995 Feb;43:146-8.
PMID: 7538586 [PubMed - indexed for MEDLINE]

59: Ateshian GA, Lai WM, Zhu WB, Mow VC.
An asymptotic solution for the contact of two biphasic cartilage layers.
J Biomech. 1994 Nov;27(11):1347-60.
PMID: 7798285 [PubMed - indexed for MEDLINE]

60: Zhu W, Chern KY, Mow VC.
Anisotropic viscoelastic shear properties of bovine meniscus.
Clin Orthop Relat Res. 1994 Sep;(306):34-45.
PMID: 8070209 [PubMed - indexed for MEDLINE]

61: Buckwalter JA, Mow VC, Ratcliffe A.
Restoration of Injured or Degenerated Articular Cartilage.
J Am Acad Orthop Surg. 1994 Jul;2(4):192-201.
PMID: 10709009 [PubMed - as supplied by publisher]

62: Muller FJ, Setton LA, Manicourt DH, Mow VC, Howell DS, Pita JC.
Centrifugal and biochemical comparison of proteoglycan aggregates from
articular cartilage in experimental joint disuse and joint instability.
J Orthop Res. 1994 Jul;12(4):498-508.
PMID: 8064480 [PubMed - indexed for MEDLINE]

63: Guilak F, Ratcliffe A, Lane N, Rosenwasser MP, Mow VC.
Mechanical and biochemical changes in the superficial zone of articular
cartilage in canine experimental osteoarthritis.
J Orthop Res. 1994 Jul;12(4):474-84.
PMID: 8064478 [PubMed - indexed for MEDLINE]

64: Setton LA, Mow VC, Muller FJ, Pita JC, Howell DS.
Mechanical properties of canine articular cartilage are significantly altered
following transection of the anterior cruciate ligament.
J Orthop Res. 1994 Jul;12(4):451-63.
PMID: 8064477 [PubMed - indexed for MEDLINE]

65: Skaggs DL, Weidenbaum M, Iatridis JC, Ratcliffe A, Mow VC.
Regional variation in tensile properties and biochemical composition of the
human lumbar anulus fibrosus.
Spine. 1994 Jun 15;19(12):1310-9.
PMID: 8066509 [PubMed - indexed for MEDLINE]

66: Guilak F, Meyer BC, Ratcliffe A, Mow VC.
The effects of matrix compression on proteoglycan metabolism in articular
cartilage explants.
Osteoarthritis Cartilage. 1994 Jun;2(2):91-101.
PMID: 11548233 [PubMed - indexed for MEDLINE]

67: Zhu W, Mow VC, Rosenberg LC, Tang LH.
Determination of kinetic changes of aggrecan-hyaluronan interactions in
solution from its rheological properties.
J Biomech. 1994 May;27(5):571-9.
PMID: 8027091 [PubMed - indexed for MEDLINE]

68: Best BA, Guilak F, Setton LA, Zhu W, Saed-Nejad F, Ratcliffe A, Weidenbaum
M, Mow VC.
Compressive mechanical properties of the human anulus fibrosus and their
relationship to biochemical composition.
Spine. 1994 Jan 15;19(2):212-21.
PMID: 8153833 [PubMed - indexed for MEDLINE]

69: Ateshian GA, Kwak SD, Soslowsky LJ, Mow VC.
A stereophotogrammetric method for determining in situ contact areas in
diarthrodial joints, and a comparison with other methods.
J Biomech. 1994 Jan;27(1):111-24.
PMID: 7508940 [PubMed - indexed for MEDLINE]

70: Lai WM, Mow VC, Zhu W.
Constitutive modeling of articular cartilage and biomacromolecular solutions.
J Biomech Eng. 1993 Nov;115(4B):474-80. Review. No abstract available.
PMID: 8302028 [PubMed - indexed for MEDLINE]

71: Mow VC, Ateshian GA, Spilker RL.
Biomechanics of diarthrodial joints: a review of twenty years of progress.
J Biomech Eng. 1993 Nov;115(4B):460-7. Review.
PMID: 8302026 [PubMed - indexed for MEDLINE]

72: Zhu W, Mow VC, Koob TJ, Eyre DR.
Viscoelastic shear properties of articular cartilage and the effects of
glycosidase treatments.
J Orthop Res. 1993 Nov;11(6):771-81.
PMID: 8283321 [PubMed - indexed for MEDLINE]

73: Gu WY, Lai WM, Mow VC.
Transport of fluid and ions through a porous-permeable charged-hydrated tissue,
and streaming potential data on normal bovine articular cartilage.
J Biomech. 1993 Jun;26(6):709-23.
PMID: 8514815 [PubMed - indexed for MEDLINE]

74: Setton LA, Zhu W, Mow VC.
The biphasic poroviscoelastic behavior of articular cartilage: role of the
surface zone in governing the compressive behavior.
J Biomech. 1993 Apr-May;26(4-5):581-92.
PMID: 8478359 [PubMed - indexed for MEDLINE]

75: Ratcliffe A, Azzo W, Saed-Nejad F, Lane N, Rosenwasser MP, Mow VC.
In vivo effects of naproxen on composition, proteoglycan metabolism, and matrix
metalloproteinase activities in canine articular cartilage.
J Orthop Res. 1993 Mar;11(2):163-71.
PMID: 8483029 [PubMed - indexed for MEDLINE]

76: Setton LA, Mow VC, Muller FJ, Pita JC, Howell DS.
Altered structure-function relationships for articular cartilage in human
osteoarthritis and an experimental canine model.
Agents Actions Suppl. 1993;39:27-48. Review.
PMID: 8456641 [PubMed - indexed for MEDLINE]

77: Ratcliffe A, Rosenwasser MP, Mahmud F, Glazer PA, Saed-Nejad F, Lane N, Mow
VC.
The in vivo effects of naproxen on canine experimental osteoarthritic articular
cartilage: composition, metalloproteinase activities and metabolism.
Agents Actions Suppl. 1993;39:207-11.
PMID: 8456630 [PubMed - indexed for MEDLINE]

78: Soslowsky LJ, Flatow EL, Bigliani LU, Mow VC.
Articular geometry of the glenohumeral joint.
Clin Orthop Relat Res. 1992 Dec;(285):181-90.
PMID: 1446435 [PubMed - indexed for MEDLINE]

79: Spilker RL, Donzelli PS, Mow VC.
A transversely isotropic biphasic finite element model of the meniscus.
J Biomech. 1992 Sep;25(9):1027-45.
PMID: 1517263 [PubMed - indexed for MEDLINE]

80: Weidenbaum M, Foster RJ, Best BA, Saed-Nejad F, Nickoloff E, Newhouse J,
Ratcliffe A, Mow VC.
Correlating magnetic resonance imaging with the biochemical content of the
normal human intervertebral disc.
J Orthop Res. 1992 Jul;10(4):552-61.
PMID: 1613629 [PubMed - indexed for MEDLINE]

81: Soslowsky LJ, Flatow EL, Bigliani LU, Pawluk RJ, Ateshian GA, Mow VC.
Quantitation of in situ contact areas at the glenohumeral joint: a
biomechanical study.
J Orthop Res. 1992 Jul;10(4):524-34.
PMID: 1613626 [PubMed - indexed for MEDLINE]

82: Ateshian GA, Rosenwasser MP, Mow VC.
Curvature characteristics and congruence of the thumb carpometacarpal joint:
differences between female and male joints.
J Biomech. 1992 Jun;25(6):591-607.
PMID: 1517255 [PubMed - indexed for MEDLINE]

83: Spilker RL, Suh JK, Mow VC.
A finite element analysis of the indentation stress-relaxation response of
linear biphasic articular cartilage.
J Biomech Eng. 1992 May;114(2):191-201.
PMID: 1602762 [PubMed - indexed for MEDLINE]

84: Hou JS, Mow VC, Lai WM, Holmes MH.
An analysis of the squeeze-film lubrication mechanism for articular cartilage.
J Biomech. 1992 Mar;25(3):247-59.
PMID: 1564060 [PubMed - indexed for MEDLINE]

85: Mow VC, Ratcliffe A, Poole AR.
Cartilage and diarthrodial joints as paradigms for hierarchical materials and
structures.
Biomaterials. 1992;13(2):67-97. Review.
PMID: 1550898 [PubMed - indexed for MEDLINE]

86: Lai WM, Hou JS, Mow VC.
A triphasic theory for the swelling and deformation behaviors of articular
cartilage.
J Biomech Eng. 1991 Aug;113(3):245-58.
PMID: 1921350 [PubMed - indexed for MEDLINE]

87: Athanasiou KA, Rosenwasser MP, Buckwalter JA, Malinin TI, Mow VC.
Interspecies comparisons of in situ intrinsic mechanical properties of distal
femoral cartilage.
J Orthop Res. 1991 May;9(3):330-40.
PMID: 2010837 [PubMed - indexed for MEDLINE]

88: Mow VC, Ratcliffe A, Rosenwasser MP, Buckwalter JA.
Experimental studies on repair of large osteochondral defects at a high weight
bearing area of the knee joint: a tissue engineering study.
J Biomech Eng. 1991 May;113(2):198-207.
PMID: 1875694 [PubMed - indexed for MEDLINE]

89: Ateshian GA, Soslowsky LJ, Mow VC.
Quantitation of articular surface topography and cartilage thickness in knee
joints using stereophotogrammetry.
J Biomech. 1991;24(8):761-76.
PMID: 1918099 [PubMed - indexed for MEDLINE]

90: Zhu W, Lai WM, Mow VC.
The density and strength of proteoglycan-proteoglycan interaction sites in
concentrated solutions.
J Biomech. 1991;24(11):1007-18.
PMID: 1761579 [PubMed - indexed for MEDLINE]

91: Spilker RL, Suh JK, Mow VC.
Effects of friction on the unconfined compressive response of articular
cartilage: a finite element analysis.
J Biomech Eng. 1990 May;112(2):138-46.
PMID: 2345443 [PubMed - indexed for MEDLINE]

92: Schmidt MB, Mow VC, Chun LE, Eyre DR.
Effects of proteoglycan extraction on the tensile behavior of articular
cartilage.
J Orthop Res. 1990 May;8(3):353-63.
PMID: 2324854 [PubMed - indexed for MEDLINE]

93: Fithian DC, Kelly MA, Mow VC.
Material properties and structure-function relationships in the menisci.
Clin Orthop Relat Res. 1990 Mar;(252):19-31. Review.
PMID: 2406069 [PubMed - indexed for MEDLINE]

94: Kwan MK, Lai WM, Mow VC.
A finite deformation theory for cartilage and other soft hydrated connective
tissues--I. Equilibrium results.
J Biomech. 1990;23(2):145-55.
PMID: 2312519 [PubMed - indexed for MEDLINE]

95: Holmes MH, Mow VC.
The nonlinear characteristics of soft gels and hydrated connective tissues in
ultrafiltration.
J Biomech. 1990;23(11):1145-56.
PMID: 2277049 [PubMed - indexed for MEDLINE]

96: Mow VC, Zhu W, Lai WM, Hardingham TE, Hughes C, Muir H.
The influence of link protein stabilization on the viscometric properties of
proteoglycan aggregate solutions.
Biochim Biophys Acta. 1989 Aug 18;992(2):201-8.
PMID: 2758065 [PubMed - indexed for MEDLINE]

97: Hou JS, Holmes MH, Lai WM, Mow VC.
Boundary conditions at the cartilage-synovial fluid interface for joint
lubrication and theoretical verifications.
J Biomech Eng. 1989 Feb;111(1):78-87.
PMID: 2747237 [PubMed - indexed for MEDLINE]

98: Muller FJ, Pita JC, Manicourt DH, Malinin TI, Schoonbeck JM, Mow VC.
Centrifugal characterization of proteoglycans from various depth layers and
weight-bearing areas of normal and abnormal human articular cartilage.
J Orthop Res. 1989;7(3):326-34.
PMID: 2703925 [PubMed - indexed for MEDLINE]

99: Proctor CS, Schmidt MB, Whipple RR, Kelly MA, Mow VC.
Material properties of the normal medial bovine meniscus.
J Orthop Res. 1989;7(6):771-82. Review.
PMID: 2677284 [PubMed - indexed for MEDLINE]

100: Mow VC, Gibbs MC, Lai WM, Zhu WB, Athanasiou KA.
Biphasic indentation of articular cartilage--II. A numerical algorithm and an
experimental study.
J Biomech. 1989;22(8-9):853-61.
PMID: 2613721 [PubMed - indexed for MEDLINE]

101: Arnoczky SP, McDevitt CA, Schmidt MB, Mow VC, Warren RF.
The effect of cryopreservation on canine menisci: a biochemical, morphologic,
and biomechanical evaluation.
J Orthop Res. 1988;6(1):1-12.
PMID: 3334728 [PubMed - indexed for MEDLINE]

102: Hardingham TE, Muir H, Kwan MK, Lai WM, Mow VC.
Viscoelastic properties of proteoglycan solutions with varying proportions
present as aggregates.
J Orthop Res. 1987;5(1):36-46.
PMID: 3819910 [PubMed - indexed for MEDLINE]

103: Mak AF, Lai WM, Mow VC.
Biphasic indentation of articular cartilage--I. Theoretical analysis.
J Biomech. 1987;20(7):703-14.
PMID: 3654668 [PubMed - indexed for MEDLINE]

104: Akizuki S, Mow VC, Muller F, Pita JC, Howell DS.
Tensile properties of human knee joint cartilage. II. Correlations between
weight bearing and tissue pathology and the kinetics of swelling.
J Orthop Res. 1987;5(2):173-86.
PMID: 3572588 [PubMed - indexed for MEDLINE]

105: Akizuki S, Mow VC, Muller F, Pita JC, Howell DS, Manicourt DH.
Tensile properties of human knee joint cartilage: I. Influence of ionic
conditions, weight bearing, and fibrillation on the tensile modulus.
J Orthop Res. 1986;4(4):379-92.
PMID: 3783297 [PubMed - indexed for MEDLINE]

106: Holmes MH, Lai WM, Mow VC.
Singular perturbation analysis of the nonlinear, flow-dependent compressive
stress relaxation behavior of articular cartilage.
J Biomech Eng. 1985 Aug;107(3):206-18.
PMID: 4046561 [PubMed - indexed for MEDLINE]

107: Armstrong CG, Lai WM, Mow VC.
An analysis of the unconfined compression of articular cartilage.
J Biomech Eng. 1984 May;106(2):165-73.
PMID: 6738022 [PubMed - indexed for MEDLINE]

108: Myers ER, Lai WM, Mow VC.
A continuum theory and an experiment for the ion-induced swelling behavior of
articular cartilage.
J Biomech Eng. 1984 May;106(2):151-8.
PMID: 6738020 [PubMed - indexed for MEDLINE]

109: Mow VC, Mak AF, Lai WM, Rosenberg LC, Tang LH.
Viscoelastic properties of proteoglycan subunits and aggregates in varying
solution concentrations.
J Biomech. 1984;17(5):325-38.
PMID: 6736068 [PubMed - indexed for MEDLINE]

110: Kwan MK, Lai WM, Mow VC.
Fundamentals of fluid transport through cartilage in compression.
Ann Biomed Eng. 1984;12(6):537-58.
PMID: 6534222 [PubMed - indexed for MEDLINE]

111: Mow VC, Holmes MH, Lai WM.
Fluid transport and mechanical properties of articular cartilage: a review.
J Biomech. 1984;17(5):377-94. Review.
PMID: 6376512 [PubMed - indexed for MEDLINE]

112: Armstrong CG, Mow VC.
The mechanical properties of articular cartilage.
Bull Hosp Jt Dis Orthop Inst. 1983 Fall;43(2):109-17.
PMID: 6317094 [PubMed - indexed for MEDLINE]

113: Armstrong CG, Mow VC.
Variations in the intrinsic mechanical properties of human articular cartilage
with age, degeneration, and water content.
J Bone Joint Surg Am. 1982 Jan;64(1):88-94.
PMID: 7054208 [PubMed - indexed for MEDLINE]

114: Grodzinsky AJ, Roth V, Myers E, Grossman WD, Mow VC.
The significance of electromechanical and osmotic forces in the nonequilibrium
swelling behavior of articular cartilage in tension.
J Biomech Eng. 1981 Nov;103(4):221-31.
PMID: 7311487 [PubMed - indexed for MEDLINE]

115: Lai WM, Mow VC, Roth V.
Effects of nonlinear strain-dependent permeability and rate of compression on
the stress behavior of articular cartilage.
J Biomech Eng. 1981 May;103(2):61-6.
PMID: 7278183 [PubMed - indexed for MEDLINE]

116: Roth V, Mow VC.
The intrinsic tensile behavior of the matrix of bovine articular cartilage and
its variation with age.
J Bone Joint Surg Am. 1980 Oct;62(7):1102-17.
PMID: 7430196 [PubMed - indexed for MEDLINE]

117: Mow VC, Kuei SC, Lai WM, Armstrong CG.
Biphasic creep and stress relaxation of articular cartilage in compression?
Theory and experiments.
J Biomech Eng. 1980 Feb;102(1):73-84. No abstract available.
PMID: 7382457 [PubMed - indexed for MEDLINE]

118: Lai WM, Mow VC.
Drag-induced compression of articular cartilage during a permeation experiment.
Biorheology. 1980;17(1-2):111-23. No abstract available.
PMID: 7407341 [PubMed - indexed for MEDLINE]

119: Mow VC.
Biphasic rheological properties of cartilage [proceedings]
Bull Hosp Joint Dis. 1977 Oct;38(2):121-4. No abstract available.
PMID: 614864 [PubMed - indexed for MEDLINE]

120: Mow VC, Mansour JM.
The nonlinear interaction between cartilage deformation and interstitial fluid
flow.
J Biomech. 1977;10(1):31-9. No abstract available.
PMID: 845175 [PubMed - indexed for MEDLINE]

121: Mansour JM, Mow VC.
The permeability of articular cartilage under compressive strain and at high
pressures.
J Bone Joint Surg Am. 1976 Jun;58(4):509-16.
PMID: 1270471 [PubMed - indexed for MEDLINE]

122: Torzilli PA, Mow VC.
On the fundamental fluid transport mechanisms through normal and pathological
articular cartilage during function - II. The analysis, solution and
conclusions.
J Biomech. 1976;9(9):587-606. No abstract available.
PMID: 965425 [PubMed - indexed for MEDLINE]

123: Torzilli PA, Mow VC.
On the fundamental fluid transport mechanisms through normal and pathological
articular cartilage during function--I. The formulation.
J Biomech. 1976;9(8):541-52. No abstract available.
PMID: 956198 [PubMed - indexed for MEDLINE]

124: Redler I, Mow VC, Zimny ML, Mansell J.
The ultrastructure and biomechanical significance of the tidemark of articular
cartilage.
Clin Orthop Relat Res. 1975 Oct;(112):357-62.
PMID: 1192647 [PubMed - indexed for MEDLINE]

125: Mow VC, Lai WM, Eisenfeld J, Redler I.
Some surface characteristics of articular cartilage. II. On the stability of
articular surface and a possible biomechanical factor in etiology of
chondrodegeneration.
J Biomech. 1974 Sep;7(5):457-68. No abstract available.
PMID: 4443359 [PubMed - indexed for MEDLINE]

126: Mow VC, Lai WM.
Some surface characteristics of articular cartilage. I. A scanning electron
microscopy study and a theoretical model for the dynamic interaction of synovial
fluid and articular cartilage.
J Biomech. 1974 Sep;7(5):449-56. No abstract available.
PMID: 4443358 [PubMed - indexed for MEDLINE]

127: Katz JL, Mow VC.
Mechanical and structural criteria for orthopaedic implants.
Biomater Med Devices Artif Organs. 1973;1(4):575-634. Review. No abstract
available.
PMID: 4600332 [PubMed - indexed for MEDLINE]

Biphasic and poroelastic

MichelleLOyen — Wed, 11 Apr 2007 10:11:04 -0400

Dear Ed,

last I had heard, there were still some open discussions about the Mow et al. "biphasic" approach, which was more or less independently developed within the biomechanics community, and to what extent and in what conditions it was the same as poroelasticity. Is there a definitive word on this?

Regardless, an even more active poroelasticity and biomechanics crowd in recent years has been within the bone community; for anyone new to the subject I recommend the review

Cowin SC, Bone poroelasticity, J. Biomech. 32, 217-38 (1999).

The review covers basic poroelastic equations as well as the application of the model to bone at two different length-scales of porosity. I know of no similarly comprehensive review for cartilage or spinal disc, but if anyone knows of one I'd love to see a complimentary reference posted here.

Poroelastic or mixture theory in biomechanics

Ed Guo — Wed, 04 Apr 2007 09:47:32 -0400

Dear Zhigang:

It would be interesting for folks in applied mechanics to check PubMed (http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?CMD=search&DB=pubmed) and type in mow vc cartilage. You will find poroelastic or mixture theory in cartilage biomechanics since early 1980s....

Best reagrds,

diffusion through pores

MichelleLOyen — Mon, 12 Mar 2007 07:46:18 -0400

Another interesting topic in which diffusion through pores is really important is in biology. Mostly within the biophysics community, the transport of small molecules through pores in cell membranes and in filtration applications such as the kidney. There is a nice treatment of this subject in the text "Intermediate Physics for Medicine and Biology" by Russell Hobbie. It will be interesting to compare this approach with the others.

Biot vs. Gibbs: Who invented poroelasticity?

Zhigang Suo — Sat, 10 Mar 2007 19:39:38 -0500

Dear Guru:

Thank you so much for your note. Following it, I looked at Gibbs's collected papers on my shelf, and found the relevant sections:

Page 184. The conditions of internal and external equilibrium for solids in contact with fields with regard to all possible states of strain of the solids
Page 201. Fundamental equations for solids
Page 215 Concerning solids which absorb fluids

I'm astonished that my notes on poroelasticity has followed his approach exactly, including the exclusive use of deformation gradient and nominal stress. Gibbs's formulation was in terms of finite deformation.

Although I have looked at his long paper many times, I don't believe that I had read these particular sections before. His approach must have permeated in our blood no matter we read him or not.

More interestingly, Biot's 1941 paper, which is widely regarded as the founding paper of the theory of poroelasticity, contained no reference to Gibbs's work. Of course, Biot went beyond equilibrium, and added a kinetic law, Darcy's law, to the theory. Still, many people have long regarded that most intriguing part of Biot's formulation is the reciprocal relation. The latter was clearly identified in Gibbs's paper.

Incidentally, Biot's 1941 paper has also been identified, by Shaofan Li, as one of the most cited papers in our field. If a great mechanician and a Timoshenko Medalist like Biot inadvertently rediscovered a result of others in his most influential work, we should all be happy if we can do anything original at all. We should all remind ourselves of this perspective in moments of despair.

Thank you again, Guru, for the detective work of these remarkable papers. It has been fun.

P.S. For those who have not read Gibbs, as I remarked elsewhere, an excellent place to start is his two short papers. Guru has also pointed out that you can read and download Gibbs's collected works for free at Google Book.

Diffuse interface diffusion equations with deformation

Mogadalai Gururajan — Sat, 10 Mar 2007 14:50:57 -0500

Dear Prof. Suo:

Thank you very much for the very interesting notes. Here are some more papers discussing diffusion in solid solutions.

A paper by Morton E Gurtin, which, using his microforce balance concept, extends the Cahn-Hilliard equation (which is a generalised diffusion equation ) to allow for deformation. Such a model is ideal for the numerical study of evolution of microstructures in the presence of elastic stresses.
Such a numerical study of diffusion in solid solutions in the presence of elastic stresses and defects (dislocations, voids, cracks etc) has been pioneered by Khachaturyan and his co-workers.

And, on a historical note, the problem of absorption of fluid in a solid (and the resulting equilibration) is discussed by Gibbs in his On the equilibrium of heterogeneous substances; however, since Gibbs was not aware of solid-state diffusion, diffusion in crystals is not discussed. In fact, the story of the acceptance of solid state diffusion by metallurgists is an interesting one -- I will try and do a post about it in my blog sometime!