Skip to main content

Advertisement

SpringerLink
Log in

Flow-dependent concentration polarization and the endothelial glycocalyx layer: multi-scale aspects of arterial mass transport and their implications for atherosclerosis

  • Original Paper
  • Published:
Biomechanics and Modeling in Mechanobiology Aims and scope Submit manuscript

Abstract

Atherosclerosis is the underlying cause of most heart attacks and strokes. It is thereby the leading cause of death in the Western world, and it places a significant financial burden on health care systems. There is evidence that complex, multi-scale arterial mass transport processes play a key role in the development of atherosclerosis. Such processes can be controlled both by blood flow patterns and by properties of the arterial wall. This short review focuses on one vascular-scale, flow-regulated arterial mass transport process, namely concentration polarization of low density lipoprotein at the luminal surface of the arterial endothelium, and on one cellular-scale, structural determinant of arterial wall mass transport, namely the endothelial glycocalyx layer. Both have attracted significant attention in recent years. In addition to reviewing and appraising relevant literature, we propose various directions for future work.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  • Adams CMW (1973) Tissue changes and lipid entry in developing atheroma. In: Porter R, Knight J (eds) Ciba foundation symposium 12-atherogenesis: initiating factors, Novartis Foundation Symposia. Wiley, Chichester

  • Adamson RH, Clough G (1992) Plasma proteins modify the endothelial cell glycocalyx of frog mesenteric microvessels. J Physiol 445:473

    Google Scholar 

  • Adamson RH, Lenz JF, Zhang X, Adamson GN, Weinbaum S, Curry FE (2004) Oncotic pressures opposing filtration across non-fenestrated rat microvessels. J Physiol 557:889

    Google Scholar 

  • Adamson RH, Sarai RK, Altangerel A, Clark JF, Weinbaum S, Curry FE (2013) Microvascular permeability to water is independent of shear stress, but dependent on flow direction. Am J Physiol Heart Circ Physiol 304:H1077

    Google Scholar 

  • Albelda SM, Sampson PM, Haselton FR, McNiff JM, Mueller SN, Williams SK, Fishman AP, Levine EM (1988) Permeability characteristics of cultured endothelial cell monolayers. J Appl Physiol 64:308

    Google Scholar 

  • Annecke T, Fischer J, Hartmann H, Tschoep J, Rehm M, Conzen P, Sommerhoff CP, Becker BF (2011) Shedding of the coronary endothelial glycocalyx: effects of hypoxia/reoxygenation vs ischaemia/reperfusion. Brit J Anaesth 107:679

    Google Scholar 

  • Atmeh RF (1990) Isolation and identification of HDL particles of low molecular weight. J Lipid Res 31:1771

    Google Scholar 

  • Berliner JA, Navab M, Fogelman AM, Frank JS, Demer LL, Edwards PA, Watson AD, Lusis AJ (1995) Atherosclerosis: basic mechanisms. Oxidation, inflammation, and genetics. Circulation 91:2488

    Google Scholar 

  • Bratzler RL, Chisolm GM, Colton CK, Smith KA, Lees RS (1977) The distribution of labeled low-density lipoproteins across the rabbit thoracic aorta in vivo. Atherosclerosis 28:289

    Google Scholar 

  • Caro CG, Fitz-Gerald JM, Schroter RC (1969) Arterial wall shear and distribution of early atheroma in man. Nature 223:1159

    Google Scholar 

  • Caro CG, Fitz-Gerald JM, Schroter RC (1971) Atheroma and arterial wall shear. Observation, correlation and proposal of a shear dependent mass transfer mechanism for atherogenesis. Proc R Soc Lond B Biol Sci 177:109

    Google Scholar 

  • Chang YS, Munn LL, Hillsley MV, Dull RO, Yuan J, Lakshminarayanan S, Gardner TW, Jain RK, Tarbell JM (2000) Effect of vascular endothelial growth factor on cultured endothelial cell monolayer transport properties. Microvasc Res 59:265

    Google Scholar 

  • Chen B, Fu BM (2004) An electrodiffusion-filtration model for effects of endothelial surface glycocalyx on microvessel permeability to macromolecules. J Biomech Eng 126:614

    Google Scholar 

  • Chen X, Jaron D, Barbee KA, Buerk DG (2006) The influence of radial RBC distribution, blood velocity profiles, and glycocalyx on coupled NO/O\(_2\) transport. J Appl Physiol 100:482

    Google Scholar 

  • Cheng C, de Crom R, van Haperen R, Helderman F, Mousavi GB, van Damme LCA, Kirschbaum SW, Slager CJ, van der Steen AFW, Krams R (2004) The role of shear stress in atherosclerosis: action through gene expression and inflammation. Cell Biochem Biophys 41:279

    Google Scholar 

  • Choi HW, Ferrara KW, Barakat AI (2007) Modulation of ATP/ADP concentration at the endothelial surface by shear stress: effect of flow recirculation. Ann Biomed Eng 35:505

    Google Scholar 

  • Choi HW, Barakat AI (2009) Modulation of ATP/ADP concentration at the endothelial cell surface by flow: effect of cell topography. Ann Biomed Eng 37:2459

    Google Scholar 

  • Curry FE, Adamson RH (2012) Endothelial glycocalyx: permeability barrier and mechanosensor. Ann Biomed Eng 40:828

    Google Scholar 

  • Curry FE, Michel CC (1980) A fiber matrix model of capillary permeability. Microvasc Res 20:96

    Google Scholar 

  • Dabagh M, Jalali P, Tarbell JM (2009) The transport of LDL across the deformable arterial wall: the effect of endothelial cell turnover and intimal deformation under hypertension. Am J Physiol Heart Circ Physiol 297:H983

    Google Scholar 

  • Damiano ER, Long DS, Smith ML (2004) Estimation of viscosity profiles using velocimetry data from parallel flows of linearly viscous fluids: application to microvascular haemodynamics. J Fluid Mech 512:1

    MATH  Google Scholar 

  • Danova-Okpetu D (2005) Macromolecular studies of the dynamic structure and mechanical properties of the endothelial surface layer, PhD thesis. Johns Hopkins

  • Deng X, Marois Y, How T, Merhi Y, King M, Guidoin R, Karino T (1995) Luminal surface concentration of lipoprotein (LDL) and its effect on the wall uptake of cholesterol by canine carotid arteries. J Vasc Surg 21:135

    Google Scholar 

  • Ding Z, Fan Y, Deng X (2009) Effect of LDL concentration polarization on the uptake of LDL by human endothelial cells and smooth muscle cells co-cultured. Acta Bioch Bioph Sin 41:146

    Google Scholar 

  • Dull RO, Jo H, Sill H, Hollis TM, Tarbell JM (1991) The effect of varying albumin concentration and hydrostatic pressure on hydraulic conductivity and albumin permeability of cultured endothelial monolayers. Microvasc Res 41:390

    Google Scholar 

  • Ebong EE, Macaluso FP, Spray DC, Tarbell JM (2011) Imaging the endothelial glycocalyx in vitro by rapid freezing/freeze substitution transmission electron microscopy. Arterioscl Throm Vas 31:1908

    Google Scholar 

  • Ethier CR (2002) Computational modeling of mass transfer and links to atherosclerosis. Ann Biomed Eng 30:461

    Google Scholar 

  • Faergeman O (2003) Coronary artery disease—genes, drugs and the agricultural connection. Elsevier, Amsterdam

    Google Scholar 

  • Fatouraee N, Deng X, Champlain A, Guidoin R (1998) Concentration polarization of low density lipoproteins (LDL) in the arterial system. Ann NY Acad Sci 858:137

    Google Scholar 

  • Flores SC, Bernauer J, Shin S, Zhou R, Huang X (2012) Multiscale modeling of macromolecular biosystems. Brief Bioinform 13:395

    Google Scholar 

  • Fry DL (1968) Acute vascular endothelial changes associated with increased blood velocity gradients. Circ Res 22:165

    Google Scholar 

  • Fu BM, Weinbaum S, Tsay RY, Curry FE (1994) A junction-orifice-fiber entrance layer model for capillary permeability: application to frog mesenteric capillaries. J Biomech Eng 116:502

    Google Scholar 

  • Fu BM, Chen B, Chen W (2003) An electrodiffusion model for effects of surface glycocalyx layer on microvessel permeability. Am J Phys Heart Circ Physiol 284:H1240

    Google Scholar 

  • Gao L, Lipowsky HH (2009) Measurement of solute transport in the endothelial glycocalyx using indicator dilution techniques. Ann Biomed Eng 37:1781

    Google Scholar 

  • Gao L, Lipowsky HH (2010) Composition of the endothelial glycocalyx and its relation to its thickness and diffusion of small solutes. Microvasc Res 80:394

    Google Scholar 

  • Gniewek P, Kolinski A (2012) Coarse-grained modeling of mucus barrier properties. Biophys J 102:195

    Google Scholar 

  • Gorog P, Born GV (1982) Increased uptake of circulating low-density lipoproteins and fibrinogen by arterial walls after removal of sialic acids from their endothelial surface. Br J Exp Pathol 63:447

    Google Scholar 

  • Hahn C, Schwartz MA (2009) Mechanotransduction in vascular physiology and atherogenesis. Nat Rev Mol Cell Biol 10:53

    Google Scholar 

  • Henry CBS, Duling BR (1999) Permeation of the luminal capillary glycocalyx is determined by hyaluronan. Am J Physiol Heart Circ Physiol 277:H508

    Google Scholar 

  • Henry CB, Duling BR (2000) TNF-\({\alpha }\) increases entry of macromolecules into luminal endothelial cell glycocalyx. Am J Physiol Heart Circ Physiol 279:H2815

    Google Scholar 

  • Hu X, Weinbaum S (1999) A new view of Starling’s hypothesis at the microstructural level. Microvasc Res 58:281

    Google Scholar 

  • Hu X, Adamson RH, Liu B, Curry FE, Weinbaum S (2000) Starling forces that oppose filtration after tissue oncotic pressure is increased. Am J Physiol Heart Circ Physiol 279:1724

    Google Scholar 

  • Jellinek H (1983) The drainage of transmural flow and the consequences of its insufficiency. In: Schettler G, Nerem RM, Schmid-Schonbein H, Morl H, Diehm C (eds) Fluid dynamics as a localizing factor for atherosclerosis. Springer, Berlin

    Google Scholar 

  • John K, Barakat AI (2001) Modulation of ATP/ADP concentration at the endothelial surface by shear stress: effect of flow-induced ATP release. Ann Biomed Eng 29:740

    Google Scholar 

  • Koo A, Dewey CF, García-Cardeña G (2013) Hemodynamic shear stress characteristic of atherosclerosis-resistant regions promotes glycocalyx formation in cultured endothelial cells. Am J Physiol Cell Physiol 304:C137

    Google Scholar 

  • Ku DN, Giddens DP, Zarins CK, Glagov S (1985) Pulsatile flow and atherosclerosis in the human carotid bifurcation. Positive correlation between plaque location and low oscillating shear stress. Arteriosclerosis 5:293

    Google Scholar 

  • Lantz J, Karlsson M (2012) Large eddy simulation of LDL surface concentration in a subject specific human aorta. J Biomech 45:537

    Google Scholar 

  • Lervik A, Bresme F, Kjelstrup S (2013) Molecular dynamics simulations of the Ca\(^{2+}\) pump: a structural analysis. Phys Chem Chem Phys 14:3543

    Google Scholar 

  • Levick JR, Michel CC (1973) The effect of bovine albumin on the Permeability of frog mesenteric capillaries. Exp Physiol 58:87

    Google Scholar 

  • Lipowsky HH, Lescanic A (2013) Shear-dependent adhesion of leukocytes and lectins to the endothelium and concurrent changes in thickness of the glycocalyx of post-capillary venules in the low-flow state. Microcirculation 20:149

    Google Scholar 

  • Liu X, Pu F, Fan Y, Deng X, Li D, Li S (2009) A numerical study on the flow of blood and the transport of LDL in the human aorta: the physiological significance of the helical flow in the aortic arch. Am J Physiol-Heart C 297:H163

    Google Scholar 

  • Liu X, Fan Y, Deng X (2011) Effect of the endothelial glycocalyx layer on arterial LDL transport under normal and high pressure. J Theor Biol 283:71

    Google Scholar 

  • Luckett PM, Fischbarg J, Bhattacharya J, Silverstein SC (1989) Hydraulic conductivity of endothelial cell monolayers cultured on human amnion. Am J Physiol 256:H1675

    Google Scholar 

  • Mackay J, Mensah G (2004) The atlas of heart disease and stroke. World Health Organization, Geneva

    Google Scholar 

  • Mason J, Curry F, Michel C (1977) The effects of proteins upon the filtration coefficient of individually perfused frog mesenteric capillaries. Microvasc Res 13:185

    Google Scholar 

  • Megens RTA, Reitsma S, Schiffers PHM, Hilgers RHP, De Mey JGR, Slaaf DW, oude Egbrink MGA, van Zandvoort MAMJ (2007) Two-photon microscopy of vital murine elastic and muscular arteries. Combined structural and functional imaging with subcellular resolution. J Vasc Res 44:87

    Google Scholar 

  • Meng W, Yu F, Chen H, Zhang J, Zhang E, Dian K, Shi Y (2009) Concentration polarization of high-density lipoprotein and its relation with shear stress in an in vitro model. J Biomed Biotechnol 2009: 695838

    Google Scholar 

  • Michel CC (1980) Filtration coefficients and osmotic reflexion coefficients of the walls of single frog mesenteric capillaries. J Physiol 309:341

    Google Scholar 

  • Michel CC, Phillips ME, Turner MR (1985) The effects of native and modified bovine serum albumin on the permeability of frog mesenteric capillaries. J Physiol 360:333

    Google Scholar 

  • Michel CC (1997) Starling: the formulation of his hypothesis of microvascular fluid exchange and its significance after 100 years. Exp Physiol 82:1

    Google Scholar 

  • Napoli C, de Nigris F, Williams-Ignarro S, Pignalosa O, Sica V, Ignarro LJ (2006) Nitric oxide and atherosclerosis: an update. Nitric Oxide-Biol Ch 15:265

    Google Scholar 

  • Pang Z, Tarbell JM (2003) In vitro study of Starling’s hypothesis in a cultured monolayer of bovine aortic endothelial cells. J Vasc Res 40:351

    Google Scholar 

  • Pries AR, Secomb TW, Gaehtgens P (2000) The endothelial surface layer. Pflugers Arch 440:653

    Google Scholar 

  • Rader DJ (2003) Regulation of reverse cholesterol transport and clinical implications. Am J Cardiol 92:42

    Google Scholar 

  • Reitsma S, Slaaf DW, Vink H, van Zandvoort MAMJ, Oude Egbrink MGA (2007) The endothelial glycocalyx: composition, functions, and visualization. Pflugers Arch 454:345

    Google Scholar 

  • Rindfleisch E (1872) A manual of pathological histology to serve as an introduction to the study of mordib anatomy. The New Sydenham Society, London

    Google Scholar 

  • Scharfstein H, Gutstein WH, Lewis L (1963) Changes of boundary layer flow in model systems: implications for initiation of endothelial injury. Circ Res 13:580

    Google Scholar 

  • Schnitzer JE, Carley WW, Palade GE (1988) Albumin interacts specifically with a 60-kDa microvascular endothelial glycoprotein. PNAS 85:6773

    Google Scholar 

  • Schnitzer JE, Carley WW, Palade GE (1988) Specific albumin binding to microvascular endothelium in culture. Am J Physiol 254:H425

    Google Scholar 

  • Schwartz CJ, Valente AJ, Sprague EA (1993) A modern view of atherogenesis. Am J Cardiol 71:9B

    Google Scholar 

  • Secomb TW, Hsu R, Pries AR (2001) Motion of red blood cells in a capillary with an endothelial surface layer: effect of flow velocity. Am J Physiol Heart Circ Physiol 281:H629

    Google Scholar 

  • Shaaban AM, Duerinckx AJ (2000) Wall shear stress and early atherosclerosis: a review. Am J Roentgenol 174:1657

    Google Scholar 

  • Smith ML, Long DS, Damiano ER, Ley K (2003) Near-wall micro-PIV reveals a hydrodynamically relevant endothelial surface layer in venules in vivo. Biophys J 85:637

    Google Scholar 

  • Stace TM, Damiano ER (2001) An electrochemical model of the transport of charged molecules through the capillary glycocalyx. Biophys J 80:1670

    Google Scholar 

  • Stevens AP, Hlady V, Dull RO (2007) Fluorescence correlation spectroscopy can probe albumin dynamics inside lung endothelial glycocalyx. Am J Physiol Lung Cell Mol Physiol 293:L328

    Google Scholar 

  • Suttorp N, Hessz T, Seeger W, Wilke A, Koob R, Lutz F, Drenckhahn D (1988) Bacterial exotoxins and endothelial permeability for water and albumin in vitro. Am J Physiol 255:C368

    Google Scholar 

  • Tarbell JM, Qiu Y (2000) Arterial wall mass transport: the possible role of blood phase resistance in the localization of arterial disease. In: Bronzino JD (ed) The biomedical engineering handbook, 2nd edn. CRC Press, New York

    Google Scholar 

  • Tarbell JM (2003) Mass transport in arteries and the localization of atherosclerosis. Annu Rev Biomed Eng 5:79

    Google Scholar 

  • Tarbell JM, Weinbaum S, Kamm RD (2005) Cellular fluid mechanics and mechanotransduction. Ann Biomed Eng 33:1719

    Google Scholar 

  • Tarbell JM (2010) Shear stress and the endothelial transport barrier. Cardiovasc Res 87:320

    Google Scholar 

  • Tedgui A, Lever MJ (1984) Filtration through damaged and undamaged rabbit thoracic aorta. Am J Physiol 247:H784

    Google Scholar 

  • Turner MR, Clough G, Michel CC (1983) The effects of cationised ferritin and native ferritin upon the filtration coefficient of single frog capillaries. Evidence that proteins in the endothelial cell coat influence permeability. Microvasc Res 25:205

    Google Scholar 

  • Turner MR (1992) Flows of liquid and electrical current through monolayers of cultured bovine arterial endothelium. J Physiol 449:1

    Google Scholar 

  • Valenta DT, Bulgrien JJ, Banka CL, Curtiss LK (2006) Overexpression of human ApoAI transgene provides long-term atheroprotection in LDL receptor-deficient mice. Atherosclerosis 189:255

    Google Scholar 

  • van den Berg BM, Vink H, Spaan JAE (2003) The endothelial glycocalyx protects against myocardial edema. Circ Res 92:592

    Google Scholar 

  • van den Berg BM, Spaan JAE, Rolf TM, Vink H (2006) Atherogenic region and diet diminish glycocalyx dimension and increase intima-to-media ratios at murine carotid artery bifurcation. Am J Physiol Heart Circ Physiol 290:915

    Google Scholar 

  • van Haaren PMA, Van Bavel E, Vink H, Spaan JAE (2003) Localization of the permeability barrier to solutes in isolated arteries by confocal microscopy. Am J Physiol Heart Circ Physiol 285:H2848

    Google Scholar 

  • Van Teeffelen JW, Brands J, Stroes ES, Vink H (2007) Endothelial glycocalyx: sweet shield of blood vessels. Trends Cardiovas Med 17:101

    Google Scholar 

  • Venturoli M, Maddalenasperotto M, Kranenburg M, Smit B (2006) Mesoscopic models of biological membranes. Phys Rep 437:1

    Google Scholar 

  • Vincent PE (2009) A cellular scale study of low density lipoprotein concentration polarisation in arteries, PhD thesis. Imperial College, London

  • Vincent PE, Sherwin SJ, Weinberg PD (2009) The effect of a spatially heterogeneous transmural water flux on concentration polarization of low density lipoprotein in arteries. Biophys J 96:3102

    Google Scholar 

  • Vincent PE, Sherwin SJ, Weinberg PD (2010) The effect of the endothelial glycocalyx layer on concentration polarisation of low density lipoprotein in arteries. J Theor Biol 265:1

    MathSciNet  Google Scholar 

  • Vink H, Duling BR (1996) Identification of distinct luminal domains for macromolecules, erythrocytes, and leukocytes within mammalian capillaries. Circ Res 79:581

    Google Scholar 

  • Vink H, Duling BR (2000) Capillary endothelial surface layer selectively reduces plasma solute distribution volume. Am J Physiol Heart Circ Physiol 278:H285

    Google Scholar 

  • Wada S, Karino T (1999) Theoretical study on flow-dependent concentration polarization of low density lipoproteins at the luminal surface of a straight artery. Biorheology 36:207

    Google Scholar 

  • Wada S, Karino T (2002) Theoretical prediction of low-density lipoproteins concentration at the luminal surface of an artery with a multiple bend. Ann Biomed Eng 30:778

    Google Scholar 

  • Wada S, Koujiya M, Karino T (2002) Theoretical study of the effect of local flow disturbances on the concentration of low-density lipoproteins at the luminal surface of end-to-end anastomosed vessels. Med Biol Eng Comput 40:576

    Google Scholar 

  • Wada S, Karino T (2002) Prediction of LDL concentration at the luminal surface of a vascular endothelium. Biorheology 39:331

    Google Scholar 

  • Wakeman W, Salpadoru N, Caro C (1976) Diffusion coefficients for protein molecules in blood serum. Atherosclerosis 25:225

    Google Scholar 

  • Wang G, Deng X, Guidoin R (2003) Concentration polarization of macromolecules in canine carotid arteries and its implication for the localization of atherogenesis. J Biomech 36:45

    Google Scholar 

  • Wei D, Wang G, Tang C, Qiu J, Zhao J, Gregersen H, Deng L (2012) Upregulation of SDF-1 is associated with atherosclerosis lesions induced by LDL concentration polarization. Ann Biomed Eng 40:1018

    Google Scholar 

  • Weinbaum S (1997) Whitaker distinguished lecture: models to solve mysteries in biomechanics at the cellular level; a new view of fiber matrix layers. Ann Biomed Eng 26:627

    Google Scholar 

  • Weinbaum S, Zhang X, Han Y, Vink H, Cowin SC (2003) Mechanotransduction and flow across the endothelial glycocalyx. Proc Natl Acad Sci USA 100:7988

    Google Scholar 

  • Weinbaum S, Tarbell JM, Damiano ER (2007) The structure and function of the endothelial glycocalyx layer. Annu Rev Biomed Eng 9:121

    Google Scholar 

  • Wolinsky H, Glagov S (1967) Nature of species differences in the medial distribution of aortic vasa vasorum in mammals. Circ Res 20:409

    Google Scholar 

  • Woolf N (1990) Pathology of atherosclerosis. Br Med Bull 46:960

    Google Scholar 

  • Yin Y, Arkhipov A, Schulten K (2009) Simulations of membrane tubulation by lattices of amphiphysin N-bar domains. Structure 17:882

    Google Scholar 

  • Zeman LJ, Zydney AL (1996) Microfiltration and ultrafiltration: principles and applications. CRC Press, Boca Raton

    Google Scholar 

  • Zhang Z, Deng X, Fan Y, Li D (2007) Ex vitro experimental study on concentration polarization of macromolecules (LDL) at an arterial stenosis. Sci China Ser C 50:486

    Google Scholar 

  • Zydney AL (1997) Stagnant film model for concentration polarization in membrane systems. J Membrane Sci 130:275

    Google Scholar 

Download references

Acknowledgments

The authors are grateful to the British Heart Foundation (BHF) and the BHF Centre of Research Excellence at Imperial College London for funding studies of arterial mass transport and its modulation by the EGL. The authors would also like to thank Fernando Bresme and Amparo Galindo for useful discussions regarding molecular-scale modeling of the EGL.

Author information

Authors and Affiliations

  1. Department of Aeronautics, Imperial College London, South Kensington, London, SW7 2AZ, UK

    P. E. Vincent

  2. Department of Bioengineering, Imperial College London, South Kensington, London, SW7 2AZ, UK

    P. D. Weinberg

Authors
  1. P. E. Vincent
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. P. D. Weinberg
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to P. E. Vincent.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Vincent, P.E., Weinberg, P.D. Flow-dependent concentration polarization and the endothelial glycocalyx layer: multi-scale aspects of arterial mass transport and their implications for atherosclerosis. Biomech Model Mechanobiol 13, 313–326 (2014). https://doi.org/10.1007/s10237-013-0512-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10237-013-0512-1

Keywords

Search

Navigation