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fbtwitterlinkedinvimeoflicker grey 14rssslideshare1
Chernyavsky, Igor L.
Languages: English
Types: Unknown
Subjects:
The human placenta is characterised by a unique circulatory arrangement, with numerous villous trees containing fetal vessels immersed in maternal blood. Placental tissue therefore manifests a multiscale structure balancing microscopic delivery of nutrients and macroscopic flow. The aims of this study are to examine the interaction between these scales and to understand the influence of placental organisation on the effectiveness of nutrient uptake, which can be compromised in pathologies like pre-eclampsia and diabetes. We first systematically analyse solute transport by a unidirectional flow past an array of microscopic sinks, taking up a dissolved nutrient or gas, for both regular and random sink distributions. We classify distinct asymptotic transport regimes, each characterised by the dominance of advective, diffusive or uptake effects at the macroscale, and analyse a set of simplified model problems to assess the accuracy of homogenization approximations as a function of governing parameters (Peclet and Damkohler numbers) and the statistical properties of the sink distribution. The difference between the leading-order homogenization approximation and the exact solute distribution is determined by large spatial gradients at the scale of individual villi (depending on transport parameter values) and substantial fluctuations that can be correlated over lcngthscales comparable to the whole domain. In addition, we consider the nonlinear advective effects of solute-carriers, such as red blood cells carrying oxygen. Homogenization of the solute-carrier-facilitated transport introduces an effective Peclet number that depends on the slowly varying leading-order concentration, so that an asymptotic transport regime can be changed within the domain. At large Peclet and Damkohler numbers (typical for oxygen transport in the human placenta), nonlinear advection due to solute-carriers leads to a more uniform solute distribution than for a linear carrier-free transport, suggesting a "homogenizing" effect of red blood cells on placental oxygen transport. We then use image analysis and homogenization concepts to extract the effective transport properties (diffusivity and hydraulic resistance) from the microscopic images of histological sections of the normal human placenta. The resulting two-dimensional tensor quantities allow us to assess the anisotropy of placental tissue for solute transport. We also show how the pattern of villous centres of mass can be characterised using an integral correlation measure, and identify the minimum spatial scale over which the distribution of villous branches appears statistically homogeneous. Finally, we propose a mathematical model for maternal blood flow in a placental functional unit (a placentone), describing flow of maternal blood via Darcy's law and steady advective transport of a dissolved nutrient. An analytical method of images and computational integration along streamlines are employed to find flow and solute concentration distributions, which are illustrated for a range of governing system parameters. Predictions of the model agree with experimental radioangiographic studies of tracer dynamics in the intervillous space. The model supports the hypothesis that basal veins are located on the periphery of the placentone in order to optimise delivery of nutrients. We also explain the importance of dilatation of maternal spiral arteries and suggest the existence of an optimal volume fraction of villous tissue, which can both be involved in the placental dysfunction. Theoretical studies of this thesis thus constitute a step towards modelling-based diagnostics and treatment of placental disorders.
  • The results below are discovered through our pilot algorithms. Let us know how we are doing!

    • 6.3.1 The method of images for Darcy's flow in a hemispherical domain 130 6.3.2 Numerical scheme to compute the solute distribution and net uptake rate 133 R e s u l t s . . . . . . . . . . . . . . . . . . . 134 6.4.1 Flow and pressure distributions. 134 6.4.2 Tracer dynamics in the placentone 136 6.4.3 Representative solute distributions 13(3 6.4.4 Influence of volume fraction of villous tissue on net uptake rate 138 6.4.5 Influence of the central cavity on solute concentration distribution 140 Discussion . . . . . . . . . . . . . . . 141 Hill, Power, Longo (1973) [122]
    • [1] ABDULLAH, N.S. & DAS, D.n. (2007), Modelling nutrient transport in hollow fibre membrane bioreactor for growing bone tissue with consideration of multi-component interactions, Chern. Eng. Sci. 62(21): 5821-5839.
    • [2] ABRAMOWICZ, J .S. & SHEINER, E. (2008), Ultrasound of the placenta: A systematic approach. Part II: Functional assessment (Doppler), Placenta 29(11): 921929.
    • [3] ACRIVOS, A., HINCH, E.J. & JEFFREY, D.J. (1980), Heat transfer to a slowly moving fluid from a dilute fixed bed of heated spheres, J. Fluid Meek. 101(2): 403 421.
    • [4] ADAr-.lS0N, S.L., Lu, Y., WHITELEY, K.J., HOLMYARD, D., HEMBERGER, M., PFARRER, C. & CROSS. J.C. (2002), Interactions between trophoblast cells and the maternal and fetal circulation in the mouse placenta, Dev. Bioi. 250(2): 358373.
    • [5] AHMED, A., DUNK, C., AHMAD, S. & KHALIQ, A. (2000), Regulation of placental VI\.';­ cular endothelial growth factor (VEGF) and placenta growth factor (PIGF) and soluble Flt-l by oxygen - A review, Placenta 21(8upplement 1): 816-824.
    • [6] AIFANTIS, E.C. (1978), Towards a rational modeling for the human placenta, Math. Bio"ci. 40(3-4): 281-301.
    • [7] ALLAIRE, G. & RAPHAEL, A.L. (2007), Homogenization of a convection-diffusion model with reaction in a porous medium, Comptes Rendus Mathematique 344(8): 523-528.
    • [8] APLIN, J. (2000), }'laternal influences on placental development, Sernin. Cell Dev. Biol. 11(2): 115-125.
    • [9] Ams, R. (1956), On the dispersion of a solute in a fluid flowing through a tube, Pmc. R. Soc. Lond. A 235(1200): 67 77.
    • [10] ATHANASSIADES, A., HAMILTON, G.S. & LALA, P.K. (1998), Vascular endothelial growth factor stimulates proliferation but not migration or invasiveness in human ('xtravillous trophoblast, Biol. Repmd. 59(3): 643 -654.
    • [11] AURIAULT, J.L. & ADLER, P.M. (1995), Taylor dispersion in porous media: Analysis by multiple scale expansions. Adv. Water Resour. 18(4): 217-226.
    • [12] AURIAULT, .1.L., GEINDREAU, C. & BOUTIN, C. (2005), Filtration law in porous media with poor separation of scales, Transport in Porous Media 60(1): 89-108.
    • [13] AURIAULT, .1.L. & SANCHEZ-PALENCIA, E. (1977), Etude du comportement macl"Oscopique d'ul1 milieu poreux sature deformable, Journal de Mccanique 16(4): 575 603, (in French).
    • [15] BABUSKA, I. (1976). Solution of interface problems by homogenization. I, SIAM J. Math. Anal. 7(G): 603 634.
    • [16] BADDELEY. A. &: .JENSEN. E.B.V. (2005), Stereology for Statisticians. Chapman & Halll CRC, Boca Raton. 3% pp.
    • [17] BADDELEY, A. &: TllRNEH. R. (2005), Spatstat: an R package for analyzing spatial point patterns, J. Stat. Software 12(6): 1~42, URL: www. j statsoft .org, ISSN: 1548-7660.
    • [18] BADDELEY. A.J. &: SILVERt-.fAN. B.W. (1984), A cautionary example on the use of secondorder methods for analyzing point patterns, Biometrics 40(4): 1089-1093.
    • [19] BAKHVALOV, N.S. (1974), A"eraged characteristics of bodies with periodic structure, Soviet PhY8ic8 Doklady 19: 650.
    • [20] BAKHVALOV, N.S. &: PANASENKO, G.P. (1989), Homogenisation: Averaging Processes in Periodic Media; Mathematical Problems in the Mechanics of Composite Materials. vol. 36 of Mathematics and its applications, Kluwer Academic Publishers, Dordrecht, 366 pp.
    • [21] BAL. G., GAHNIEH, J., MOTSCH, S. & PERRIER, V. (2008), Random integrals and correctors in homogenization, Asymptotic Analysis 59(1): 1-26.
    • [22] BAL, G. &: JING. \V. (2010). Homogenization and corrector theory for linear transport in random media. Discret. Contino Dyn. Syst. 28(4): 1311~1343.
    • [23] BALHOFF. i\1., i\iIKELIC. A. & \VHEELEH, M. (2009), Polynomial filtration laws for low reynolds number flows through porous media, Transport in Porous Media 81(1): 35--60.
    • [24] BANERJEE, R.K., KWON, 0., VAIDYA, V.S. & BACK, L.H. (2008), Coupled oxygen transport analysis in the avascular wall of a coronary artery stenosis during allgioplasty, 1. Biomech. 41(2): 475-479.
    • [25] BARTELS. H. & i\10LL, W. (1964), Passage of inert substances aud oxygen ill the human placenta. Pfiiigers Arch. Eur. 1. Physiol. 280(2): 165~177.
    • [26] BARTH. \V.H., MCCURNIN. D.C .. DEE CAREY, K. & HANKINS, G.D.V. (2006), Contra.-;t sonography, video densitometry and intervillous blood flow: A pilot project, Placenta 27(6-7): 719 726.
    • [27] BATCHELOR, G.K. (2000), An Introduction to Fluid Dynamic8. Cambridge Mathematical Library, Cambridge University Press, 635 pp.
    • [28] BATCHELOR, G.K. & O'BRIEN, R.W. (1977), Thermal or electrical conduction through a granular material, Proc. R. Soc. Land. A 355(1682): 313~333.
    • [29] BEAR, J. (1988), Dynamics of Fluids in Porous Media. Dover Publications, 784 pp.
    • [30] BEAVERS, G.S. & JOSEPH, D.D. (1967), Boundary conditions at a naturally permeable wall, J. Fluid Mech. 30(1): 197~207.
    • [31] BEES, M.A. & CROZE, O.A. (2010), Dispersion of biased swimming rnicro-orgallisllls in a fluid flowing through a tube, Proc. R. Soc. A 466(2119): 2057-2077.
    • [32] BENDER, C.M. & BETTENCOURT, L.M.A. (1996), Multiple-scale analysis of the quantulll anharmonic oscillator, Phys. Rev. Lett. 77(20): 4114-4117.
    • [33] BENIRSCHKE, K., KAUFMANN, P. & BAERGEN, R.N. (2006), Pathology of the Human Placenta. Springer, 5th edn, 1050 pp.
    • [34] BENSOUSSAN, A., LIONS, J.L. & PAPANICOLAOU, G. (1978), Asymptotic Analysis fm' Periodic Structures. vol. 5 of Studies in mathematics and its applications, Elsevier NorthHolland, 700 pp.
    • [35] BENSOUSSAN, A., LIONS, J.L. & PAPANICOLAOU, G.C. (1979), Boundary layers and homogenization of transport processes, Publ. Res. Inst. Math. Sci., Kyoto Univ. 15: 53157.
    • [36] BERDICHEVSKII. V.L. (1975), Spatial averaging of periodic structures, Soviet Physics Doklady 20: 334.
    • [37] BERGMAN, D.J. (1979), The dielectric constant of a simple cubic array of identical spheres, J. Phys. C 12(22): 4947-4960.
    • [38] BERGMAN, D.J. (1979), Dielectric constant of a two-component granular composite: A practical scheme for calculating the pole spectrum, Phys. Rev. B 19(4): 2359-2368.
    • [48] BOYD, J.D. & HAMILTON, W.J. (1966), Placental septa, Cdl Tissue Res. m)(1): 613 6:3·1.
    • [49] BOYD, J.D. & HAMILTON, W.J. (1970), The Human Placenta. W.Heffer&Sons Ltd., Cambridge, 365 pp.
    • [50] BRENNER, H. (1980), Dispersion resulting from flow through spatially periodic porous media, Phil. Trans. R. Soc. Land. A 297(1430): 81-133.
    • [51] BRENNER. H. & EDWARDS, D.A. (1993), Macrotmnsport Processes. Buttt'rworthHeinemann, Boston, 714 pp.
    • [52] BRINKMAN, H. (1947), A calculation of the viscous force exerted by a flowing fluid 011 It dense swarm of particles, Applied Scientific Resear'ch Al (1): 27 34.
    • [53] BURGER, :M., CAPASSO, V. & PIZZOCCHERO, L. (2006), Mesoscale averagillg of nucleation and growth models, Multiscale Model. Sirnul. 5(2): 564 592.
    • [54] BURRIDGE, R. & KELLER, J.B. (1981), Poroelasticity equations derived frollllllicrostructure, J. Acoust. Soc. Am. 70(4): 1140-1146.
    • [55] BUHTON, G.J., JAUNIAUX, E. & CHARNOCK-JONES, D.S. (2007), Human l'arly placl'lltal development: Potential roles of the endometrial glands, Placenta 28(SlIpplclllcnt 1): S64-S69.
    • [56] BURTON, G.J., JAUNIAUX, E. & WATSON, A.L. (1999), Matel'llal arterial COllIIl'ctiollS to the placental intervillous space during the first trimester of human pregnancy: TIll' Boyd Collection revisited, Am. J. Obstet. Gynecol. 181 (3): 718 -724.
    • [57] BURTON, G.J., WOODS, A.W., JAUNIAUX, E. & KINGDOM, J.C.P. (2009), Rlll'ological and physiological consequences of conversion of the maternal spiral arteries for utcwplacental blood flow during human pregnancy, Placenta 30(6): 473 482.
    • [58] BUTLER, S.F.J. (1953), A note on Stokes's stream function for motion with a spherical boundary, Math. Proc. Camb. Philos. Soc. 49(1): 169-174.
    • [59] BYRNE, H., GOWLAND, P., JENSEN, 0., MAYHEW, T., MCGUINNESS, ~l., PLEASE, C. & \VILSON, S. (2001), Flow and transport in the placenta, In: H. Byl'lll', O . .JeIlSl'II, J. King & S. Waters, eds, Proceedings of the Sccond Mathcmatics-iu-Ml'diciuc Study Group, University of Nottingham, pp. 11-17.
    • [60] BYRNE, H.}.1., CHAPLAIN, M.A.J., PETTET, G.J. & McELWAIN, D.L.S. (2001), An analysis of a mathematical model of trophoblast inva.'.;ion, Appl. Math. Lctt. 14(8): 1005-1010.
    • [61] CANIC, S., TAMBACA, J., GUIDOBONI, G., MIKELI(\ A., HARTLEY, C ..J. & ROSENSTRAUCH, D. (2006), Modeling viscoelastic behavior of arterial walls and thcir int('raction with pulsatile blood flow, SIAM J. Appl. Math. 67(1): 164-193.
    • [62] CAPASSO, V. (2009), Multiple scales and geometric structures: additioual SOlll'C('S of randomness, J. Math. Biol. 59 (1): 143-146.
    • [63] CAPASSO, V., MICHELETTI, A. & MORALE, D. (2008), Stochastic gcometric modl'ls, and related statistical issues in tumour-induced angiogenesis, Math. Biosci. 214(1-2): 20 31.
    • [64] CARSON, D.O., BAGCHI, I., DEY, S.K., ENDERS, A.C., FAZLEABAS, A.T., LESSEY, B.A. & YOSHINAGA, K. (2000), Embryo implantation, Dev. Biol. 223(2): 217 237.
    • [65] CARTER, A.M. (1997), When is the maternal placental circulation cstablished in UUIlI'!. Placenta 18(1): 83-87.
    • [66] CARTER, A.M. (2007), Animal models of human placentatiou 28(Supplcment 1): S41-S47.
    • [67] CARTER, A.M., ENDERS, A.C., JONES, C ..I.P., MESS, A., PFAIlHER. C .. PI.JNENBORG, R. & SOMA, H. (2006), Comparativc placentation and auilllal models: Pattl'rJls of trophoblast invasion - A workshop report, Placenta 27(Supplcllll'ut 1): 30 33.
    • [68] CARTWRIGHT, J.E., HOLDEN, D.P. & WHITLEY, G.S.J. (1999), Hepatocyt.l' growt.h factor rcgulatcs human trophoblast motility and invasion: a role for nitric oxidl" B,·. J. Phannacol. 128(1): 181-189.
    • [69] CARTWRIGHT, J.E., KENNY, L.C., DASH, P.R., CROCJ
    • [70] CASTELLUCCI, M., SCHEPE, M., SCHEFFEN, 1., CELONA, A. & KAUFMANN, P. (WUO). The development of the human placental villous tree, Anat. Emln7Jol. 181(2): 117 12S.
    • [71] CHAPMAN, S.J., SHIPLEY, R.J. & JAWAD, R. (2008), Multiscale lIl(}(h'1iug of fluid transport in tumors, Bull. Math. Bioi. 70(8): 2334 -2357.
    • [72] CHARNOCK-JONES, D.S., KAUFMANN, P. & MAYHEW, T.M. (2004), Aspt'cts of hlll1l1ll1 fetoplacental vasculogenesis and angiogenesis. 1. Molecular regulation, Placenta 25(2-3): 103--113.
    • [73] CHEN, R.R., SILVA, E.A., YUEN, W.W., BROCK, A.A., FISCHBACH, C., LIN, A.S., GULDBERG, R.E. & MOONEY, D.J. (2007), Integrated approach to designing growth factor delivery systems, FASEB J. 21: 3896-3903.
    • [74] CHERNYAVSKY, I.L., JENSEN, O.E. & LEACH, L. (2010), A mathcmatical lIIodd of intervillous blood flow in the human placentone, Placenta 31(1): 44-52.
    • [75] CHERNYAVSKY, LL., LEACH, L., DRYDEN, LL. & JENSEN, O.E. (2011), Transport ill the placenta: homogenizing haemodynamics in a disordcrcd mediuUl, Phil. Trans. R. So('. A 369(1954): 4162-4182.
    • [76] CLARK, A., FEDERSPIEL, W., CLARK, P. & COKELET, G. (1985), Oxygcn deliwl'Y fl'OllI red cells, Biophysical J. 47(2): 171-181.
    • [77] COSTA, A., COSTANTINO, M. & FUMERO, R. (1992), Oxygen exchange mechanisms in the human placenta: mathematical modelling and simulation, J. Biorneci. Eng. 1.1(5): 385-389.
    • [78] CRAVEN, C.M., ZHAO, L. & WARD, K. (2000), Lateral placental growth occurs by trophoblast cell invasion of decidual veins, Placenta 21(2-3): 160 169.
    • [79] DARCY, H.P.G. (1856), Les Fontaines Publiques de la Ville de Dijon: E1'lJOsitioll t'f application asuivre et des formules aemployer dans les questions cil! duistr'ifmtion d '('(l1t. Victor Dalmont, Paris, 647 pp., (in French).
    • [80] DEMIR, R., KAYISLI, V.A., SEVAL, Y., CELIK-OZENCI, C., KOltGUN, E.T., DE1\IIHWEUSTEN, A.Y. & HUPPERTZ, B. (2004), Sequential expression of VEGF ftlld its \'('('('Ptors in human placental villi during very carly prcgnancy: differcllcl's b('tw('('11 pllu'(,llt III vasculogenesis and angiogenesis., Placenta 25(6): 560 572.
    • [81] DHEIN, S. (2005), Practical methods in cardiovascular 1·esearch. Springer, I3t'rlin, 1010 pp.
    • [82] DIGGLE, P.J. (2003), Statistical Analysis of Spatial Point Patterns. Aruold, London, 21ld edn, 159 pp.
    • [83] DRYDEN, LL. & MARDIA, K.V. (1998), Statistical Shape Analysis. Wiley, Chil'ht'st<,I', 347 pp.
    • [84] ENDERS, A.C. & KING, B.F. (1991), Early stages of trophohla."itk invn.".iion of til<' 11111- ternal vascular system during implantation in the macaqul' and baboon, Am. J. A/Hit. 192(4): 329-346.
    • [85] ENE, H.I, & SANCHEZ-PALENCIA, E. (1975), Equations ct phenolllell(,s de slll'fll(,(, pOI\l' I'ecoulement dans un modele de milieu porcux, J. Mecaniq'llc 14(1): 73 lOH, (in Fr<'ll('h).
    • [86] ERIAN, F.F., COHRSIN, S. & DAVIS, S.H. (1977), Maternal, placental hlood flo\\': A model with velocity-dependent permeability, .J. Biomech. 10(11-12): 807 814.
    • [87J ESPINOZA, J., ROMERO, R., MEE KIM, Y., KUSANOVIC, J.P., HASSAN, S., EREZ, 0., GOTSCH, F., GABOR THAN, N., PAPP, Z. & JAI KIM, C. (2006), Normal and abnormal transformation of the spiral arteries during pregnancy, J. Perinat. Mcd. 34(6): 447--458.
    • [88J FABER, J.J. (1969), Application of the theory of heat exchangers to the transfer of inert materials in placentas, Circ. Res. 24(2): 221-234.
    • [89] FANNJIANG, A. & PAPANICOLAOU, G. (1994), Convection enhanced diffusion for periodic flows, SIAM J. Appl. Math. 54(2): 333--408.
    • [90J FANNJIANG. A. & PAPANICOLAOU, G. (1997), Convection-enhanced diffusion for randolll flows, J. Stat. Phys. 88{5/6): 1033-1076.
    • [91] FINN, M.D., LEACH, L., GOWLAND, P.A. & JENSEN, O.E. (2004), Hemodynalllics in II lobule: a computational model, Placenta 25(8-9): A23, abstracts to be prcsented at the Placenta Association of the Americas 2004 conference/10th Meeting of thc Intcl'llational Federation of Placenta Associations.
    • [92] FINN, M.D., LEACH, L., GOWLAND, P.A., WILTON, B. & JENSI~N, O.E. (2004), Plac('l1- tal blood flow: end of year report, Tech. rep., University of Nottinghalll, (unpuhlished).
    • [93J FLEISCHER, A.C., ApPLEBAUM, M.I. & PARSONS, A.K. (1997), Ultm8ouTI.d and Ihl' Endometrium, Informa Healthcare, vol. 8 of Progress in Obstetric and Gyn('('ologiclll Sonography Series, ch. Transvaginal sonography of normal cndollletriulll. pp. 1 W.
    • [94J FORCHHEIMER, P. (1901), Wa.-;serbewegung durch Bodcn (Fluid motion in soil). Z. Vel'. Deutsch. Ing. 45: 1782-1788, (in German).
    • [95J FRANCIS, S.T., DUNCAN, K.R., MOORE, R.J., BAKER, P.N., JOHNSON, I.R. & GowLAND, P.A. (1998), Non-invasive mapping of placental perfusion, The Lancet 351(0113): 1397-1399.
    • [96] FREESE, V.E. (1968), The uteroplacental va.'icular relationship in the' hU1lllln. Am. J. Obstet. Gynecol. 101(1): 8-16.
    • [101] FRICKE, H. (1955), The complex conductivity uf a suspellsion of stratifi<·d particks of spherical or cylindrical form, J. Phys. Chern. 59(2): 1G8-l70.
    • [102] GAYKEMA, W.P.J., HOL, W.G.J., VEREIJKEN, J.M., SOETER, N.l\1., 13AK, 11..1. & BEINTEMA, J.J. (1984), 3.2 A structure of the copper-containing, oxygen-carryillg prot ('ill Panulirus interruptus haemocyanin, Nature 309(59G3): 23--29.
    • [103] GOLDEN, K. & PAPANICOLAOU, G. (1983), Bounds for effective paralllt'ters of ht't('wg('­ neous media by analytic continuation, Cornrnun. Math. PhY8. 90(4): 47:3 ·191.
    • [104] GORDON, Z., EYTAN, 0., JAFFA, A.J. & ELAD, D. (2007), Fetal hlood flow in brallching models of the chorionic arterial vasculature, Annal.s New York Amd. S('i. 1101(1): 250265.
    • [105] GRIFFITH, L.G. & SWARTZ, M.A. (2006), Capturing complex 3D tissllt· physiology in vitro, Natur'c Rev. Mol. Cell. mol. 7(3): 211- 224.
    • [106] GRIMMETT, G.R. & STIRZAKER, D.R. (1992), Probability and Random P1'OCt'H8t'H. Oxford science publications, Clarendon Press, 2nd edn, 541 pp.
    • [107] GROOME, L.J. (1991), A theoretical analysis of the effect of plae('lltallll<'tai>olislIl 011 fdal oxygenation under conditions of limited oxygen availability, Bio8]j8it'm8 2G( I): 45 ;,G.
    • [108] GRUENWALD, P. (1977), The development of the plac(,lItalloilular pattl'l'I1 ill t hI' hlllllall. Review and reinterpretation of the material, Obstet. Gynecol. 49(G): 72H 732.
    • [109] GUILBEAU, E.J., RENEAU, D.O. & KNISELY, M.H. (1972), Th(' (·rfpets of plac(,lIll1l oxygen consumption and the contractions of labor 011 fetal oxyg('11 sllpply: A st<'ady IIlId unsteady state mathematical simulation, In: 1. O. Longo & H. Bartels, ('
    • [110] HASHIN, Z. & SHTRIKMAN, S. (1962), A variational approach to t.he tht'ory of 1,11(' ('ff('ctiw magnetic permeability of multiphase materials, J. Appl. Ph1J8. 3:3(10): :l12;I:H:n.
    • [111] HASHIN, Z. & SHTRIKMAN, S. (1963), A variatiollal approach to t.IIe th<'Ol'Y of Ih(' ('IIl.'.;lic behaviour of rnultiphase materials, J. Mech. Ph1J8. Solids 11 (2): 127 140.
    • [128] JAUNIAUX, E. & GREENWOLD, N. (2003), Fdal Car'diolo!JY, Taylor 8.: Francis. ('h. Placental circulations, pp. 41-53.
    • [132] KEENER, J.P. & SNEYD, .1. (2001), Mathematicnl Physiology. Intl'rdisciplinary appli(·d mathematics, Springer, New York, 766 pp., COlTcctl'd 2nd printing.
    • [133] KELLER, J .B. (1963), Conductivity of It mediulII containing It d('nsl' array of p(·rf(·ctl.\' conducting spheres or cylinders or nonconducting cylinders, .I. Appl. Plil/s. :l·j (.1): !)!)) !)!):J.
    • [134] KELLER, J.B. (1964), Viscous flow through It grating or latt.in· of cylind(·rs . .I. Fluid Meeh. 18(01): 94-96.
    • [135] KELLER, J .B. (1977), Effective behavior of heterogellcolls 1Il('dia, III: E. W. I\lonl roll k U. Landman, eds, Statistical Mechanics and Statistical 1\1(·tho
    • [142] KINGDOM, J., HUPPERTZ, B., SEAWARD, G. & KAUFMANN, P. (2000), DevelopllIellt of the placental villous tree and its consequences for fetal growth, Eur. 1. Obstet. Gynecol. Reprod. Biol. 92(1): 35-43.
    • [143] KIRSCHBAU~1, T.H. & SHAPIRO, N.Z. (1969), A mathematical model of placental oxygclI transfer, J. Theor. Bioi. 25(3): 380-402.
    • [144] KLIMAN, H.J. (2000), Uteroplacental blood flow: The story of decidualizatioll, 1l\('llstrnation, and trophoblast invasion, Am. J. Pathol. 157(6): 1759 1768.
    • [145] KNIGHT, J. (2002), Artificial wombs: An out of body experience, Nat'llT·c 419(GD03): 106-107.
    • [146] KOHLER, W. & PAPANICOLAOU, G.C. (1982), Bounds for the effcctive conductivity of random media, In: Macroscopic Properties of Disordered Media, Springer-Verlag. vol. 154 of Lecture notes in physics, pp. 111-130, proc. conf. Courant Inst., .June 1981.
    • [147] KOLUMBAN, J. & Soos, A. (2006), Homogenization with lIlultiple scale expansion 011 selfsimilar structures, Studia Universitatis Babes-Bolyai Mathematica 51(4): 129 144.
    • [148] KONJE, J.C., HUPPERTZ, B., BELL, S.C., TAYLOR, 0 ..1. & KAUFr.IANN, P. (2003), 3-dimensional colour power angiography for staging human placental dcveloplll('nt, The Lancet 362(9391): 1199-1201.
    • [149] KORFF, T., KRAVSS, T. & AUGUSTIN, H.G. (2004), Three-dimcllsiollal spheroidal culture of cytotrophoblast cells mimics the phenotype and differentiation of cytotrophoblasts from normal and preeclamptic pregnancies, Exp. Cell Res. 297(2): 415-423.
    • [150] KORN, G.A. & KORN, T.M. (2000), Mathematical Handbook for Scientists and Enyinc(Ts: Definitions, Theorems, and Formulas for Reference and Review. Dover PublicatiollS, 1\Iineola, N.Y, 1152 pp.
    • [151] KRAMPL, E.R., ESPINOZA-DoRADO, J., LEES, C.C., Moscoso, G., BLAND, .1.1\1. k CAMPBELL, S. (2001), Maternal uterine artery Doppler studies at high altitude alld sm level, Ultrasound Obstet. Gynecol. 18(6): 578--582.
    • [156] LEACH, L., GRAY, C., STATON, S., BAI3AWALE, M.O., GRUCHY, A., FOSTEH, C., MAYHEW, T.1-1. & JAMES, D.K. (2004), Vascular endothelial cadherin aud f3-catcnin in human fetoplacental vessels of pregnancies complicated by Type 1 diabetes: associations with angiogenesis and perturbed barrier function, Diabetologia 47(4): 695 709.
    • [157] LEACH, L., LAMMIMAN, M.J., BAI3AWALE, M.O., HOBSON, S.A., BROMILOlJ, B., LoVAT, S. & SIMMONDS, M.J.R. (2000), Molecular organization of tight and adherens juuctions in the human placental vascular tree, Placenta 21 (5-6): 547557.
    • [158] LEDERBERG, J. & MCCRAY, A.T. (2001), 'Orne sweet 'omics . A gellealogical tl'l'a.'.mry of words, The Scientist 15(7): 8-9.
    • [159] LICK, W. (1969), Two-variable expansions and singluar perturbatioll problems, SIAA! .f. Appl. Math. 17(4): 815-825.
    • [186] MOORE, K.L. & PERSAUD, T.V.N. (2003), The Developing Human: Clinically Oriented Embryology. Saunders, Philadelphia, 7th edn, 560 pp.
    • [187] NIELD, D.A. & BEJAN, A. (2006), Convection in Porous Media. Springer, New York, 3rd edn, 640 pp.
    • [188] OYEN, M.L. (2010), 3D models of placental blood flow and oxygen diffusion ill chorionic villi, In: Proc. 6th World Congress Biomech. 1-6 August, Singapore, p. 362.
    • [189] PAPADOPULOS, F., SPINELLI, 1"1., VALENTE, S., FORONI, L., ORRICO, C., ALVIANO, F. & PASQUINELLI, G. (2007), Common tasks in microscopic and ultrastructural image analysis using imagej, Ultrastructural Pathology 31 (6): 401-407.
    • [190] PARNELL, \V.J. & ABRAHAMS, I.D. (2008), A new integral equation approach to elastodynamic homogenization, Proc. R. Soc. A 464(2094): 14611482.
    • [191] PAVLJOTIS, G.A. & STUART, A.M. (2008), Multiscale Methods: Averaging and Homogenization. vol. 53 of Texts in Applied Mathematics, Springer, 310 Pl'.
    • [203] PRENDERGAST, C.H., PARKER, K.H., GRAY, R., VENKATESAN, S., BANNISTER, P., CASTRO-SOARES, J., MURPHY, K.W., BEARD, RW., REGAN, L., ROI3JNSON, S., STEER, P., HALLIDAY, D. & JOHNSTON, D.C. (1999), Glucose production by the human placenta in vivo, Placenta 20(7): 591-598.
    • [204] PRIES, A.R & SECOMB, T. W. (2005), Control of blood vessel structure: insights fWIII theoretical models, Am. J. Physiol. Heart Circ. Physiol. 288(3): RI01O-1015.
    • [230] SANGANI, A.S. & ACRIvos, A. (1983), The effective conductivity of It periodic array uf spheres, Proc. R. Soc. Land. A 386(1791): 263-275.
    • [245] SIKLOSI, M., JENSEN, OLIVER, E., TEW, RICHARD, H. & LOGG, A. (2008), Multiscale modeling of the acoustic properties of lung parenchyma, ESAIM: Pmc. 23: 78 97.
    • [246] SIMPSON, N.A.B., NIMROD, C.A. & VERMETTE, R.D. (1998), Doppler evidence of intervillous flow in the embryonic period, J. Maternal-Fetal Invest. 8(1): 1116.
    • [259] TAYLOR, G. (1954), Conditions under which dispersion of a solute in a strealll of solvent can be used to measure molecular diffusion, Proc. R. Soc. Lond. A 225(1163): 473 477.
    • [273] WILBUR, W.J., POWER, G.G. & LONGO, L.D. (1978), Water exchange ill the plac(,lIta: a mathematical model, Am J Physial Regul Integr Camp Physiol 23G(3): RISI 199.
    • [274] WILKIN, P. (1954), Contribution to the study of the fetal placental circulatioll, GYTlA:ol. et Obstet. 53: 239-263, (in French).
    • [275] WOOD, B.D., QUINTARD, M. & WHITAKER, S. (2002), Calculation of effective diff'usivities for biofilms and tissues, Biotechnol. Bioeng. 77(5): 495516.
    • [276] WOOD, B.D. & WHITAKER, S. (2000), Multi-species diffusion alld reaction in hiofilms and cellular media, Chern. Eng. Sd. 55(17): 3397 3418.
    • [277] XIA, Q., SALAFIA, C. & MORGAN, S. (2010), Optimal transport and the placenta, Tech. rep., Los Alamos National Laboratory, (IEEE Vhmal Communications and Imag(' Processing, Huang Shan, An Hui, China, 11-14 July).
    • [278] YANIV, S., ELAD, D., JAFFA, A.J. & EYTAN, O. (2003), I3iofluid II.'ipects of emhryo transfer, Ann. Hiorned. Eng. 31(10): 12G5-I262.
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