Deciphering the lactate transport within the uteroplacental unit should be aided by a theoretical model in light of the insurmountable difficulties involved with in-vivo relevant measurements. Here we formulate a boundary value problem that predicts the direction and extent of lactate fluxes within the human placenta under various physiological conditions. It accounts for metabolic processes within the placenta and transporters’ activity at the two membranes that confine the terminal villi. Lactate concentration inside the terminal villi and its fluxes at the membranes are being computed. Under normal conditions lactate flux from fetal arterioles to the placenta surpasses the flux to the fetus via the umbilical vein. Within the placenta, it adds to the lactate that originates in the glycolysis, some of it degrades to pyruvate and surpluses are delivered to the maternal circulation. The apparent permeabilities of the placental membranes with respect to lactate as well as the specific characterizations of the placental lactate production, hitherto unknown, are being estimated. We determine the range of parameter values that induce sustainable, healthy fetal lactate levels and demonstrate the versatility of lactate exchange between the placenta and the fetus by computing the effect of extreme conditions (e.g., cesarean section, intrauterine growth restriction) on lactate fluxes.

The high demand of the fetus for Docosahexaenoic acid, DHA, is satisfied by a concert of several mechanisms that take place in the placental terminal villi. Scarcity of laboratory data makes the detailed description of these mechanisms elusive. Here, the DHA transport across the placenta is modeled as a boundary value problem that accounts for diffusion, reactions with fatty acids binding proteins, FABPs, and metabolic consumption within the Syncytiotrophoblast, ST. For any given DHA fluxes at the bordering membranes, analytical and numerical solutions yield the DHA concentration profile within the ST. We find that in order to comply with adequate DHA delivery to the fetus and with physiological DHA concentrations in the maternal and fetal circulations, it is essential to have a significant rise of DHA concentration at the microvillus membrane, MVM and a rapid dissociation of the DHA from the FABP. The model establishes the relations between the concentrations of the FABPs in the ST, their equilibrium dissociation constant from the DHA, and the placental DHA metabolic degradation rate, hitherto unknown. We conclude that the bound (to the protein) DHA molecule is degraded at a rate of 0.3–0.45 s−1.

Long-chain fatty acids cross a few membranes on their way from the capillary blood to the cardiomyocyte cytosol, where they are utilized as an essential source of energy. Details of the transport mechanism across those membranes remained elusive despite decades of laboratory and theoretical work. Here we inspect several optional scenarios for the crossing of the luminal membrane of the endothelial cell, the first barrier that should be crossed: a passive diffusion, facilitation by receptors for albumin and facilitation by fatty acids transporters. Related measured rate constants are incorporated in a theoretical simulation that is based on reaction–diffusion equations. Asymptotic analytical solutions for the resulting stiff boundary value problems are formulated based on singular perturbations theory. We conclude that a passive diffusion has to be supplemented with facilitation mechanisms in order to meet energy requirements. Binding sites for albumin, scattered on the membrane face, might enhance the flux provided that they internalize the captured fatty acids and speed up the dissociation of the albumin-fatty acids complex. As such enhancement is moderate, another mechanism seems to be essential for an adequate supply of fatty acids. Lack of experimental data prohibits us from computing the quantitative effect of membrane fatty acids transporters but their involvement in the membrane crossing is inferred.

AIMS:To characterize placental glucose delivery under normoglycemic conditions, gestational and pre-gestational diabetes and to relate the clinical data to theoretical predictions.METHODS:Data from 125 pregnancies: 50 normal gestations and 75 ones with various types of diabetes were collected. In parallel, we formulated a theoretical model for the transport of glucose under various diabetic conditions. Measured glucose blood levels were fed into the theoretical model that predicts glucose supply to the fetus and the results were confronted with measured fetal weights.RESULTS:Measured fetal weight and computed glucose delivery in gestational diabetic parturients resemble the situation in normal pregnancies. However, pre-gestational diabetes has a major effect as it involves heavier fetuses and enhanced computed glucose fluxes via placental membranes.CONCLUSIONS:Fetal weight (increased in pre-gestational and unaltered in gestational diabetes) correlates with the predicted rate of glucose delivery through the placenta.

Fatty acids are transported in a multistep process from the plasma to the mitochondria, where they are oxidized in order to meet energy requirements of the myocardium. Some of those steps, mainly the crossing of the involved cells’ membranes are far from being understood. Here, by means of mathematical modeling we address the problem of the fatty acid transport from the microvascular compartment to the endothelium. Values of parameters that are incorporated in the model are deduced from relevant experimental work. Concentration profiles are established as solutions of diffusion–reaction equations both numerically and using an analytical asymptotic approximation. The analytical solution accurately determines the fatty acid flux for any set of parameter values in contrast to off-the-shelf numerical solvers that fail under quite a few circumstances due to the stiffness of the differential equation system. Sensitivity analysis indicates that in spite of few uncertain parameter values, most of our conclusions are expected to be valid throughout the physiological range of operation. We find that in order to have an adequate fatty acid uptake rate it is essential for the luminal endothelial membrane to have very fast fatty acid transporters and/or specific sites that interact with the albumin-fatty acids complex.

The process of glucose transport via the placenta is not fully deciphered. Here, we apply a theoretical model to compute glucose fluxes via the terminal villi of the human placenta for various sets of parameter values and conclude on characteristics of transport across the two bordering membranes. Based on available measured data, the spatial geometry of the terminal villi is being simulated. Within this region, glucose concentrations and fluxes are computed by a numerical scheme that solves the diffusion equation with boundary conditions that account for transporter mediated diffusion at the membranes. Feasible parameter values (ones that induce physiological glucose fluxes) are determined for four optional symmetry characteristics of the membranes. Confronting computed results with clinical knowledge reveals the most plausible scenario-symmetric activity of the transporter at the microvillous membrane. Thus, sensitivity analysis of the computed results enables deduction about micro-scale mechanisms at the bordering membranes based on macro-scale knowledge.

Abdur Rub Abdur Rahman Kingsley Eromoses Abhulimen John Patrick Abraham Steven Abramowitch Ziad O. Abu-Faraj Memis Acar Judith Adams Klaus Affeld Anant Agrawal Guillermo Aguilar Shandar Ahmad Bummo Ahn Tabassum Ahsan Lisong Ai Santiago Aja-Fernandez Mustafa Akdis Mohammed P. Akhter Ata Akin Alptekin Aksan Ian G. Aldous Ahmed M. Al-Jumaily Kyle D. Allen Alejandro Almarza Jose Alvarez Rui Alves Manoel Alves Paulo Eduardo Ambrosio Amir A. Amini Jennifer R. Amos M. Andersen Charles Anderson Andrew Anderson Stelios Andreadis James F. Antaki Luca Antiga David Antonetti Mark Appleford Robert Appleyard George Archontis K. P. Arkill Antonis A. Armoundas Allison Arnold-Rife Theo M. G. J. Arts M. G. Ascenzi Bahman Asgharian Sara Assecondi Anand R. Asthagiri Krishna Asundi Gerard H. A. Ateshian Said H. Audi Bruno Averbeck Alberto Avolio Vibhudutta Awasthi Leon Axel Ali Azarbarzin Robert Azencott Keith Baar Abbas Babajani Stephen F. Badylak Sriram Balasubramanian J. Ballyns Peter Bannerman Zhirong Bao Gilda A. Barabino Danny Baranes Riccardo Barbieri Berj L. Bardakjian Roger C. Barr Efrath Barta Ward Bartels Cameron Bass Jason H. T. Bates Mathias Baumert Scott Beardsley Jacques Beaumont Khosrow Behbehani Marek Behr Essy Behravesh Jose Bernal Joel Berry Thor Besier Walter Grant Besio Anne Beuter Michael J. Bey Anastasios G. Bezerianos Archana Bhat Kristen Lawrence Billiar Ravi K. Birla Ruediger Blindt Guido Boerrigter Stephane Bolduc Harvey S. Borovetz Edward Botchwey Fergal Boyle Christoph Braun Audrius Brazdeikis Michael Breen Liam Breen Lori Bridal Mathias Brieu Gerd Brunner Stephanie Bryant Thomas Budinger William Buford, Jr. Joseph L. Bull P. Buma Laura Burattini Jason Burdick Monica Burdick Greg Burgreen Thomas Burkholder T. R. Bush Oguz Buskurt Bill Bussone Jonathan Butcher James Butler Ruggero Cadossi B. Calvo Jon Camp Lisa Marie Campana Michael R. Caplan Dana Carpenter Rupp Carriveau Gráinne T. Carroll Josh Cates Juan Raul Cebral Pietro Cerveri Mario Cesarelli Niranjan Chakravarthy V. S. Chakravarthy John Challis Rosa H. M. Chan Eric Chan Krishnan B. Chandran Shyang Chang W. Art Chaovalitwongse P. Bryant Chase George P. Chatzimavroudis Kinon Chen Xin Chen Huafu Chen Annals of Biomedical Engineering, Vol. 39, No. 2, February 2011 ( 2011) pp. 594–599 DOI: 10.1007/s10439-011-0251-3

The flow regime in the vicinity of oscillatory slender bodies, either an isolated one or a row of many bodies, immersed in viscous fluid (i.e. under creeping flow conditions) is studied. Applying the slender-body theory by distributing proper singularities on the bodies' major axes yields reasonably accurate and easily computed solutions. The effect of the oscillations is revealed by comparisons with known Stokes flow solutions and is found to be most significant for motion along the normal direction. Streamline patterns associated with motion of a single body are characterized by formation and evolution of eddies. The motion of adjacent bodies results, with a reduction or an increase of the drag force exerted by each body depending on the direction of motion and the specific geometrical set-up. This dependence is demonstrated by parametric results for frequency of oscillations, number of bodies, their slenderness ratio and the spacing between them. Our method, being valid for a wide range of parameter values and for densely packed arrays of rods, enables simulation of realistic flapping of bristled wings of some tiny insects and of locomotion of flagella and ciliated microorganisms, and might serve as an efficient tool in the design of minuscule vehicles. Its potency is demonstrated by a solution for the flapping of thrips.

The factors that affect and govern the glucose transfer from maternal blood to the fetus are not completely deciphered. We present a steady state, one dimensional mathematical simulation which integrates the main mechanisms that have been shown to exist: metabolic consumption of the placenta, simple and facilitated diffusion via the two membranes of the microvillous and simple diffusion within the placenta. The model uses all available physiologic data we could collect. Numerical results indicate that the most crucial factor in determining the fetal glucose concentration is the facilitated diffusion process at the basal membrane or, more specifically: the permeability of the basal membrane and the density of the transporter GLUT1 on its faces. The gradient between the maternal and the fetal glucose concentration is important as is the metabolic consumption of the placenta. The diffusion within the placenta and the conditions that prevail at the apical microvillous plasma membrane are much less significant. Intrasyncytial concentration of glucose is close to that of maternal blood. The adjustment of the fetal glucose concentration to abrupt changes of its surrounding is estimated to be quite rapid hence for all practical purposes this steady state model can serve as a reasonable approximation. Parameters that await experimental determination are identified.

Abbas Kader Abbas Shimon Abboud Mona Abdolrazaghi John Patrick Abraham Steven Abramowitch Nurettin Acýr R. H. Adamson Sudha Agarwal Guillermo Aguilar Tabassum Ahsan Metin Akay Mohammed P. Akhter Ata Akin Ian G. Aldous Adriano Mesquita Alencar Francisco Alencar, Jr. Ahmed M. Al-Jumaily Kyle D. Allen Alejandro Almarza Anton Amann Davide Ambrosi Paulo Eduardo Ambrosio Guillermo Ameer Farid Amirouche John Amoore Jennifer R. Amos Gary Chun-I An Mark Anderson Dr. Antaki Mariya Lyubenova Antonova Adamantios Arampatzis Theo M. G. J. Arts Bahman Asgharian Richard M. Aspden Janie Astephen Krishna Asundi Vassilis Athitsos Les Atlas Carl-Eric Aubin Said Audi Alberto Avolio Serap Aydin Evren U. Azeloglu Julia E. Babensee Chilman Bae Oswaldo Baffa Catalin Baicu James W. Baish K. Balakrishnan E. Baltali Peter Bandettini Gilda A. Barabino Abdul I. Barakat Kenneth A. Barbee Riccardo Barbieri Alex Barker Juan Gabriel Barra Efrath Barta Jennifer Barton James B. Bassingthwaighte Jason H.T. Bates Mathias Baumert Philip Bayly Scott Beardsley Jacques Beaumont Khosrow Behbehani Marek Behr Ruth Bellairs Ravi V. Bellamkonda Joanne M. Belovich Scott Anthony Berceli L. Bernardi A. Bernhardt Kamen Beronov Walter Grant Besio Margrit Betke Anne Beuter Michael J. Bey Rafael Beyar John C. Bischof Ashok Biyani Lindsay Black Brett Blackman Ruediger Blindt Evangelos Boutsianis Samuel Philip Bowen Alper Bozkurt Robert Brown L. Brubaker Eugene N. Bruce Stephanie Bryant Gregory Dale Buckner Joseph L. Bull Andrew J. Burghardt Greg Burgreen Jonathan Butcher Peter J. Butler A. R. Butler James Butler Chris Butson Paola Campadelli Michael R. Caplan Kristen O’Halloran Cardinal Luis Cardoso Brian E. Carlson Darrell Carney Dana Carpenter John Carroll David Carter Sarah Cartmell Theresa Cassino Francis Cassot John Challis Hunter Champion Kris Chan Warren Chan Krishnan B. Chandran Shyang Chang W. Art Chaovalitwongse John James Charonko Guillaume Charras George P. Chatzimavroudis Sara Checa Denis Chemla Kinon Chen Xiaoming Chen Jiande Chen Cheng-fu Chen Xuewen Chen Leo K. Cheng Boyle C. Cheng Jeffrey Tao Cheng Yan Chevalier D. Chhetri Charles T. M. Choi Alexander Chong Li-Shan Chou Edward Chow Eric Chern-Pin Chua Cheng-Jen Chuong Edward J. Ciaccio Annals of Biomedical Engineering, Vol. 38, No. 2, February 2010 ( 2010) pp. 550–555 DOI: 10.1007/s10439-009-9875-y

d = distance between two adjacent bodies within the row e = ellipsoid eccentricity l = rod half-length m = number of rods within a row p = pressure s = a point along the rods axis u = velocity vector u; v; w = components of velocity in the normal, n, tangential, s, and binormal, b, directions respectively ji s , j i s = intensities of Stokeslets and doublets at point s " = slenderness ratio of an individual rod = dynamical viscosity = density

The heart is the first organ to be function in the embryo. Life depends on the heart's ability to respond to the temporal demands of the organism for oxygen and nutrients for energetics and body heat maintenance. The cardiac system, denoted as the Cardiome, is a one-organ component of the Physiome, and represents the multi-parametric complexity of the multi-leveled cardiac system, from organ to molecules. The major elements of interest in this Organ can be grouped as Structure, State, Kinetics and Function .The next levels of interest, the Tissues, the Cells, the Organelles and the Molecular (including genetics) level can similarly be defined by structure, state, kinetics and function. Clearly, an awesome array of interacting micro and macro physiological parameters and functional characteristics! The uni-intra-level and inter-level interactions involve various transport phenomena (e.g. molecular diffusion, facilitated transport, trans-membrane channels, receptors etc) and energetics (e.g. metabolism, contraction, energy consumption, power and heat generation, electrical excitation, blood circulation etc) and, importantly, pathological factors affecting the cardiac function. The presentation includes a short review of biochemical and physiological system analyses approaches and two examples of sub-systems analyses: 1) organ -level system analysis and determination of the transmural temperature distribution in the left ventricular wall, based on transmural mechanics (stress, pressure), hemodynamical (blood perfusion) and metabolical (local oxygen consumption) distributions, and 2) cellular level modeling involving intracellular mechanics, metabolism and energy control via calcium transfer between the cellular compartments, the cytosol and the intra-cellular organelles (sarcomere, mitochondria and sarcoplasmic reticulum). The interrelation between intracellular power generation and energy consumption for whole organ functioning, contraction, metabolism and circulation will be highlighted. In summary: gaining insight and control of this complex multi-parameter, multi-leveled biological system requires the development of sophisticated programs and computational concepts for the integration of interacting functional models and application of novel experimental procedures.

We present a mathematical simulation which integrates the mechanisms that are currently believed to govern the concentration of the growth factor, IGF1, in cartilage. Articular cartilage is treated as a two-layer continuum: a thin surface layer, exposed to synovial fluid, with a higher cell density, and a deeper layer with impermeable bony endplate. A system of differential equations accounts for diffusion of IGF1 from synovial fluid into, and throughout, the cartilage; IGF1 synthesis, its reactions with soluble binding protein, with cell receptors, and with immobile binding sites on the extracellular matrix. We have collected all available physiologic data relevant to the solution of these equations and used it to compute numerical solutions that yield time dependent profiles for free and complex IGF1 throughout the depth of normal cartilage. Equations for osteoarthritic cartilage were formulated as well. Numerical results indicate a time-scale of several days for IGF1 profiles to settle down after a disturbance. The number of cell receptors for IGF1 appears to be more important than their rate of internalization. There is a lower bound to the number of cell receptors and of immobile binding sites. Parameters that await experimental determination are identified.

The flow through and around a finite row of parallel slender bodies in close proximity moving in a viscous incompressible fluid is studied. The motion occurs under creeping flow ($\hbox{\it Re}\,{\ll}\,1$) conditions. This row is a model of a comb-wing configuration found in insects of the Thrips family and being developed for use for flying vehicles of mm size, operating in the creeping flow regime. We show here that such wings utilize viscous effects to carry along enough fluid to approximate continuous surfaces. The comb is described as a row of rod-like ellipsoids of slenderness ratio smaller than 0.01 at distances apart of order 10 times the minor axis and the flow field is computed by distributing singularities along the major axes of the ellipsoids. Results for the drag on the individual rods, as well as for the full row are presented. It is shown that above a certain number of rods, dependent on the geometric parameters of the comb, the row acts very much like a continuous surface, with over 95% of the flow moving around, and not through the comb. This allows a potential saving of tens of percents in wing weight. Parametric results for number of rods, rod density (ratio of inter-rod distance to rod length) and slenderness ratio are presented demonstrating the dependence of the flow field on the configuration. It is found that 50–80 rods are required to approach the asymptotic limit of large number of rods, for various combinations of rod parameters with inter-rod distances of order of the cross-section diameter.

Facilitated transport is characteristic of most living systems, and usually involves a series of consecutive adjacent transfer regions, each having different transport properties. As a first step in the analysis of the multiregional problem, we consider in a single unstirred layer the facilitated diffusion of fatty acid ( F ) in albumin ( A ) solution under conditions of slow versus rapid association–dissociation, accounting for differing diffusivities of the albumin-fatty acid complex ( AF ). Diffusion gradients become established in an unstirred layer between a source of constant concentration of A , AF , and F in equilibrium, and a membrane permeable to F . The posited system does not reduce to a thin- or thick-layer approximation. The transient state is prolonged by slower on/off binding rates and by increasing the thickness of the unstirred layer. Solutions to transient and steady state depend upon the choice of boundary conditions, especially for thin regions. When there are two regions (each with its specific binding protein) separated by a permeable membrane, the steady-state fluxes and concentration profiles depend on the rates of association and dissociation reactions, on the diffusion coefficients, local consumption rates, and on the membrane permeability. Sensitivity analysis reveals the relative importance of these mechanisms. © 2000 Biomedical Engineering Society. PAC00: 8717Aa, 8715Kg