Modeling Fatty Acid Transfer from Artery to Cardiomyocyte
[['The heart acts as a pump to supply oxygenized blood to all organs in the body .', 'The energy required for cyclic contraction and relaxation of the cardiac muscle cells ( cardiomyocytes ) is provided by oxidation of blood-borne substrates .', 'Normally , long-chain fatty acids ( Fa ) , such as palmitate ( C16:0 ) and oleate ( C18:1 ) , constitute the major group of substrates for cardiac energy conversion [1 , 2] .', 'Fa , supplied to the heart by coronary arterial blood , travel from the capillary lumen through the endothelial and interstitial compartments to the cardiomyocytes .', 'As Fa are poorly soluble in water , carrier proteins ( Cp ) , like albumin in blood plasma and interstitial fluid and Fatty Acid Binding Proteins ( FABP ) in the cytoplasm of endothelial and cardiac muscle cells , are required to guarantee sufficient supply of Fa to the cardiomyocyte interior [3] .', 'Upon arrival in the cytoplasm of the cardiomyocytes , Fa are metabolized to acyl-CoA by mitochondrial acyl-CoA synthetase and subsequently oxidized inside the mitochondria for energy conversion , while part of the Fa moieties is incorporated in the cardiomyocyte triacylglycerol pool [1 , 2] .', 'In the past decades , several crucial steps in Fa uptake in the heart have been identified .', 'From the collective data , the following physiological concept emerges .', 'Coronary blood supplies Fa , predominantly bound to plasma albumin , to the myocardial capillaries almost exclusively by convection .', 'Due to the high affinity of albumin for Fa [4–6] with physiological albumin concentrations of 0 . 6–0 . 8 mmol l-1 , in blood plasma the concentration of total Fa ( 0 . 2–0 . 5 mmol l-1 ) exceeds that of free Fa by a factor of 105 .', 'Since the endothelium , lining the capillary lumen , is virtually impermeable to albumin [3] , Fa must detach from albumin before passing the endothelial cell membrane .', 'From capillary to cardiomyocyte interior , Fa permeate three phospholipid bilayers and three aqueous compartments .', 'The bilayers are the luminal and abluminal endothelial cell membranes and the cardiomyocyte membrane .', 'The aqueous compartments are the endothelial cytoplasm , the pericapillary interstitium , and the cardiomyocyte cytoplasm .', 'Transfer of Fa through membranes most likely occurs by diffusion [7] .', 'Because of the very low solubility of Fa in water [8] , transfer of Fa through the aqueous compartments occurs by carrier-mediated diffusion , implying temporary binding of Fa to a compartment-specific diffusible carrier protein Cp to form the complex CpFa [9] .', 'Another more well-known example of carrier-mediated diffusion is that of oxygen transport in blood , facilitated by hemoglobin .', 'Within the capillary compartment and interstitium , albumin plays the role of Cp .', 'Within the cytoplasm of the endothelial and cardiac muscle cells , low-molecular weight Fa binding proteins ( FABP ) are thought to facilitate Fa diffusion [10 , 11] .', 'Despite the importance of unimpeded Fa supply to the cardiomyocytes , physicochemical understanding of Fa transfer from plasma to the cardiomyocyte interior is still incomplete .', 'Bassingthwaighte and co-investigators [12 , 13] were the first to model the entire compound trajectory from arterial inflow to the site of metabolism in the cardiomyocyte , including the outflow of non-metabolized compound through the veins .', 'In the GENTEX version of this model [14] aqueous solutes permeate the endothelial cell membrane by diffusion , possibly supported by carrier-mediated transport .', 'In this model , however , transport of non-soluble Fa through the aqueous compartments was not considered to be a hindrance .', 'To fulfill the physiological needs of intra-myocardial Fa transfer , among others , the binding reaction of Fa to the Cp in intra- and extracellular fluids and the related carrier-mediated diffusion should be considered , but these aspects were not included in the GENTEX model .', 'Musters and colleagues [15] extended the GENTEX-type model to Fa transfer across the membrane .', 'Their model , however , only considered Fa to cross the cell membrane by a flip-flop mechanism .', 'They concluded that the flip-flop rate had to be very high for adequate cardiac Fa uptake .', 'Because of the fact that this rate was substantially higher than experimentally found by Cupp and coworkers [16] , Musters and colleagues introduced the involvement of a membrane-protein transporter , ignoring other aspects of importance in this Fa transfer , not necessarily requiring transporters .', 'Besides , only the sarcolemma was considered .', 'The shortcomings of Musters’ model were thoughtfully summarized by Kamp and Hamilton [17] .', 'Weisiger and co-investigators [18] designed a mathematical model of Fa ( oleate ) transfer from Cp ( albumin ) containing plasma through a stagnant water layer into a lipid space , representing the phospholipid bilayer of a cellular membrane .', 'Barta and co-investigators [19] described a numerical solution using slightly modified versions of Weisiger’s equations .', 'With this model , they evaluated the dependency of Fa transfer through the plasma-membrane boundary on the kinetics of Fa binding to Cp in capillary plasma near the endothelial membrane .', 'To the best of our knowledge , at present there is no model available that fully describes the transfer of lipophilic substances , such as Fa , from artery to cardiomyocyte , incorporating kinetics of Fa binding to Cp in all aqueous compartments with specific Fa and Cp concentration profiles in the boundary zones near the membranes and including Fa transfer through the phospholipid bilayers to be crossed .', 'The present study was designed to get better insight into the cardiac uptake , and myocardial transport and storage of Fa .', 'We have chosen for a unique quantitative modeling approach , incorporating the several interacting mechanisms based upon standard physical and physicochemical principles .', 'The model includes convection by flowing blood , diffusion through cell membranes and aqueous compartments , and metabolic conversion in the cardiomyocytes .', 'The aqueous compartments include plasma , endothelium , interstitium and the cardiomyocyte .', 'Fa are known to traverse aqueous compartments by carrier-mediated diffusion , involving binding of Fa to compartment-specific Cp , but none of the models presented so far incorporated this essential feature for lipophilic substances .', 'Furthermore , as main hindrances for Fa transfer , we consider the aqueous boundary zones on both sides of the membranes , where Fa bind to or detach from Cp .', 'When presenting a model of a physiological process , the design of the model should allow for experimental testing .', 'In the present study , we tested the model by comparing simulated and experimentally determined trans-coronary washout curves of radioactively-labeled albumin and Fa in a multiple indicator dilution experiment at different albumin and Fa concentrations in the coronary perfusate .', 'Such a comparison requires a model design that can handle time dependency of Fa concentrations in all compartments .'], ['To the best of our knowledge , we designed and tested for the first time a model of long-chain fatty acid ( Fa ) transfer through the coronary system and from coronary capillary to the cardiomyocyte that can handle dynamic changes in Fa concentration .', 'Capillary lumen , endothelial cell interior , pericapillary interstitium and the cardiomyocyte interior were handled as compartments .', 'The phospholipid membranes separating these compartments were considered to be passed by diffusion of free Fa .', 'Delivery of Fa to the cellular membrane surface can be achieved by two separate pathways: the detach pathway , i . e . , diffusion of free Fa , and the contact pathway , i . e . , the transfer of Fa from CpFa to the membrane by direct contact .', 'Applying standard physicochemical principles of convection , diffusion and reaction kinetics of Fa binding to compartment-specific carrier proteins , the transfer of Fa from capillary to cardiomyocyte appeared to be within the experimentally determined range , at least under the present experimental conditions .', 'Although this Fa transfer was achieved without the support of auxiliary proteins attached to or residing inside the cellular membrane , it cannot be excluded that the involvement of such proteins is required under higher cardiac loading conditions and , hence , an increased need for Fa as energy-rich substrates .', 'Their facilitating action is covered by the model parameter dCp , increasing the contribution of the contact pathway in overall Fa transmembrane transfer .', 'Three multiple tracer dilution experiments with labeled albumin and labeled Fa , carried out in the isolated rabbit heart , were simulated successfully .', 'We conclude that the present computational model is a useful tool to obtain quantitative information about cardiac uptake and intramyocardial transfer and storage of blood-borne Fa .'], ['The experiments with the rabbit hearts were performed in accordance with Guide for Care and use of laboratory animals published by the US National Institute of Health ( NIH publication Nr 85–23 ) .', 'In transferring Fa across the boundary from an aqueous fluid compartment into the phospholipid bilayer of a cellular membrane , the complex CpFa reaches the boundary zone by radial diffusion ( Fig 3 ) .', 'A small fraction of CpFa dissociates to form free Fa .', 'Approaching the boundary , transfer of Fa occurs increasingly by diffusion of free Fa at the cost of the fraction carried by carrier-mediated diffusion .', 'Since Fa disappear from the aqueous compartment at the boundary , free Cp moves back from the boundary zone into the aqueous bulk .', 'Besides this so-called detach pathway we consider the contact pathway , in which the complex CpFa delivers Fa by direct physical contact to the phospholipid membrane .', 'First , we will derive the equations , describing transfer of Fa through the boundary on the basis of the detach pathway only .', 'Thereafter , we add effects of the parallel contact pathway through direct contact of CpFa with the respective membrane .', 'Transfer of compounds through a boundary surface is generally quantified by flux φ in [mol m-2s-1] .', 'If we assume that a total Fa flux φFa , tot is forced to permeate the boundary into the phospholipid bilayer in steady state , then , at all distances x from the boundary , flux φFa , tot is constant and equal to the sum of complex Fa flux φCpFa and free Fa flux φFa:', 'φFa , tot=φCpFa ( x ) +φFa ( x )', '( 17 )', 'Note that coordinate z has been used for axial distance from the capillary entrance , and that coordinate x is perpendicular to z , pointing in the direction perpendicular to the membranes between the compartments .', 'For the derivation below we assume stagnancy of the fluid near the membrane boundary .', 'Assuming that concentrations at a given location do not change with time , an increase of CpFa flux along distance coordinate x implies that CpFa is formed at that location by binding of Fa to Cp .', 'This phenomenon is described by the following relation between the spatial gradient of flux φCpFa and the local rate of CpFa formation:', 'dφCpFa ( x ) dx=[Cp] ( x ) [Fa] ( x ) −[CpFa] ( x ) KCpFaKCpFa\u2009τCpFa', '( 18 )', 'Symbols KCpFa and τCpFa indicate equilibrium constant and dissociation time constant of the binding reaction of Fa to Cp , respectively .', 'Note that with continuous formation of CpFa there is no chemical equilibrium , implying that the right term of Eq ( 18 ) is not equal to zero .', 'For free Fa , free Cp and complex CpFa , flux depends on the location x relative to the membrane , the concentration gradient and the diffusion coefficients DFa and DCp:', 'φFa ( x ) =−DFad[Fa] ( x ) dx', '( 19 )', 'φCpFa ( x ) =−DCpd[CpFa] ( x ) dx', '( 20 )', 'φCp ( x ) =−DCpd[Cp] ( x ) dx', '( 21 )', 'Diffusion coefficients of free Cp ( DCp ) and the complex CpFa are considered to be the same , because mobility of the large Cp is assumed not to be influenced by carrying the relatively small Fa molecule .', 'Considering the detach pathway ( Fig 3 ) only , CpFa flux equals zero at the boundary , because the complex cannot enter the membrane at that location:', 'φCpFa ( 0 ) =0', '( 22 )', 'Using the software package Mathematica 7 ( Wolfram Research ) , we solved Eqs ( 17–22 ) analytically , while neglecting the terms in flux φFa , tot of the order of 2 and higher .', 'For [CpFa] as a function of distance x from the boundary , we found:', '[CpFa] ( x ) =[Cptot]−[Cp]0+φFa , tot ( −x+dFaex/dFa ) DCp ( 1+α )', '( 23 )', 'with α=DFaKCpFa[Cptot]DCp[Cp]02 and dFa≈DFaKCpFa\u2009τCpFa[Cp]0 Total Cp concentration [Cptot] is constant and equal to the concentration in the aqueous compartment .', 'Concentration [Cp]0 indicates the concentration of free Cp , as extrapolated linearly from the concentration profile in the aqueous bulk to the boundary .', 'Since gradients in concentration CpFa ( x ) are small ( Fig 3 ) , and [Cptot] is constant , gradients in the difference [Cp] ( x ) are small too .', 'Therefore , in Eq ( 23 ) , as a first approximation , we assumed a single value [Cp]0 to be representative of [Cp] ( x ) in general .', 'Variable α represents the ratio of Fa transfer by diffusion of free Fa relative to transfer by carrier-mediated diffusion far from the membrane boundary .', 'Commonly , α is much smaller than 1 , e . g . , in the capillary plasma α<0 . 002 .', 'Variable dFa represents the distance constant of exponential decay in the boundary zone .', 'The solution for fluxes and concentrations as a function of x is presented graphically in Fig 3 , panels B-D .', 'As indicated above , by neglecting the contact pathway ( Fig 3 ) for Fa transfer , complex flux φCpFa ( 0 ) equals zero at the boundary according to Eq ( 22 ) .', 'By allowing CpFa to deliver Fa to the membrane by direct physical contact , we introduce a new boundary condition , located at xb , so that we can still use the solution of the differential equations as presented above .', 'At this new boundary , CpFa delivers free Fa to the phospholipid surface , while free Cp returns into the aqueous boundary zone .', 'Thus , CpFa flux is converted to an equal free Fa flux into the membrane and an equal free Cp flux in backward direction .', 'In the state of equilibrium without Fa flux , both the detach pathway and the contact pathway bear no flux , because flux cannot be circular without adding external energy .', 'In the presence of Fa-flux , at boundary xb , CpFa flux is proportional to the deviation from the state of equilibrium .', 'Thus Eq ( 22 ) is replaced by the following boundary equation , using Eq ( 18 ) to define the deviation from the state of zero flux equilibrium:', 'φCpFa ( xb ) =\u2009dCp ( [Fa] ( xb ) [Cp] ( xb ) −KCpFa[CpFa] ( xb ) KCpFa\u2009τCpFa )', '( 24 )', 'Note that membrane reaction rate parameter dCp represents the product of τCpFa and the ratio of Fa flux due to CpFa dissociation at the membrane surface and the CpFa concentration in the aqueous boundary zone in virtual absence of any free Fa in the membrane .', 'Parameter dCp appears to have the physical dimension of a distance , expressing membrane dissociation rate versus bulk dissociation rate of CpFa .', 'Now we search for a distance xb in the solution as represented by Eq ( 18 ) , so that the boundary condition in Eq ( 24 ) is satisfied exactly .', 'Substitution of Eq ( 18 ) in Eq ( 24 ) yields', 'φCpFa ( xb ) =dφCpFa ( xb ) dxdCp', '( 25 )', 'Substitution of the x-derivative of Eq ( 23 ) in Eq ( 20 ) yields', 'φCpFa ( x ) =φFa , tot1−ex/dFa1+α', '( 26 )', 'Substitution of φCpFa ( x ) obtained from Eq ( 26 ) into the left and right term of Eq ( 25 ) renders a solution for xb , so that the boundary condition Eq ( 24 ) is satisfied:', 'xb=−dFaln ( 1+dCp/dFa )', '( 27 )', 'Note that if dCp<<dFa , approximation xb ≈ -dCp may be used .', 'In Fig 3 , related solutions for concentrations [CpFa] ( x ) and [Fa] ( x ) and fluxes φCpFa ( x ) and φFa ( x ) are shown graphically .', 'For zero flux φFa , tot , [Fa] equals the equilibrium concentration for the given [Cptot] and [Cp]0 , resulting in [Fa]equ = KCpFa ( [Cptot]/[Cp]0−1 ) .', 'In the presence of Fa-flux , [Fa] depends on x by adding to the equilibrium concentration a term proportional with flux φFa , tot .', 'The proportionality factor is found by integration of flux φFa ( x ) according to Eq ( 19 ) , while using φFa ( x ) = φFa , tot—φCpFa ( x ) according to Eq ( 17 ) .', 'The solution for flux φCpFa ( x ) is presented in Eq ( 26 ) .', 'Thus for concentration [Fa] ( x ) , it is derived:', '[Fa] ( x ) =kCpFa ( [Cptot][Cp]0−1 ) −φFa , totdFaex/dFa\u2009+α\u2009x ( 1+α ) DFa', '( 28 )', 'Permeability P of a layer with thickness h equals the ratio of flux divided by the Fa-concentration drop from point x = -h+xb to point x = xb .', 'For a given flux φFa , tot with Eq ( 28 ) , [Fa] is calculated for x = xb and x = xb+h , being used to calculate the drop of [Fa] .', 'Permeability P equals flux divided by [Fa]-drop , resulting in:', 'P=11/Pb+1/Paqu', '( 29 )', 'with Pb= ( 1+α ) ( 1−e−h/dFa ) DFadFa ( 1+dCpdFa ) ≈DFadFa ( 1+dCpdFa ) and Paqu=1h ( DFa+DCp[Cp]02\u2009kCpFa[Cptot] ) Permeability Pb represents the effect of detachment of Fa from CpFa in a thin aqueous layer in the boundary zone , in close vicinity of the cellular phospholipid membrane , the thickness of which is determined by decay distance constant dFa ( Eq 23 , e . g . in Fig 3 dFa = 7 nm ) .', 'Permeability Paqu represents the effect of carrier-mediated diffusion in the aqueous layer , excluding boundary effects .', 'The resulting equations for Pb and Paqu are presented by Eqs ( 6 ) and ( 8 ) , respectively .', 'Often α<<1 and h>>dFa , so that for Pb the approximation can be used as indicated in Eq ( 29 ) .', 'In the derivation , flux is assumed to be directed from aqueous bulk into the membrane .', 'The derivation is also valid for a negative sign of the flux , implying that calculated permeabilities are also valid for Fa-flux from membrane to aqueous compartment , e . g . , occurring in the boundary zone on the other side of the membrane .', 'Capillary length dispersion is described by a Gaussian distribution of the logarithm of capillary length z , resulting in the probability density function plen ( z )', 'plen ( z ) =1z\u2009σcapπexp ( − ( σcap4+ln ( z/z0 ) σcap ) 2 )', 'with', '∫0∞plen ( z ) dz=1', '( 30 )', 'Symbols z0 and σcap indicate mean length and relative dispersion , respectively .', 'Assuming that all capillaries have the same diameter , total capillary cross-sectional area Acap ( z ) is proportional to the number of capillaries , longer than length z .', 'So , for small z , all capillaries are included , implying that Acap ( z ) is maximal , while with increasing z ever more short capillaries become excluded , eventually causing Acap ( z ) to decrease to zero .', 'At the capillary entrance , Acap ( 0 ) equals total capillary volume Vcap divided by mean capillary length z0 .', 'Thus by backward integration of plen ( z ) it is found:', 'Acap ( z ) =Vcapz0∫z∞plen ( z ) dz', '( 31 )', 'Substitution of Eq ( 30 ) into Eq ( 31 ) , followed by determination of the integral , results in Eq ( 9 ) .', 'Besides Acap , the capillary wall area available for diffusion ( dScap ( z ) /dz ) is also proportional to the number of capillaries as a function of z , resulting in Eq ( 11 ) .', 'Supposing that the arterio-venous blood pressure drop is the same for all capillaries , we assumed that blood flow velocity is inversely proportional to the length of the capillary .', 'Defining qtot to be the sum of blood flow in all capillaries at the entrance , for capillary blood flow qcap ( z ) it follows:', 'qcap ( z ) =qtot∫z∞plen ( z ) zdz/∫0∞plen ( z ) zdz', '( 32 )', 'Substitution of Eq ( 30 ) into Eq ( 32 ) results in Eq ( 10 ) .', 'Mean capillary blood flow velocity v ( z ) is calculated as total blood flow qcap ( z ) divided by total cross-sectional area Acap ( z ) ( Eq 12 ) .', 'Normalized capillary wall surface S ( z ) is found by integration of normalized Acap ( z ) to variable z .', 'This function is used in Eq ( 11 ) .', 'Fig 6 shows the z-dependent functions plen , and the normalized values of Acap , qcap , dqcap/dz and Scap , as represented by A , q , dq/dz and S , for relative dispersion of capillary length σcap = 0 . 5 ( Eq 30 ) .', 'In the model of Fa transfer from capillary to cardiomyocyte , many parameters were obtained from experimental data .', 'Recently , we assessed the myocardial volume fractions of compartments , the surface areas for diffusion and the thicknesses of diffusion layers , as summarized in Table 1 [23] .', 'In solving differential equation Eq ( 4 ) with Eq ( 7 ) , for the scaling constant Scap , tot/Vcap in Eq ( 11 ) we substituted the experimentally determined ratio Scap/Vcap as can be derived from Table 1 .', 'Capillary length dispersion σcap in Eqs ( 9 and 10 ) was taken to be 0 . 5 .', 'The volume fraction of the compartments is related to total volume Vall , being the sum of tissue compartments including all blood compartments .', 'Area S is attributed to thin and flat structures .', 'Permeability thickness hdiff of the thin and flat compartments ec and is1 is representative of the thickness for diffusion .', 'It is determined as the reciprocal of the mean of reciprocals of compartment thickness .', 'Since the is2 compartment is flat , we could attribute a mid-compartment surface to it , parallel to the cardiomyocyte membranes on both sides .', 'In Table 2 , physicochemical properties of myocardial constituents are summarized .', 'Most data is obtained from literature .', 'First the values of the general properties are presented , followed by those related to the specific ones per compartment , mostly because type and concentration of Cp vary between compartments .', 'Compartments cap and is1 are combined because in both compartments albumin fulfills the role of Cp .', 'For many physicochemical properties estimates were used , because no data is available about the true values .', 'The diffusion coefficient DCp , cap of albumin in plasma is derived from bovine albumin .', 'Decay time constant τCpFa , cap of the Alb-Fa complex is estimated , but the true value is a matter of debate .', 'About the dissociation time of the other CpFa complexes no information is available .', 'The membrane reaction rate parameter dCp , having the physical dimension of length , is not known for any fluid-membrane interface .', 'For small values of dCp relative to dFa , dCp is approximately equal to the virtual distance shift xb ( Eq 27 ) of the membrane boundary towards the aqueous compartment .', 'As a primary estimate , we assumed the value of this parameter to be equal to the average radius of the CpFa complex [36] .', 'The diffusion coefficients of the Cp in the ec and myo compartment are assumed to be twice that of albumin , because their molecular weight is about one quarter of that of albumin .', 'The albumin concentration in the is1 compartment is normally about 70–86% of that in the capillary plasma [32] .', 'We used the data of Tschubar et al [29] , because they found the ratio of 86% to be valid in a large range of arterial Alb concentrations ( 0 . 033–0 . 394 mol m-3 ) .', 'The Cp concentration in the endothelium is known to be less than 4% of the FABP concentration in the cardiomyocyte [30] , but accurate data is not available .', 'According to our model , the concentration should not be much less , because then the Cp concentration may be too low to fulfill the role of carrier protein for Fa .', 'However , if the decay time constant of the endothelial CpFa complex is smaller than that of albumin in the capillary lumen , the same boundary permeability can be obtained with lower Cp concentrations ( Eq 6 ) .']]
['Introduction', 'Discussion', 'Materials and Methods']
['Despite the importance of oxidation of blood-borne long-chain fatty acids ( Fa ) in the cardiomyocytes for contractile energy of the heart , the mechanisms underlying the transfer of Fa from the coronary plasma to the cardiomyocyte is still incompletely understood .', 'To obtain detailed insight into this transfer process , we designed a novel model of Fa transfer dynamics from coronary plasma through the endothelial cells and interstitium to the cardiomyocyte , applying standard physicochemical principles on diffusion and on the chemical equilibrium of Fa binding to carrier proteins Cp , like albumin in plasma and interstitium and Fatty Acid-Binding Proteins within endothelium and cardiomyocytes .', 'Applying these principles , the present model strongly suggests that in the heart , binding and release of Fa to and from Cp in the aqueous border zones on both sides of the cell membranes form the major hindrance to Fa transfer .', 'Although often considered , the membrane itself appears not to be a significant hindrance to diffusion of Fa .', 'Proteins , residing in the cellular membrane , may facilitate transfer of Fa between Cp and membrane .', 'The model is suited to simulate multiple tracer dilution experiments performed on isolated rabbit hearts administrating albumin and Fa as tracer substances into the coronary arterial perfusion line .', 'Using parameter values on myocardial ultrastructure and physicochemical properties of Fa and Cp as reported in literature , simulated washout curves appear to be similar to the experimentally determined ones .', 'We conclude therefore that the model is realistic and , hence , can be considered as a useful tool to better understand Fa transfer by evaluation of experimentally determined tracer washout curves .']
['The energy required for pump work of the heart is generated primarily by oxidation of long-chain fatty acids ( Fa ) , transferred to the heart by plasma albumin .', 'In coronary capillaries , Fa detach from albumin , cross endothelial cells , pericapillary interstitium and cardiomyocyte membrane prior to oxidation .', 'The exact mechanism underlying the transfer process , however , is unknown .', 'We designed a computer model of this Fa transfer using parameter values in the physiological range .', 'We postulate that known physical principles of diffusion , Fa-protein complex binding , and Fa solubility in water and lipid membranes can describe intra-cardiac transfer .', 'Model simulations were compared with multiple indicator dilution experiments , administrating a bolus of labeled Fa and albumin into the coronary artery .', 'The resulting dilution time courses of label concentrations in the coronary veins compared favorably with the model simulations .', 'We conclude that the model appears to be realistic , providing a useful tool to study in detail the mechanisms of intra-cardiac Fa transfer .']
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