Transcapillary transport of water, small solutes and proteins during hemodialysis

The semipermeable capillary walls not only enable the removal of excess body water and solutes during hemodialysis (HD) but also provide an essential mechanism for maintaining cardiovascular homeostasis. Here, we investigated transcapillary transport processes on the whole-body level using the three-pore model of the capillary endothelium with large, small and ultrasmall pores. The transcapillary transport and cardiovascular response to a 4-h hemodialysis (HD) with 2 L ultrafiltration were analyzed by simulations in a virtual patient using the three-pore model of the capillary wall integrated in the whole-body compartmental model of the cardiovascular system with baroreflex mechanisms. The three-pore model revealed substantial changes during HD in the magnitude and direction of transcapillary water flows through small and ultrasmall pores and associated changes in the transcapillary convective transport of proteins and small solutes. The fraction of total capillary hydraulic conductivity attributed to ultrasmall pores was found to play an important role in the transcapillary water transport during HD thus influencing the cardiovascular response to HD. The presented model provides a novel computational framework for a detailed analysis of microvascular exchange during HD and as such may contribute to a better understanding of dialysis-induced changes in blood volume and blood pressure.


THREE-PORE MODEL OF THE CAPILLARY WALL
Fluid filtration from the capillary compartment to the interstitial compartment depends on the imbalance between the Starling forces acting across the capillary walls [1]: the hydraulic capillary blood pressure, the hydrostatic interstitial pressure and the osmotic (mainly oncotic) pressures exerted by all solutes on both sides of the capillary wall [2,3]. In the three-pore model (3PM) the transcapillary filtration needs to be defined separately for each type of pore (Ji) as follows: where LpS is the whole-body hydraulic conductivity of capillary walls (assumed constant), αi is the fraction of LpS contributed by the i-th type of pore (αLP + αSP + αUP = 1), Psc is the mean hydraulic pressure of systemic capillary blood, Pis is the hydrostatic pressure of the interstitial fluid, σp,i and σs,i are the Staverman's reflection coefficients of protein p and solute s at the i-th pore, πp,pl,sc and πp,is are the oncotic pressures (colloid osmotic pressures) of protein p (albumin or globulins) in the capillary plasma and interstitial fluid, φs is the osmotic activity coefficient of solute s, αs is the Gibbs-Donnan coefficient for ion s with charge zs (for simplicity αs=α Zs [8], where α is determined from the steadystate conditions), and RT is a constant (= 19.3 mmHg/mmol/L). ( It was assumed that the mean hydraulic pressure of capillary plasma (Psc) is resistant to isolated changes in arterial pressure (the auto-regulatory capacity of the capillary bed), whereas 80% of changes in venous pressure are transmitted to the capillaries [4]. Psc is hence calculated as: where Psc,0 is the initial mean capillary pressure calculated from the initial steady-state conditions, wv is a parameter (assumed value of 0.8, based on experimental data [4]) and Psv,0 is the assumed initial (normal) pressure in the small veins compartment (12 mm Hg [4]).
The hydrostatic pressure of the interstitial fluid was described as a linear function of the interstitial volume [2,5]: where Pis,n is the normal interstitial pressure corresponding to the normal interstitial volume (Vis,n) and Cis is the interstitial compliance, which was assumed to be 12% of normal interstitial volume per mm Hg [6].
The plasma oncotic pressure (in mm Hg) exerted by albumin (πalb,pl,sc) and globulins (πglob,pl,sc) are calculated using the following equations [4] (based on Landis-Pappenheimer equations [7] where cp,sc is the total protein concentration in capillary plasma in g/dL, whereas asc and bsc are variable albumin and globulins mass fractions of total plasma proteins (asc + bsc = 1).
Similar equations were used for calculating the oncotic pressure of interstitial albumin and globulins based on the total concentration of proteins in the interstitial compartment (cp,is) and the corresponding ais and bis fractions (also variable).
The transcapillary transport of small solutes (except other anions) through the i-th type of pore can be described as a sum of diffusive and convective flows using the following equation [ where PSs,i is the permeability-surface product for solute s at the i-th type of pore (assumed constant), αs is the Gibbs-Donnan coefficient for ion s, cs,pl,sc and cs,is are the concentrations of solute s in the capillary plasma and interstitial fluid, Fpl,sc and Fis are variable water fractions of the capillary plasma and interstitial fluid, Jw,i is the water flow through i-th pore from capillaries to interstitium (calculated as the difference between fluid filtration and the volumetric flow of convective protein leakage), Ss,i is the sieving coefficient for solute s at the i-th type of pore and fs,i is defined as follows [ where λs,i is the ratio of solute and pore radii (λs,i = rs/ri).
Analogically, the transport of protein p through each type of pore is using the diffusive-convective equation [8,10] ( 11 ) where p denotes albumin or globulins, PSp,i is the permeability-surface product of the lumped capillary wall for protein p (assumed constant), Ji is the rate of fluid filtration from the capillaries to the interstitium through i-th type of pore, Sp,i is the capillary sieving coefficient of protein p, and fp is defined as in the equation (8).
The transport of other anions (A 2-) is calculated to obtain a zero net flow of charge across the capillary wall.
The volumetric flow of proteins from capillary plasma to interstitium through i-th type of pore is calculated as: where MWp is the molecular weight of protein p (assumed 69,000 g/mol for albumin and 170,000 g/mol for globulins [11,12]) and ρp is the protein density (assumed 1.37 g/cm 3 for both albumin and globulins [13]).
The permeability-surface product for solute s and the i-th type of pore is calculated from the following equation [ where NA is the Avogadro number, rs is the solute radius and ηH2O is water dynamic viscosity at 37 o C (=0.0007 Pa·s), A0,i is the total cross-sectional area of pores of type i, Ai is the effective pore area available for restricted