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J L Stephenson

Publications and source records attributed to J L Stephenson.

At least 37 records · Page 2Linked to original sources
PubMed1995

Convective uphill transport of NaCl from ascending thin limb of loop of Henle.

In this paper we describe a mathematical model of the renal inner medulla based on a previously proposed model [A.S. Wexler, R.E. Kalaba, and D.J. Marsh. Am. J. Physiol. 260 (Renal Fluid Electrolyte Physiol. 29): F368-F383, 1991] in which in the inner medullary ascending thin limb of Henle's loop (ATL) and collecting duct (CD) exchange with a local capillary node with the reabsorbed water and solutes flowing radially toward a central vascular bundle. Our model differs in that ascending and descending vasa recta and surrounding interstitial space are replaced by a central core. Our analysis of the coupled ATL-CD system shows that it is theoretically capable of transporting NaCl out of the ATL into the central vascular space (approximated by the central core) against a concentration gradient, which in the absence of radial diffusion can be arbitrarily large. By numerical solution of the model with the radial diffusion coefficient (D(r)) for NaCl of 0, we find that the ATL can be more than 100 mosmol/l hypotonic with respect to the core. We also find that with restricted diffusion the osmolality of the CD at the papilla is significantly greater than that of the loop of Henle. As D(r) approaches the diffusion coefficient of NaCl in free solution, the osmolality of the loop increases and that of the CD decreases. Thus, overall, contrary to intuitive expectations, the radial separation and uphill transport of NaCl do not give any significant increase in loop concentration, which depends primarily on the quantity of urea reabsorbed from the CD.

Animals↗
PubMed1995

Comparison of central core and radially separated models of renal inner medulla.

In this paper we describe the effect of partitioning exchange of ascending thin limb (ATL) and collecting duct (CD) between a central vascular space (CORE) and a radially separated capillary node (NODE) in a mathematical model of the concentrating mechanism of the renal inner medulla. A detailed description of the model has been provided [J. L. Stephenson, J. F. Jen, H. Wang, and R. P. Tewarson. Am. J. Physiol. 268 (Renal Fluid Electrolyte Physiol. 37): F680-F692, 1995]. We define a partition coefficient theta, which denotes the fractional exchange of CD and ATL with the NODE. Thus with theta = 0 we have a central core model, in which the ATL and CD exchange with the CORE only, and with theta = 1 we have a totally radially separated model, in which the ATL and CD exchange with the NODE only. Decreasing the partition coefficient from 1 to 0 effects a continuous transition from a totally radially separated model to a central core model. As this transition progresses with increasing exchange with the CORE, the osmolalities in all structures become nearly the same at the papilla, and the ability to transport salt uphill is lost. This is true even with no radial diffusion. However, radial diffusion and direct exchange with the CORE act synergistically in decreasing osmolality differences at the papilla and the capacity for convective uphill transport. These are lost in a more or less parallel way. There is, however, no significant concomitant change in concentrating ability. These results indicate that models with radial mixing of the interstitial vascular space are probably reasonably good approximations for the inner medulla.

Animals↗
PubMed1995

Effect of vasa recta flow on concentrating ability of models of renal inner medulla.

In this study we extend the analysis of the preceding two studies [J. L. Stephenson, J. F. Jen, H. Wang, and R. P. Tewarson. Am. J. Physiol. 268 (Renal Fluid Electrolyte Physiol. 37): F698-F709, 1995; and J. F. Jen, H. Wang, R. P. Tewarson, and J. L. Stephenson. Am. J. Physiol. 268 (Renal Fluid Electrolyte Physiol. 37): F000-F000, 1995] to a model that includes vasa recta. Distribution of nephron and vasa recta lengths is represented by shunting from descending to ascending flow. It is found that the effect of radial separation of structures on concentrating ability is closely linked to vasa recta flow. With minimal or no vasa recta flow the extent of radial mixing has little effect on concentrating ability. As vasa recta flow increases, concentrating ability is decreased by radial mixing. Convective uphill transport of NaCl is again observed, but concentrating ability appears to depend primarily on urea delivery to the inner medulla from the collecting duct rather than on the mechanism of salt transport out of thin ascending limb. Central core models give an upper bound on concentrating ability but do not attain the maximum urine osmolality of the rat with experimental values of tubular permeabilities.

Animals↗
PubMed1994

Externally driven countercurrent multiplication in a mathematical model of the urinary concentrating mechanism of the renal inner medulla.

Substitution of measured permeabilities into mathematical models of the concentrating mechanism of the renal inner medulla yields less than the known urine osmolalities. To gain a better understanding of the mechanism we analyse a model in which a force of unspecified origin [expressed as fraction, epsilon, of entering descending thin limb (DTL) concentration] drives fluid from DTL to interstitial vascular space (CORE), thus concentrating the solution in DTL. When flow in the DTL reverses at the hairpin bend of the loop of Henle, the high solute permeability of ascending thin limb (ATL) permits solute to diffuse into the CORE thus permitting epsilon to be multiplied many-fold. Behavior of the model is described by two non-linear differential equations. In the limit for infinite salt permeability of ATL the two equations reduce to a single equation that is formally identical with that for the Hargitay and Kuhn multiplier, which assumes fluid transport directly from DTL to ATL (Z. Electrochem. Angew. Phys. Chem. 55, 539, 1951). Solutions of the equations describing the model with parameters taken from perfused thin limbs show that urine osmolalities of the order of 5000 mosm L-1 can be generated by forces of the order of 20 mosm L-1. It seems probable that mammals including desert rodents use some variant of this basic mechanism for inner medullary concentration.

Animals↗
PubMed1992

A mathematical model of the rabbit cortical collecting tubule.

The epithelium of the cortical collecting tubule of the rabbit is represented as four well-stirred compliant compartments corresponding to principal cell, alpha- and beta-intercalated cells, and lateral interspace. Model variables include the concentrations of Na, K, Cl, and HCO3, pH, cell volume, and electrical potential. The model equations specify mass conservation and chemical equilibrium for buffer reactions. Ionic conductance is represented by the Goldman constant-field equation. For the intercalated cells, phenomenological expressions describing the proton pumps are structured to agree with data of O. S. Andersen, J. E. N. Silveira, and P. R. Steinmetz (J. Gen. Physiol. 86: 215-234, 1985) in the turtle bladder. Coupled transport via Na/H and Cl/HCO3 exchangers is represented according to the formalism of linear nonequilibrium thermodynamics. To construct the tubule model, the flat epithelium is wrapped into a cylinder, creating a luminal compartment. Luminal variables include volume flow, hydrostatic pressure, electrical potential, and ionic concentrations. A specific aim of this investigation was to simulate the capability of the epithelium to maintain Na reabsorption in the presence of low luminal salt concentration. In this regard, critical features of the model include tight junctional conductance and the apical Na permeability of the principal cell. In particular, we examine a principal cell apical Na permeability inversely dependent on luminal and intracellular Na concentrations (M. M. Civan and R. J. Bookman. J. Membr. Biol. 65: 63-80, 1982). This concentration-dependent permeability together with a low junctional conductance produces three results congruent with experimental data: 1) dilution of luminal Na and maintenance of reabsorptive Na transport despite a steep transtubular gradient, 2) a relatively constant level of K secretion over a wide range of luminal Na concentrations, and 3) a relatively constant transepithelial potential over this range of luminal Na.

Absorption↗
PubMed1992

Regulation of K transport in a mathematical model of the cortical collecting tubule.

The effect of luminal flow rate and peritubular pH on Na and K transport is investigated in a mathematical model of the rabbit cortical collecting tubule. The model is used to simulate a 0.4-cm segment of tubule comprised of principal cell, alpha- and beta-intercalated cells, and lateral interspace. Calculations produce luminal profiles of Na, K, Cl, HCO3, and phosphate, as well as of electrical potential and pH. Parameter sets are developed that permit representation of both unstimulated and deoxycorticosterone acetate-stimulated tubules. A series of simulations is performed in which initial luminal flow rate is varied over the range of values between 0.1 and 30 nl/min. A marked flow-dependent enhancement of Na reabsorption and K secretion is seen, especially at lower flows, while Cl and HCO3 transport remain relatively constant. In experimental studies, it has been observed that metabolic alkalosis stimulates and metabolic acidosis inhibits K secretion, while leaving Na transport relatively unaffected [B. A. Stanton and G. Giebisch. Am. J. Physiol. 242 (Renal Fluid Electrolyte Physiol. 11): F544-F551, 1982; K. Tabei, S. Muto, Y. Ando, Y. Sakairi, and Y. Asano. J. Am. Soc. Nephrol. 1: 693, 1990; and K. Tabei, S. Muto, H. Furuya, and Y. Asano. J. Am. Soc. Nephrol. 2: 752, 1991]. Model calculations indicate that, when ion permeabilities are fixed and not dependent on pH, the impact of peritubular HCO3 on K secretion cannot be simulated. When junctional Cl permeability decreases with increasing interspace pH (E. M. Wright and J. M. Diamond. Biochim. Biophys. Acta 163: 57-74, 1968) in the model, there is a marked stimulation of K secretion with alkalosis and inhibition with acidosis. Furthermore, inclusion of a pH-dependent apical Na permeability [L. G. Palmer and G. Frindt. Am. J. Physiol. 253 (Renal Fluid Electrolyte Physiol. 22): F333-F339, 1987] that increases with increasing principal cell pH significantly reduces the change in Na+ reabsorption seen with the pH-dependent junctional Cl permeability alone. In these calculations, a pH-dependent apical K permeability [W. Wang, A. Schwab, and G. Giebisch. Am. J. Physiol. 259 (Renal Fluid Electrolyte Physiol. 28): F494-F502, 1990] that increases with increasing principal cell pH shows relatively little impact on K secretion.

Animals↗
PubMed1990

Volume-activated chloride permeability can mediate cell volume regulation in a mathematical model of a tight epithelium.

Cell volume regulation during anisotonic challenge is investigated in a mathematical model of a tight epithelium. The epithelium is represented as compliant cellular and paracellular compartments bounded by mucosal and serosal bathing media. Model variables include the concentrations of Na, K, and Cl, hydrostatic pressure, and electrical potential, and the mass conservation equations have been formulated for both steady-state and time-dependent problems. Ionic conductance is represented by the Goldman constant field equation (Civan, M.M., and R.J. Bookman. 1982. Journal of Membrane Biology. 65:63-80). A basolateral cotransporter of Na, K, and Cl with 1:1:2 stoichiometry (Geck, P., and E. Heinz. 1980. Annals of the New York Academy of Sciences. 341:57-62.) and volume-activated basolateral ion permeabilities are incorporated in the model. MacRobbie and Ussing (1961. Acta Physiologica Scandinavica. 53:348-365.) reported that the cells of frog skin exhibit osmotic swelling followed by a volume regulatory decrease (VRD) when the serosal bath is diluted to half the initial osmolality. Similar regulation is achieved in the model epithelium when both a basolateral cotransporter and a volume-activated Cl permeation path are included. The observed transepithelial potential changes could only be simulated by allowing volume activation of the basolateral K permeation path. The fractional VRD, or shrinkage as percent of initial swelling, is examined as a function of the hypotonic challenge. The fractional VRD increases with increasing osmotic challenge, but eventually declines under the most severe circumstances. This analysis demonstrates that the VRD response depends on the presence of adequate intracellular chloride stores and the volume sensitivity of the chloride channel.

Animals↗
PubMed1989

Electrolyte, urea, and water transport in a two-nephron central core model of the renal medulla.

A one-nephron model has been extended to include both short-looped and long-looped nephrons. Variables are volume flow, Na+, K+, Cl-, urea, hydrostatic pressure, and electric potential. The ratio of short-to-long-looped nephrons, one of the parameters of the model, is 5 to 1. With either rabbit or hamster permeability data from perfusion experiments, the model develops an osmolality of approximately 600 mosmol/l at the junction of inner and outer medulla but no osmolality gradient in the inner medulla. With the rabbit data, osmolalities in excess of 1,000 mosmol/l can be generated in the papilla with no active transport if urea permeabilities are less than 10(-5) cm/s; with the hamster data, electrolyte permeabilities must also be reduced. With these modified parameters, urea concentrations are less in the long loops than has been found on micropuncture. These can be increased to experimental levels by increasing the urea permeability and decreasing the hydraulic permeability of thin descending limbs in the inner half of the inner medulla, but to maintain loop osmolality at 1,000 mosmol/l it is necessary to postulate active NaCl transport in thin ascending limbs in the outer half of the inner medulla. This gives an alternative mode of concentration without active transport in the inner half of the inner medulla, in which electrolytes diffuse out of and urea diffuses into both limbs of Henle's loop and mix in the core with urea and water entering from the collecting duct. Concentration in either mode requires significant modification of perfusion data.

Animals↗
PubMed1989

Renal actions of atrial natriuretic factor: a mathematical modeling study.

Atrial natriuretic factor (ANF) is a peptide hormone that increases renal NaCl and water excretion. Several renal sites of ANF action have been identified, but general agreement has not been reached concerning the quantitative contribution of each action to the natriuresis and diuresis. Using a five-nephron central core model of NaCl, urea, KCl, and water transport in the rat kidney, we have quantitatively evaluated the hypothetical effects on whole kidney function of three experimentally observed ANF actions: 1) inhibition of active NaCl absorption in the collecting duct, 2) inhibition of osmotic water permeability in the collecting duct, and 3) increased NaCl and water delivery out of the proximal convoluted tubule simulating an increase in glomerular filtration rate. The simulations show that inhibition of collecting duct active NaCl absorption by greater than or equal to 50% can increase NaCl and water excretion to levels that match experimental values. In addition, the model predicted that the urinary sodium concentration will increase to greater than plasma levels as observed experimentally. Simulated decreases in collecting duct water permeability predicted an increase in water excretion with little change in NaCl excretion. Simulated 2.5-5% increases in glomerular filtration rate also increased simulated NaCl and water excretion rates to experimentally observed levels in response to ANF. However, this action was less effective than inhibition of collecting duct active NaCl absorption in increasing the urinary NaCl concentration. We conclude that a combination of several actions are likely to account for the overall renal effect of ANF.

Animals↗
PubMed1987

Electrolyte transport in a central core model of the renal medulla.

Transport of Na+, K+, Cl-, urea, and water is described in a central core model of the renal medulla. Equations for mass balance, Poiseuille flow, and the Nernst-Planck equation describe the continuous behavior of the system along the medullary axis and along the distal nephron; the Kedem and Katchalsky phenomenology describes passive transmural transport; active transmural transport obeys Michaelis-Menten kinetics. Numerical solution of the differential equations shows that to a close approximation any combination of active Na+ and active Cl- transport can generate the same concentration profiles but will generate very different potential profiles, and consequently, very different K+ absorption in thick ascending limb of Henle's loop. If a net transport stoichiometry of 2 Cl- ions to 1 Na+ ion is selected for the pumps, an active Cl- transport rate of approximately 10,000 peq.s-1.cm-2 gives K+ and Na+ concentrations in early distal nephron and a medullary osmolality profile in reasonable agreement with experimental data.

Biological Transport, Active↗
PubMed1985

On the solution of equations for renal counterflow models.

The results of a comparative study of three discretization techniques and the solution of the resulting algebraic equations by three methods is given. For this study, a four-tube central core model with diffusion in the core was selected and equations were derived for a coherent and efficient implementation. The results of this study show that sparse matrix techniques that take the physiological connectivity of the kidney lead to significant savings in computer storage, running time and overall cost.

Animals↗
PubMed1983

The renal concentrating mechanism: fundamental theoretical concepts.

Five theoretical principles that follow from qualitative consideration of renal architecture and tubular permeabilities are proposed to explain the concentration of urine in the mammalian kidney. These are: 1) The medullary loop of the doubly folded S-shaped configuration of the nephron permits solute supplied by ascending Henle's limb (AHL) to extract water from descending Henle's limb (DHL) and collecting duct (CD). 2) The cortical loop allows the diluted AHL fluid to return to isotonicity with cortical plasma before returning to the medulla. 3) The folded vasa recta and surrounding interstitium (the central core) provide an expansion chamber for the performance of osmotic work and a mixing chamber for salt and urea. This mixing induces passive salt transport out of AHL. 4) Overall, the system acts as a solute cycling multiplier from the AHL to vascular core and the osmotically equilibrated DHL and CD. 5) The short-looped nephrons provide urea to drive salt transport out of AHL of long nephrons in the inner medulla.

Animals↗
PubMed1981

Models of coupled salt and water transport across leaky epithelia.

A general formulation is presented for the verification of isotonic transport and for the assignment of a degree of osmotic coupling in any epithelial model. In particular, it is shown that the concentration of the transported fluid in the presence of exactly equal bathing media is, in general, not a sufficient calculation by which to decide the issue of isotonicity of transport. Within this framework, two epithelial models are considered: (1) A nonelectrolyte compartment model of the lateral intercellular space is presented along with its linearization about the condition of zero flux. This latter approximate model is shown to be useful in the estimation of deviation from isotonicity, intraepithelial solute polarization effects, and the capacity to transport water against a gradient. In the case of uphill water transport, some limitations of a model of fixed geometry are indicated and the advantage of modeling a compliant interspace is suggested. (2) A comprehensive model of cell and channel is described which includes the major electrolytes and the possible presence of intraepithelial gradients. The general approach to verification of isotonicity is illustrated for this numerical model. In addition, the insights about parameter dependence gained from the linear compartment model are shown to be applicable to understanding this large simulation.

Animals↗
PubMed1981

Coupled water transport in standing gradient models of the lateral intercellular space.

A standing gradient model of the lateral intercellular space is presented which includes a basement membrane of finite solute permeability. The solution to the model equations is estimated analytically using the "isotonic convection approximation" of Segel. In the case of solute pumps uniformly distributed along the length of the channel, the achievement of isotonic transport depends only on the water permeability of the cell membranes. The ability of the model to transport water against an adverse osmotic gradient is the sum of two terms: The first term is simply that for a well-stirred compartment model and reflects basement membrane solute permeability. The second term measures the added strength due to diffusion limitation within the interspace. It is observed, however, that the ability for uphill water transport due to diffusion limitation is diminished by high cell membrane water permeability. For physiologically relevant parameters, it appears that the high water permeability required for isotonic transport renders the contribution of the standing gradient relatively ineffective in transport against an osmotic gradient. Finally, when the model transports both isotonically and against a gradient, it is shown that substantial intraepithelial solute polarization effects are unavoidable. Thus, the measured epithelial water permeability will grossly underestimate the water permeability of the cell membranes. The accuracy of the analytic approximation is demonstrated by numerical solution of the complete model equations.

Animals↗
PubMed1981

Carbon dioxide permeability of rabbit proximal convoluted tubules.

CO2 kinetics were studied under conditions in which CO2 partial pressure and either the bicarbonate or hydrogen ion concentrations were unequal in perfusate and bath. A glass pH microelectrode and microcalorimeter were used to measure pH and total CO2 in perfused and collected fluids. Luminal appearance or disappearance of CO2 was determined from the change in concentrations of CO2 and acidic moieties of the buffers between perfused and collected fluids. The pH was not measurably affected by the tubule processes of metabolism, hydrogen ion secretion, and buffer transport because of relatively high flow rates. Since CO2 appearance and disappearance were directly related to CO2 partial pressure differences across the tubule (r = 0.94), this technique provides a valid estimate of transepithelial CO2 flux in response to the driving force of a CO2 partial pressure difference. From flux per unit of driving force and from estimates of resistances to CO2 diffusion in both internal and external unstirred layers, we obtained a transepithelial CO2 permeability of approximately 10(-4) cm3 . s-1 . cm tubule length-1. This corresponds to a diffusion coefficient through the tubule epithelium about half that through an equivalent thickness of water. We conclude that rabbit proximal convoluted tubules are so highly permeable to CO2 that even if all the filtered bicarbonate were reabsorbed by the generation of CO2 in the lumen, the tubular fluid CO2 partial pressure would exceed that of the peritubular blood by less than 4 mmHg.

Absorption↗
PubMed1979

A mathematical model of proximal tubule absorption.

A previous model of the mechanisms of flow through epithelia was modified and extended to include hydrostatic and osmotic pressures in the cells and in the peritubular capillaries. The differential equations for flow and concentration in each region of the proximal tubule were derived. The equations were solved numerically by a finite difference method. The principal conclusions are: (i) Cell NaCl concentration remains essentially isotonic over the pressure variations considered; (ii) channel NaCl concentration varies only a few mosmol from isotonicity, and the hydrostatic and osmotic pressure differences across the cell wall are of the same order of magnitude; (iii) both reabsorbate osmolality and pressure-induced flow are relatively insensitive to the geometry of the system; (iv) a strong equilibrating mechanism exists in the sensitivity of the reabsorbate osmolality to luminal osmolality; this mechanism is far more significant than any other parameter change.

Absorption↗