Biomedical subjects

A S Wexler

Publications and source records attributed to A S Wexler.

18 recordsLinked to original sources

PubMed2001

Application of the ART-2a algorithm to laser ablation aerosol mass spectrometry of particle standards.

Single-particle mass spectrometers are now commonly used to analyze atmospheric particles and generate tens of thousands of spectra from typical measurement campaigns. The ART-2a spectrum algorithm has been used to classify these spectra. In this work, we generate a range of particles that are models of those that are common in the atmosphere. A single-particle mass spectrometer is used to analyze these known particles, and the spectra are classified using ART-2a. The optimum vigilance parameter is approximately 0.5 while the optimum learning rate is approximately 0.05. The classifications elucidate limitations in generation of test particles, their analysis by single-particle techniques, and their classification by ART-2a.

Journal Article↗

PubMed2000

The role of dispersion in particle deposition in human airways.

Aerosol dispersion and deposition are processes that occur concurrently in human airways. However, dispersion has not been properly accounted for in most deposition models. In this paper we have incorporated the latest understanding of dispersion into a dosimetry model and study the influence of dispersion on particle deposition in the lung. We show that dispersion influences the total deposition of inhaled particles and in particular increases the pulmonary deposition of fine mode particles. We also discuss how dispersion can help elucidate a number of clinical and epidemiologic results associated with particle deposition in the lung.

Administration, Inhalation↗

PubMed2000

Development of a mathematical model that predicts optimal muscle activation patterns by using brief trains.

Because muscles must be repetitively activated during functional electrical stimulation, it is desirable to identify the stimulation pattern that produces the most force. Previous experimental work has shown that the optimal pattern contains an initial high-frequency burst of pulses (i.e., an initial doublet or triplet) followed by a low, constant-frequency portion. Pattern optimization is particularly challenging, because a muscle's contractile characteristics and, therefore, the optimal pattern change under different physiological conditions and are different for each person. This work describes the continued development and testing of a mathematical model that predicts isometric forces from fresh and fatigued muscles in response to brief trains of electrical pulses. By use of this model and an optimization algorithm, stimulation patterns that produced maximum forces from each subject were identified.

Algorithms↗

PubMed2000

Detailed flow patterns in the nasal cavity.

The human nasal cavity filters and conditions inspired air while providing olfactory function. Detailed experimental study of nasal airflow patterns has been limited because of the complex geometry of the nasal cavity. In this work, particle image velocimetry was used to determine two-dimensional instantaneous velocity vector fields in parallel planes throughout a model of the nasal cavity that was subjected to a nonoscillatory flow rate of 125 ml/s. The model, which was fabricated from 26 computed tomography scans by using rapid prototyping techniques, is a scaled replica of a human right nasal cavity. The resulting vector plots show that the flow is laminar and regions of highest velocity are in the nasal valve and in the inferior airway. The relatively low flow in the olfactory region appears to protect the olfactory bulb from particulate pollutants. Low flows were also observed in the nasal meatuses, whose primary function has been the subject of debate. Comparison of sequentially recorded data suggests a steady flow.

Adult↗

PubMed2000

A predictive model of fatigue in human skeletal muscles.

Fatigue is a major limitation to the clinical application of functional electrical stimulation. The activation pattern used during electrical stimulation affects force and fatigue. Identifying the activation pattern that produces the greatest force and least fatigue for each patient is, therefore, of great importance. Mathematical models that predict muscle forces and fatigue produced by a wide range of stimulation patterns would facilitate the search for optimal patterns. Previously, we developed a mathematical isometric force model that successfully identified the stimulation patterns that produced the greatest forces from healthy subjects under nonfatigue and fatigue conditions. The present study introduces a four-parameter fatigue model, coupled with the force model that predicts the fatigue induced by different stimulation patterns on different days during isometric contractions. This fatigue model accounted for 90% of the variability in forces produced by different fatigue tests. The predicted forces at the end of fatigue testing differed from those observed by only 9%. This model demonstrates the potential for predicting muscle fatigue in response to a wide range of stimulation patterns.

Electric Stimulation↗

PubMed1998

Outer medullary anatomy and the urine concentrating mechanism.

In earlier work, mathematical models of the urine concentration mechanism were developed incorporating the features of renal anatomy. However, several anatomic observations showed inconsistencies in the modeling representation of the outer stripe (OS) anatomy. In this study, based on observations from comparative anatomy and morphometric studies, we propose a new structural model of outer medullary anatomy, different from that previously presented [A. S. Wexler, R. E. Kalaba, and D. J. Marsh. Am. J. Physiol. 260 (Renal Fluid Electrolyte Physiol. 29): F368-F383, 1991]. The modifications include the following features of rat outer medullary anatomy, for example, 1) in the OS, the limbs of long loops of Henle surround the descending and ascending vasa recta that develop into the vascular bundles in the inner stripe (IS), whereas the limbs of short loops are close to the collecting ducts; and 2) the descending limbs of short loops shift from the tubular region in the OS to near the vascular bundle in the IS, whereas the limbs of long loops are situated away from the vascular bundles in the tubular region. The sensitivity of the concentrating process to the relative position of loops and vessels was investigated in the different medullary regions. With these modifications, the model predicts a more physiological, axial osmolarity gradient in both outer and inner medulla with membrane parameters that are all in the range of measured physiological values, including the urea permeabilities of descending vasa recta reported by Pallone and co-workers (T. L. Pallone, J. Work, R. L. Myers, and R. L. Jamison. J. Clin.Invest. 93: 212-222, 1994).

Animals↗

PubMed1998

Two-step, predictive, isometric force model tested on data from human and rat muscles.

Functional electrical stimulation can assist paralyzed individuals to perform functional movements, but muscle fatigue is a major limitation to its practical use. An accurate and predictive mathematical model can facilitate the design of stimulation patterns that optimize aspects of the force transient while minimizing fatigue. Solution nonuniqueness, a major shortcoming in previous work, was overcome with a simpler model. The model was tested on data collected during isometric contractions of rat gastrocnemius muscles and human quadriceps femoris muscles under various physiological conditions. For each condition tested, parameter values were identified using the force response to one or two stimulation trains. The parameterized model was then used to predict forces in response to other stimulation patterns. The predicted forces closely matched the measured forces. The model was not sensitive to initial parameter estimates, demonstrating solution uniqueness. By predicting the force that develops in response to an arbitrary pattern of stimulation, we envision the present model helping identify optimal stimulation patterns for activation of skeletal muscle during functional electrical stimulation.

Animals↗

PubMed1997

A mathematical model that predicts skeletal muscle force.

This study demonstrates the validity of a mathematical model that predicts the force generated by rat skeletal muscles during brief subtetanic and tetanic isometric contractions. The model consists of three coupled differential equations (ODE's). The first two equations represent the calcium dynamics and the third equation represents force dynamics. The model parameters were identified from brief trains of regularly spaces pulses [constant-frequency trains (CFT's)] that produce subtetanic muscle responses. Using these parameters, the model was able to predict isometric forces from other stimulation patterns. For the gastrocnemius muscles predictions were made for responses to CFT's with interpulse intervals (IPI's) ranging from 10 to 50 ms and variable-frequency trains (VFT's), where the initial IPI = 10 ms and the remaining IPI's were identical to those used for the CFT's. For the soleus muscles predictions were made for 10-100-ms CFT's. The shape of the predicted responses closely match the experimental data. Comparisons between experimental and modeled force-time integrals, peak forces, and time-to-peak also suggest excellent agreement between the model and the experiment data. Many physiological parameters predicted by the model agree with values obtained independently by others. In conclusion, the model accurately predicts isometric forces generated by rat gastrocnemius and soleus muscles produced by brief stimulation trains.

Actins↗

PubMed1996

The effects of collecting duct active NaCl reabsorption and inner medulla anatomy on renal concentrating mechanism.

First, the representation of the inner medulla incorporates an exaggerated radial separation between tubules, vessels, and collecting ducts; and, second, the hydraulic permeability in the upper portion of the inner medullary collecting ducts was erroneously set to zero. In the current work, we explore the role of collecting duct hydraulic permeability and anatomical heterogeneity via mathematical modeling. The model predicts concentrated urine for measured values of the hydraulic permeability and homogeneous lower inner medulla as long as net active NaCl reabsorption is incorporated in the upper inner medullary collecting duct epithelium. This new three-dimensional model results in two recycling paths. The upper portion of the inner medulla recycles NaCl, whereas the lower portion recycles urea.

Absorption↗

PubMed1996

Growth and neutralization of sulfate aerosols in human airways.

Evidence derived from in vivo and in vitro laboratory experiments, controlled human exposure studies, and epidemiological studies on mortality and morbidity point to a positive correlation between acid aerosol inhalation and lung impairment. The lung has two important lines of defense against acid aerosols: 1) neutralization by oral or nasal airway ammonia and 2) buffering by mucus lining of the airway. A mathematical model is developed to study the growth and endogenous ammonia neutralization of sulfate-containing aerosol particles in the human respiratory tract. It is shown that an accurate prediction of the luminal ammonia concentration and relative humidity in each generation is essential for quantifying the degree of neutralization of the acidic particles. The model predicts substantial growth and neutralization for small particles (< 0.1 micron), whereas larger particles (> 1.0 micron) experience negligible neutralization. The predicted neutralization of intermediate-sized particles depends on the parameter values used in the model. Water supersaturations that occur in the respiratory tract when ambient conditions are cool and humid cause rapid particle growth and consequently enhance neutralization. Thus the neutralization depends on the particle size as well as on ambient conditions.

Aerosols↗

PubMed1995

Inner medullary external osmotic driving force in a 3-D model of the renal concentrating mechanism.

The mechanism by which the renal medulla establishes and maintains a gradient of osmolarity along the corticomedullary axis, especially in the inner medulla, where there is no active transmural flux out of the ascending limbs of Henle, remains a source of controversy. We show here that, if realistic values of urea permeability in the inner medullary descending limbs and water permeability in the upper inner medullary section of the collecting ducts are taken into account, even a model including the three-dimensional vascular bundle structures [A. S. Wexler, R. E. Kalaba, and D. J. Marsh. Am. J. Physiol. 260 (Renal Fluid Electrolyte Physiol. 29): F368-F383, 1991] fails to explain the experimentally observed inner medullary osmolality gradient. We show here that this failure can be overcome by application of an external osmotic driving force, an idea recently revived by J. F. Jen and J. L. Stephenson (Bull. Math. Biol. 56: 491-514, 1994) in the context of a single-solute, single-loop central core model. We show that inclusion of such an external driving force with a value equivalent to at least 100 mosM of inner medullary interstitial osmolytes in the three-dimensional model of Wexler et al. accounts for a physiological osmolality gradient, even in the face of realistic permeability values. Furthermore, inclusion of the external driving force makes the model less dependent on the positions of descending and ascending limbs of Henle with respect to the collecting ducts. In an effort to assess whether there is any experimental basis for osmolytes, we show that a significant amount of extra inner medullary interstitial osmolytes is plausible, based on extrapolation from existing experimental data.

Animals↗

PubMed1994

The effect of solution non-ideality on membrane transport in three-dimensional models of the renal concentrating mechanism.

Previous models of the renal concentrating mechanism employ ideal approximations of solution thermodynamics for membrane transport calculation. In three-dimensional models of the renal medulla, predicted urine concentrations reach levels where these idealized approximations begin to break down. In this paper we derive equations that govern membrane transport for non-dilute solutions and use these equations in a three-dimensional model of the concentrating mechanism. New numerical methods were employed that are more stable than those employed previously. Compared to ideal solution models, the urea non-ideality tends to increase predicted osmolarities, whereas NaCl non-ideality decreases predictions.

Biological Transport↗

PubMed1991

Three-dimensional anatomy and renal concentrating mechanism. I. Modeling results.

Simulations were performed to test the hypothesis that the three-dimensional organization of the renal medulla is essential for formation of hypertonic urine. As in previous models, representations of loops of Henle, distal tubules, collecting ducts, and vasa recta and recent estimates of tubule characteristics were included in a simulation of NaCl, urea, and fluid transport. In addition, this model specifies the relative positions of the medullary structures. By assuming that the structure of the minimum functional unit is a vascular bundle surrounded by tubules and ascending vessels, we have represented the three-dimensional organization of the medulla by a cylindrically symmetric two-dimensional model. The resulting set of equations gives rise to a nonlinear boundary value problem with linear boundary conditions, which was solved numerically via quasi linearization. Compared with previous simulations, the concentrations predicted by this model more accurately match measured quantities in two regards. First, papillary tip concentrations of NaCl and urea are significantly higher, and, second, a monotonic increase in osmolarity is observed in the inner medulla. The three-dimensional organization permitted development of local concentration gradients, which are essential to the final result.

Absorption↗

PubMed1991

Three-dimensional anatomy and renal concentrating mechanism. II. Sensitivity results.

A mathematical model has been developed to simulate hypertonic urine formation in the renal medulla. The model uses published values of membrane transport parameters, as have other models, but is unique in its representation of the three-dimensional anatomy of the medulla. The model successfully predicts measured fluid flows, osmolarities, and NaCl and urea concentrations. The model results are presented in the companion to this paper [A. S. Wexler, R. E. Kalaba, D. J. Marsh. Am. J. Physiol. 260 (Renal Fluid Electrolyte Physiol. 29): F368-F383, 1991.]. In this paper we provide tests of the sensitivity of model performance to variations in the description of the anatomy and in membrane transport parameters. From these studies we conclude that 1) strict counterflow arrangements are required in the outer stripe to prevent loss of NaCl to the systemic circulation, 2) the radial organization in the inner stripe materially improves performance of the inner medulla, 3) radial organization of the inner medulla is essential to hypertonic urine formation there, 4) the model is most sensitive to variation in collecting duct parameters, and 5) reabsorption of urea in the distal tubule improves system performance. The results support the claim that the three-dimensional structure, as captured in the model, provides a crucial framework for the production of hypertonic urine.

Absorption↗

PubMed1990

Model of TGF-proximal tubule interactions in renal autoregulation.

Previous models, assuming constant reabsorption in the proximal tubule, have shown that tubuloglomerular feedback (TGF) can explain only a fraction of glomerular filtration rate (GFR) and renal blood flow autoregulation. Increased arterial pressure inhibits proximal tubule fluid reabsorption, an effect that should increase the efficacy of TGF because of the resulting increased flow rate in the loop of Henle. Models describing pressure and flow in a glomerulus and a nephron were derived to test this prediction. The models were coupled by a TGF function with tubular flow rate at the end of the proximal tubule (superficial nephron) or at the macula densa (juxtamedullary nephron) as input and with afferent arteriolar resistance as output. In agreement with others, the model predicted that TGF alone could account for about one-half of autoregulation. Pressure-dependent inhibition of proximal reabsorption increased the ability of TGF to account for autoregulation, providing compensation for increases in arterial pressure comparable to published whole kidney values. The inclusion of an approximation of an effect of arterial pressure on TGF marginally improved predicted autoregulation. Although the results suggest that the proximal tubule-TGF interaction can provide a quantitatively adequate explanation for autoregulation, they also indicate that the effect of the interaction is spent at arterial pressures greater than 130 mmHg. Additional mechanisms are required to extend this range.

Animals↗

PubMed1987

Passive, one-dimensional countercurrent models do not simulate hypertonic urine formation.

Simulations were performed to test the ability of the countercurrent hypothesis to predict measured concentrations of NaCl and urea in the interstitium of the renal medulla. The simulations included one-dimensional representations of loops of Henle, distal tubules, collecting ducts, and vasa recta, and recent estimates of descending limb, thick ascending limb, and collecting duct transport parameters. The nonlinear two-point boundary value problem was solved numerically via quasi-linearization. The simulations failed to predict measured concentrations or concentration gradients of NaCl in the inner medulla. Including countertransport of urea and NaCl in thin ascending limbs added minimally to the performance of the system. The single most effective change in the model was the inclusion of a coefficient to permit preferential solute exchange among vasa recta. This result suggests that the three-dimensional ordering of blood vessels and tubules is an essential construct in the concentrating mechanism.

Kidney Medulla↗

PubMed1986

Fluid waves in renal tubules.

Autoregulation of renal blood flow is ineffective when arterial pressure perturbations occur at frequencies above 0.05 Hz. To determine whether wave propagation velocity to the macula densa is rate limiting, we estimated compliances of the proximal tubule and the loop of Henle, and used these values in a model of pressure and flow as functions of time and distance in the nephron. Compliances were estimated from measurements of pressures and flows in early proximal, late proximal, and early distal tubules in rats under normal and Ringer-loaded conditions. A model of steady pressure and flow in a compliant, reabsorbing tubule was fitted to these results. The transient model was a set of nonlinear, hyperbolic partial differential equations with split, nonlinear boundary conditions, and was solved with finite difference methods. The loop of Henle compliance was larger than the proximal tubule compliance, and impulses in glomerular filtration rate were attenuated in magnitude and delayed in time in the loop of Henle. Simulated step forcings revealed a similar pattern. Periodic variations of GFR were attenuated at frequencies greater than 0.05 Hz, and there was a delay of 5 s between variations in GFR and macula densa flow rate. The high compliance of the loop slows wave propagation to the macular densa and reduces the amplitude of high frequency waves originating in the glomerulus, but other parts of the signal chain also contribute to the slow response of macula densa feedback.

Animals↗

PubMed1986

Automatic derivative evaluation in solving boundary value problems: the renal medulla.

Automatic evaluation of derivatives becomes essential when large systems of equations of many variables are to be solved. This paper presents a set of easy-to-use FORTRAN subroutines that perform automatic derivative evaluation. They were used in conjunction with the method of quasilinearization to solve a 13th-order boundary-value problem. This problem has been proposed as a test of numerical methods used to solve models of the renal concentrating mechanism. Quasilinearization gives the same result as has been reported by others with finite difference or multiple shooting methods. The approach described here offers the important potential advantage of being easier to apply to larger problems, which can be anticipated when attempts are made to simulate the three-dimensional structure of the renal medulla.

Biological Transport↗