Personalized Diabetes Management Using Electronic Medical Records

OBJECTIVE

Current clinical guidelines for managing type 2 diabetes do not differentiate based on patient-specific factors. We present a data-driven algorithm for personalized diabetes management that improves health outcomes relative to the standard of care.

RESEARCH DESIGN AND METHODS

We modeled outcomes under 13 pharmacological therapies based on electronic medical records from 1999 to 2014 for 10,806 patients with type 2 diabetes from Boston Medical Center. For each patient visit, we analyzed the range of outcomes under alternative care using a k-nearest neighbor approach. The neighbors were chosen to maximize similarity on individual patient characteristics and medical history that were most predictive of health outcomes. The recommendation algorithm prescribes the regimen with best predicted outcome if the expected improvement from switching regimens exceeds a threshold. We evaluated the effect of recommendations on matched patient outcomes from unseen data.

RESULTS

Among the 48,140 patient visits in the test set, the algorithm's recommendation mirrored the observed standard of care in 68.2% of visits. For patient visits in which the algorithmic recommendation differed from the standard of care, the mean posttreatment glycated hemoglobin A_1c (HbA_1c) under the algorithm was lower than standard of care by 0.44 ± 0.03% (4.8 ± 0.3 mmol/mol) (P < 0.001), from 8.37% under the standard of care to 7.93% under our algorithm (68.0 to 63.2 mmol/mol).

CONCLUSIONS

A personalized approach to diabetes management yielded substantial improvements in HbA_1c outcomes relative to the standard of care. Our prototyped dashboard visualizing the recommendation algorithm can be used by providers to inform diabetes care and improve outcomes.

Lifetime medical costs of knee osteoarthritis management in the United States: impact of extending indications for total knee arthroplasty

OBJECTIVE

The impact of increasing utilization of total knee arthroplasty (TKA) on lifetime costs in persons with knee osteoarthritis (OA) is understudied.

METHODS

We used the Osteoarthritis Policy Model to estimate total lifetime costs and TKA utilization under a range of TKA eligibility criteria among US persons with symptomatic knee OA. Current TKA utilization was estimated from the Multicenter Osteoarthritis Study and calibrated to Health Care Cost and Utilization Project data. OA treatment efficacy and toxicity were drawn from published literature. Costs in 2013 dollars were derived from Medicare reimbursement schedules and Red Book Online. Time costs were derived from published literature and the US Bureau of Labor Statistics.

RESULTS

Estimated average discounted (3% per year) lifetime costs for persons diagnosed with knee OA were $140,300. Direct medical costs were $129,600, with $12,400 (10%) attributable to knee OA over 28 years. OA patients spent a mean ± SD of 13 ± 10 years waiting for TKA after failing nonsurgical regimens. Under current TKA eligibility criteria, 54% of knee OA patients underwent TKA over their lifetimes. Estimated OA-related discounted lifetime direct medical costs ranged from $12,400 (54% TKA uptake) when TKA eligibility was limited to Kellgren/Lawrence grades 3 or 4 to $16,000 (70% TKA uptake) when eligibility was expanded to include symptomatic OA with a lesser degree of structural damage.

CONCLUSION

Because of low efficacy of nonsurgical regimens, knee OA treatment-attributable costs are low, representing a small portion of all costs for OA patients. Expanding TKA eligibility increases OA-related costs substantially for the population, underscoring the need for more effective nonoperative therapies.

Treatment of cannabis dependence using escitalopram in combination with cognitive-behavior therapy: a double-blind placebo-controlled study

BACKGROUND

Cannabis is the most frequently used illegal substance in the United States and Europe. There is a dramatic increase in the demand for treatment for cannabis dependence. Cannabis users frequently have co-morbid mood symptoms, especially depression and anxiety, and regular cannabis users may self-medicate for such symptoms.

OBJECTIVES

We report a double-blind, placebo-controlled treatment study, for the prevention of cannabis use in cannabis-dependent individuals.

METHOD

Regular cannabis-dependent users (n = 52) were treated for 9 weeks with weekly cognitive-behavior and motivation-enhancement therapy sessions together with escitalopram 10 mg/day. Urine samples were collected to monitor delta-9 tetrahydrocannabinol (THC) during treatment and questionnaires were administered to assess anxiety and depression.

RESULTS

We observed a high rate of dropout (50%) during the 9-week treatment program. Fifty-two patients were included in the intention-to-treat analysis. Of these, ten (19%) remained abstinent after 9 weeks of treatment as indicated by negative urine samples for THC. Escitalopram provided no advantage over placebo in either abstinence rates from cannabis or anxiety and depression scores during the withdrawal and abstinent periods.

CONCLUSIONS

Escitalopram treatment does not provide an additional benefit either for achieving abstinence, or for the treatment of the cannabis withdrawal syndrome. Due to limitations of our study, namely, a high dropout rate and effects of low abstinence rates on measures of anxiety, depression and withdrawal, it is premature to conclude that selective serotonin reuptake inhibitors are not effective for treatment of the cannabis withdrawal syndrome.

Lifetime risk and age at diagnosis of symptomatic knee osteoarthritis in the US

OBJECTIVE

To estimate the incidence and lifetime risk of diagnosed symptomatic knee osteoarthritis (OA) and the age at diagnosis of knee OA based on self-reports in the US population.

METHODS

We estimated the incidence of diagnosed symptomatic knee OA in the US by combining data on age-, sex-, and obesity-specific prevalence from the 2007-2008 National Health Interview Survey, with disease duration estimates derived from the Osteoarthritis Policy (OAPol) Model, a validated computer simulation model of knee OA. We used the OAPol Model to estimate the mean and median ages at diagnosis and lifetime risk.

RESULTS

The estimated incidence of diagnosed symptomatic knee OA was highest among adults ages 55-64 years, ranging from 0.37% per year for nonobese men to 1.02% per year for obese women. The estimated median age at knee OA diagnosis was 55 years. The estimated lifetime risk was 13.83%, ranging from 9.60% for nonobese men to 23.87% in obese women. Approximately 9.29% of the US population is diagnosed with symptomatic knee OA by age 60 years.

CONCLUSION

The diagnosis of symptomatic knee OA occurs relatively early in life, suggesting that prevention programs should be offered relatively early in the life course. Further research is needed to understand the future burden of health care utilization resulting from earlier diagnosis of knee OA.

Estimating the burden of total knee replacement in the United States

BACKGROUND

In the last decade, the number of total knee replacements performed annually in the United States has doubled, with disproportionate increases among younger adults. While total knee replacement is a highly effective treatment for end-stage knee osteoarthritis, total knee replacement recipients can experience persistent pain and severe complications. We are aware of no current estimates of the prevalence of total knee replacement among adults in the U.S.

METHODS

We used the Osteoarthritis Policy Model, a validated computer simulation model of knee osteoarthritis, and data on annual total knee replacement utilization to estimate the prevalence of primary and revision total knee replacement among adults fifty years of age or older in the U.S. We combined these prevalence estimates with U.S. Census data to estimate the number of adults in the U.S. currently living with total knee replacement. The annual incidence of total knee replacement was derived from two longitudinal knee osteoarthritis cohorts and ranged from 1.6% to 11.9% in males and from 2.0% to 10.9% in females.

RESULTS

We estimated that 4.0 million (95% confidence interval [CI]: 3.6 million to 4.4 million) adults in the U.S. currently live with a total knee replacement, representing 4.2% (95% CI: 3.7% to 4.6%) of the population fifty years of age or older. The prevalence was higher among females (4.8%) than among males (3.4%) and increased with age. The lifetime risk of primary total knee replacement from the age of twenty-five years was 7.0% (95% CI: 6.1% to 7.8%) for males and 9.5% (95% CI: 8.5% to 10.5%) for females. Over half of adults in the U.S. diagnosed with knee osteoarthritis will undergo a total knee replacement.

CONCLUSIONS

Among older adults in the U.S., total knee replacement is considerably more prevalent than rheumatoid arthritis and nearly as prevalent as congestive heart failure. Nearly 1.5 million of those with a primary total knee replacement are fifty to sixty-nine years old, indicating that a large population is at risk for costly revision surgery as well as possible long-term complications of total knee replacement.

Impact of obesity and knee osteoarthritis on morbidity and mortality in older Americans

BACKGROUND

Obesity and knee osteoarthritis are among the most frequent chronic conditions affecting Americans aged 50 to 84 years.

OBJECTIVE

To estimate quality-adjusted life-years lost due to obesity and knee osteoarthritis and health benefits of reducing obesity prevalence to levels observed a decade ago.

DESIGN

The U.S. Census and obesity data from national data sources were combined with estimated prevalence of symptomatic knee osteoarthritis to assign persons aged 50 to 84 years to 4 subpopulations: nonobese without knee osteoarthritis (reference group), nonobese with knee osteoarthritis, obese without knee osteoarthritis, and obese with knee osteoarthritis. The Osteoarthritis Policy Model, a computer simulation model of knee osteoarthritis and obesity, was used to estimate quality-adjusted life-year losses due to knee osteoarthritis and obesity in comparison with the reference group.

SETTING

United States.

PARTICIPANTS

U.S. population aged 50 to 84 years.

MEASUREMENTS

Quality-adjusted life-years lost owing to knee osteoarthritis and obesity.

RESULTS

Estimated total losses of per-person quality-adjusted life-years ranged from 1.857 in nonobese persons with knee osteoarthritis to 3.501 for persons affected by both conditions, resulting in a total of 86.0 million quality-adjusted life-years lost due to obesity, knee osteoarthritis, or both. Quality-adjusted life-years lost due to knee osteoarthritis and/or obesity represent 10% to 25% of the remaining quality-adjusted survival of persons aged 50 to 84 years. Hispanic and black women had disproportionately high losses. Model findings suggested that reversing obesity prevalence to levels seen 10 years ago would avert 178,071 cases of coronary heart disease, 889,872 cases of diabetes, and 111,206 total knee replacements. Such a reduction in obesity would increase the quantity of life by 6,318,030 years and improve life expectancy by 7,812,120 quality-adjusted years in U.S. adults aged 50 to 84 years.

LIMITATIONS

Comorbidity incidences were derived from prevalence estimates on the basis of life expectancy of the general population, potentially resulting in conservative underestimates. Calibration analyses were conducted to ensure comparability of model-based projections and data from external sources.

CONCLUSION

The number of quality-adjusted life-years lost owing to knee osteoarthritis and obesity seems to be substantial, with black and Hispanic women experiencing disproportionate losses. Reducing mean body mass index to the levels observed a decade ago in this population would yield substantial health benefits.

PRIMARY FUNDING SOURCE

The National Institutes of Health and the Arthritis Foundation.

Impact of obesity and knee osteoarthritis on morbidity and mortality in older Americans

BACKGROUND

Obesity and knee osteoarthritis are among the most frequent chronic conditions affecting Americans aged 50 to 84 years.

OBJECTIVE

To estimate quality-adjusted life-years lost due to obesity and knee osteoarthritis and health benefits of reducing obesity prevalence to levels observed a decade ago.

DESIGN

The U.S. Census and obesity data from national data sources were combined with estimated prevalence of symptomatic knee osteoarthritis to assign persons aged 50 to 84 years to 4 subpopulations: nonobese without knee osteoarthritis (reference group), nonobese with knee osteoarthritis, obese without knee osteoarthritis, and obese with knee osteoarthritis. The Osteoarthritis Policy Model, a computer simulation model of knee osteoarthritis and obesity, was used to estimate quality-adjusted life-year losses due to knee osteoarthritis and obesity in comparison with the reference group.

SETTING

United States.

PARTICIPANTS

U.S. population aged 50 to 84 years.

MEASUREMENTS

Quality-adjusted life-years lost owing to knee osteoarthritis and obesity.

RESULTS

Estimated total losses of per-person quality-adjusted life-years ranged from 1.857 in nonobese persons with knee osteoarthritis to 3.501 for persons affected by both conditions, resulting in a total of 86.0 million quality-adjusted life-years lost due to obesity, knee osteoarthritis, or both. Quality-adjusted life-years lost due to knee osteoarthritis and/or obesity represent 10% to 25% of the remaining quality-adjusted survival of persons aged 50 to 84 years. Hispanic and black women had disproportionately high losses. Model findings suggested that reversing obesity prevalence to levels seen 10 years ago would avert 178,071 cases of coronary heart disease, 889,872 cases of diabetes, and 111,206 total knee replacements. Such a reduction in obesity would increase the quantity of life by 6,318,030 years and improve life expectancy by 7,812,120 quality-adjusted years in U.S. adults aged 50 to 84 years.

LIMITATIONS

Comorbidity incidences were derived from prevalence estimates on the basis of life expectancy of the general population, potentially resulting in conservative underestimates. Calibration analyses were conducted to ensure comparability of model-based projections and data from external sources.

CONCLUSION

The number of quality-adjusted life-years lost owing to knee osteoarthritis and obesity seems to be substantial, with black and Hispanic women experiencing disproportionate losses. Reducing mean body mass index to the levels observed a decade ago in this population would yield substantial health benefits.

PRIMARY FUNDING SOURCE

The National Institutes of Health and the Arthritis Foundation.

Pharmacological treatment of cannabis dependence

Cannabis is the most frequently used illegal psychoactive substance in the world. There is a significant increase in the number of treatment admissions for cannabis use disorders in the past few years, and the majority of cannabis-dependent individuals who enter treatment have difficulty in achieving and maintaining abstinence. Thus, there is increased need for medications that can be used to treat this population. So far, no medication has been shown broadly and consistently effective; none has been approved by any national regulatory authority. Medications studied have included those that alleviate symptoms of cannabis withdrawal (e.g., dysphoric mood, irritability),those that directly affect endogenous cannabinoid receptor function, and those that have shown efficacy in treatment of other drugs of abuse or psychiatric conditions. Buspirone is the only medication to date that has shown efficacy for cannabis dependence in a controlled clinical trial. Results from controlled human laboratory studies and small open-label clinical trials suggest that dronabinol, the COMT inhibitor entacapone, and lithium may warrant further study. Recent pre-clinical studies suggest the potential of fatty acid amide hydrolase (FAAH) inhibitors such as URB597, endocannabinoid-metabolizing enzymes, and nicotinic alpha 7 receptor antagonists such as methyllycaconitine (MLA).Controlled clinical trials are needed to evaluate the clinical efficacy of these medications and to validate the laboratory models being used to study candidate medications.

Modeling epithelial cell homeostasis: steady-state analysis

Critical to epithelial cell viability is the homeostasis of cell volume and composition during changes in transcellular transport. In this study, two previously developed mathematical models (principal cell of the collecting duct and proximal tubule cell) are approximated by their linearizations about a reference condition. This yields matrices which estimate cell volume, cell composition, and transcellular fluxes in response to perturbations of bath conditions and membrane transporter activity. These approximations are themselves extended with the inclusion of linear dependence of membrane transport coefficients on cell variables (e.g., volume, solute concentrations, or electrical potential). This provides cell models with variable permeabilities, which may be homeostatic, and which can be examined systematically: sequentially testing each membrane permeability and its controlling cell variable. In the proximal tubule approximation, volume-mediated increases in peritubular K-Cl or Na-3HCO3 cotransport, and volume-mediated decreases in Na,K-ATPase activity are homeostatic; modulation of peritubular K permeability has little impact. In the principal cell model, volume homeostasis is afforded by volume-sensitive peritubular Na/H exchange or Cl- conductance. Predictions from the linear analysis are confirmed in the full models. This approach yields a systematic examination of homeostasis in an epithelial model, and identifies candidate control parameters.

A mathematical model of rat cortical collecting duct: determinants of the transtubular potassium gradient

In assessing disorders of potassium excretion, urine composition is used to calculate the transtubular gradient (TTKG), as an estimate of tubule fluid concentration, at a point when the fluid was last isotonic to plasma, namely, within the cortical collecting duct (CCD). A mathematical model of the CCD has been developed, consisting of principal cells and α- and β-intercalated cells, and which includes Na+, K+, Cl−, HCO[Formula: see text], CO2, H2CO3, phosphate, ammonia, and urea. Parameters have been selected to achieve fluxes and permeabilities compatible with data obtained from perfusion studies of rat CCD under the influence of both antidiuretic hormone and mineralocorticoid. Both epithelial (flat sheet) and tubule models have been configured, and model calculations have focused on the determinants of the TTKG. Using the epithelial model, luminal K+ concentrations can be computed at which K+secretion ceases (0-flux equilibrium), and this luminal concentration derives from the magnitude of principal cell peritubular uptake of K+ via the Na-K-ATPase, relative to principal cell peritubular membrane K+ permeability. When the model is configured as a tubule and examined in the context of conditions in vivo, osmotic equilibration of luminal fluid produces a doubling of the initial K+ concentration, which, depending on delivered load, may be substantially greater than the zero-flux equilibrium value. Under such circumstances, the CCD will be a site for K+ reabsorption, although the relatively low permeability ensures that this reabsorptive flux is likely to be small. Osmotic equilibration may also raise luminal NH3 concentrations well above those in cortical blood. In this situation, diffusive reabsorption of NH3 provides a mechanism for base reclamation without the metabolic cost of active proton secretion.

An evaluation of skeletal attachment to LTI pyrolytic carbon, porous titanium, and carbon-coated porous titanium implants

Porous titanium, carbon-coated porous titanium, and low-temperature isotropic (LTI) pyrolytic carbon transcortical implants were placed in the femora of mongrel dogs. Mechanical and histologic analyses were performed in specimens that remained in situ for six months. Qualitative histologic results indicated that the bone formed a direct appositional interface with as-deposited LTI carbon. The bone tissue response to the two systems with porous coatings was similar. Both systems showed little fibrous tissue interposition and a high degree of mineralized bone ingrowth. The ingrown bone was well organized. However, there was some evidence that the ingrown bone mineral differed significantly from the bulk bone mineral. The only difference between carbon-coated and uncoated porous systems was a significant increase in the percentage of bone ingrowth, with carbon-coated specimens having a 4% increase in bone volume. The strength of appositional attachment to LTI carbon was shown to be at least one order of magnitude weaker than bone ingrowth attachment to the porous systems. The interface shear stiffness of the two porous systems was equivalent; however, the attachment shear strength of bone growth into carbon-coated porous titanium was significantly increased compared with that of bone growth into the uncoated porous titanium. Correlation of the percentage of bone ingrowth and pushout strength was also found to be statistically significant, suggesting that the presence of the carbon coating enhanced bone ingrowth, which resulted in significantly increased shear strengths.

The processing of automatic thoughts of drug use and craving in opiate-dependent individuals

This study investigated the processing of sentences describing craving and withdrawal in opiate-dependent individuals. Eighteen patients who attended a methadone maintenance clinic for obtaining methadone, 18 patients who were not treated with methadone, and 18 control family members performed on a computerized contextual priming task. The task was priming sentences (craving, withdrawal, or neutral) to words (addiction, neutral, or nonwords). The methadone group was slower to process all sentences compared with family members. They were also faster to process drug-related words following withdrawal-related sentences compared with neutral words following neutral sentences. Finally, they were slower to recognize neutral words following neutral sentences compared with the nonmethadone group. Results suggest that the processing of information describing withdrawal and craving for drugs plays an important role in opiate dependence.

A hydrodynamic mechanosensory hypothesis for brush border microvilli

In the proximal tubule of the kidney, Na(+) and HCO(3)(-) reabsorption vary proportionally with changes in axial flow rate. This feature is a critical component of glomerulotubular balance, but the basic mechanism by which the tubule epithelial cells sense axial flow remains unexplained. We propose that the microvilli, which constitute the brush border, are physically suitable to act as a mechanosensor of fluid flow. To examine this hypothesis quantitatively, we have developed an elastohydrodynamic model to predict the forces and torques along each microvillus and its resulting elastic bending deformation. This model indicates that: 1) the spacing of the microvilli is so dense that there is virtually no axial velocity within the brush border and that drag forces on the microvilli are at least 200 times greater than the shear force on the cell's apical membrane at the base of the microvilli; 2) of the total drag on a 2.5-microm microvillus, 74% appears within 0.2 microm from the tip; and 3) assuming that the structural strength of the microvillus derives from its axial actin filaments, then a luminal fluid flow of 30 nl/min produces a deflection of the microvillus tip which varies from about 1 to 5% of its 90-nm diameter, depending on the microvilli length. The microvilli thus appear as a set of stiff bristles, in a configuration in which changes in drag will produce maximal torque.

A mathematical model of the outer medullary collecting duct of the rat

A mathematical model of the outer medullary collecting duct (OMCD) has been developed, consisting of alpha-intercalated cells and a paracellular pathway, and which includes Na(+), K(+), Cl(-), HCO(3)(-), CO(2), H(2)CO(3), phosphate, ammonia, and urea. Proton secretion across the luminal cell membrane is mediated by both H(+)-ATPase and H-K-ATPase, with fluxes through the H-K-ATPase given by a previously developed kinetic model (Weinstein AM. Am J Physiol Renal Physiol 274: F856-F867, 1998). The flux across each ATPase is substantial, and variation in abundance of either pump can be used to control OMCD proton secretion. In comparison with the H(+)-ATPase, flux through the H-K-ATPase is relatively insensitive to changes in lumen pH, so as luminal acidification proceeds, proton secretion shifts toward this pathway. Peritubular HCO(3)(-) exit is via a conductive pathway and via the Cl(-)/HCO(3)(-) exchanger, AE1. To represent AE1, a kinetic model has been developed based on transport studies obtained at 38 degrees C in red blood cells. (Gasbjerg PK, Knauf PA, and Brahm J. J Gen Physiol 108: 565-575, 1996; Knauf PA, Gasbjerg PK, and Brahm J. J Gen Physiol 108: 577-589, 1996). Model calculations indicate that if all of the chloride entry via AE1 recycles across a peritubular chloride channel and if this channel is anything other than highly selective for chloride, then it should conduct a substantial fraction of the bicarbonate exit. Since both luminal membrane proton pumps are sensitive to small changes in cytosolic pH, variation in density of either AE1 or peritubular anion conductance can modulate OMCD proton secretory rate. With respect to the OMCD in situ, available buffer is predicted to be abundant, including delivered HCO(3)(-) and HPO(4)(2-), as well as peritubular NH(3). Thus, buffer availability is unlikely to exert a regulatory role in total proton secretion by this tubule segment.

Quantitative IgE antibody assays in allergic diseases

During the past several years, immunoassays for specific IgE antibodies have been refined to permit reporting results in mass units. Thus quantitative immunoassays for IgE antibodies may be an adjunct to skin tests. In cases of food allergy among children with atopic dermatitis, cutoff values for IgE antibody concentrations to egg, milk, peanut, and fish have been derived to provide 95% positive and 90% negative predictive values. Food-specific IgE antibody determinations can also be used to predict which food allergies are resolving spontaneously. Elevated egg-specific IgE antibody levels in infancy are associated with significantly increased risk for development of inhalant allergies later in childhood. In cases of inhalant allergy, specific IgE antibody levels correlate closely with results of inhalation challenge studies in cat-sensitive persons. Also, mite-specific IgE antibody levels correlate significantly with the mite allergen contents of reservoir dust in the homes of mite-sensitive persons. Immunoassays for quantitation of specific IgE antibodies may be used to document allergen sensitization over time and to evaluate the risk of reaction on allergen exposure. However, immunoassays and skin tests are not entirely interchangeable, and neither will replace the other in appropriate circumstances.

Insights from mathematical modeling of renal tubular function

Mathematical models of proximal tubule have been developed which represent the important solute species within the constraints of known cytosolic concentrations, transport fluxes, and overall epithelial permeabilities. In general, model simulations have been used to assess the quantitative feasibility of what appear to be qualitatively plausible mechanisms, or alternatively, to identify incomplete rationalization of experimental observations. The examples considered include: (1) proximal water reabsorption, for which the lateral interspace is a locus for solute-solvent coupling; (2) ammonia secretion, for which the issue is prioritizing driving forces - transport on the Na+/H+ exchanger, on the Na,K-ATPase, or ammoniagenesis; (3) formate-stimulated NaCl reabsorption, for which simple addition of a luminal membrane chloride/formate exchanger fails to represent experimental observation, and (4) balancing luminal entry and peritubular exit, in which ATP-dependent peritubular K+ channels have been implicated, but appear unable to account for the bulk of proximal tubule cell volume homeostasis.

Water does not flow across the tight junctions of MDCK cell epithelium

Although it has been known for decades that the tight junctions of fluid-transporting epithelia are leaky to ions, it has not been possible to determine directly whether significant transjunctional water movement also occurs. An optical microscopic technique was developed for the direct visualization of the flow velocity profiles within the lateral intercellular spaces of a fluid-absorptive, cultured renal epithelium (MDCK) and used to determine the velocity of the fluid flow across the tight junction. The flow velocity within the lateral intercellular spaces fell to near zero adjacent to the tight junction, showing that significant transjunctional flow did not occur, even when transepithelial fluid movement was augmented by imposition of osmotic gradients.

A mathematical model of the inner medullary collecting duct of the rat: pathways for Na and K transport

A mathematical model of the inner medullary collecting duct (IMCD) of the rat has been developed representing Na+, K+, Cl-, HCO3-, CO2, H2CO3, phosphate, ammonia, and urea. Novel model features include: finite rates of hydration of CO2, a kinetic representation of the H-K-ATPase within the luminal cell membrane, cellular osmolytes that are regulated in defense of cell volume, and the repeated coalescing of IMCD tubule segments to yield the ducts of Bellini. Model transport is such that when entering Na+ is 4% of filtered Na+, approximately 75% of this load is reabsorbed. This requirement renders the area-specific transport rate for Na+ comparable to that for proximal tubule. With respect to the luminal membrane, there is experimental evidence for both NaCl cotransport and an Na+ channel in parallel. The experimental constraints that transepithelial potential difference is small and that the fractional apical resistance is greater than 85% mandate that more than 75% of luminal Na+ entry be electrically silent. When Na+ delivery is limited, an NaCl cotransporter can be effective at reducing luminal Na+ concentration to the observed low urinary values. Given the rate of transcellular Na+ reabsorption, there is necessarily a high rate of peritubular K+ recycling; also, given the lower bound on luminal membrane Cl- reabsorption, substantial peritubular Cl- flux must be present. Thus, if realistic limits on cell membrane electrical resistance are observed, then this model predicts a requirement for peritubular electroneutral KCl exit.

A mathematical model of the inner medullary collecting duct of the rat: acid/base transport

A mathematical model of the inner medullary collecting duct (IMCD) of the rat has been developed that is suitable for simulating luminal buffer titration and ammonia secretion by this nephron segment. Luminal proton secretion has been assigned to an H-K-ATPase, which has been represented by adapting the kinetic model of the gastric enzyme by Brzezinski et al. (P. Brzezinski, B. G. Malmstrom, P. Lorentzon, and B. Wallmark. Biochim. Biophys. Acta 942: 215-219, 1988). In shifting to a 2 H+:1 ATP stoichiometry, the model enzyme can acidify the tubule lumen approximately 3 pH units below that of the cytosol, when luminal K+ is in abundance. Peritubular base exit is a combination of ammonia recycling and HCO3- flux (either via Cl-/HCO3- exchange or via a Cl- channel). Ammonia recycling involves NH4(+) uptake on the Na-K-ATPase followed by diffusive NH3 exit [S. M. Wall. Am. J. Physiol. 270 (Renal Physiol. 39): F432-F439, 1996]; model calculations suggest that this is the principal mode of base exit. By virtue of this mechanism, the model also suggests that realistic elevations in peritubular K+ concentration will compromise IMCD acid secretion. Although ammonia recycling is insensitive to carbonic anhydrase (CA) inhibition, the base exit linked to HCO3- flux provides a CA-sensitive component to acid secretion. In model simulations, it is observed that increased luminal NaCl entry increases ammonia cycling but decreases peritubular Cl-/HCO3- exchange (due to increased cell Cl-). This parallel system of peritubular base exit stabilizes acid secretion in the face of variable Na+ reabsorption.

Dynamics of cellular homeostasis: recovery time for a perturbation from equilibrium

In the collecting duct in vivo, the principal cell encounters a wide range in luminal flow rate and luminal concentration of NaCl. As a consequence, there are substantial variations in the transcellular fluxes of Na+ and Cl-, conditions which would be expected to perturb cell volume and cytosolic concentrations. Several control mechanisms have been identified which can potentially blunt these perturbations, and these entail cellular regulation of the luminal membrane Na+ channel and peritubular membrane K+ and Cl- channels. To illustrate the impact of these regulated channels, a mathematical model of the principal cell of the rat cortical collecting duct has been developed, in which ion channel permeabilities are either constant or regulated. In comparison to the model with fixed permeabilities, the model with regulated channels demonstrates enhanced cellular homeostasis following steady-state variation in luminal NaCl. However, in the transient response to a cytosolic perturbation, the difference in recovery time between the models is small. An approximate analysis is presented which casts these models as dynamical systems with constant coefficients. Despite the presence of regulated ion channels, concordance of each model with its linear approximation is verified for experimentally meaningful perturbations from the reference condition. Solution of a Lyapunov equation for each linear system yields a matrix whose application to a perturbation permits explicit estimation of the time to recovery. Comparison of these solution matrices for regulated and non-regulated cells confirms the similarity of the dynamic response of the two models. These calculations suggest that enhanced homeostasis by regulated channels may be protective, without necessarily hastening recovery from cellular perturbations.

Coupling of entry to exit by peritubular K+ permeability in a mathematical model of rat proximal tubule

In the proximal tubule in vivo, glomerulotubular balance requires that tubule epithelial cells accommodate a twofold variation in Na+ reabsorption through the Na+/H+ exchanger of the luminal membrane. In a mathematical model of proximal tubule, in which permeability coefficients are fixed, doubling flux through the Na+/H+ antiporter produces a substantial increase in cell volume and cytosolic HCO3-. In this model, it is possible to vary peritubular K+ permeability with changes in luminal Na+ entry, so that cell volume is constrained to be constant. In these calculations, the model predicts that peritubular hyperpolarization and nearly constant cytosolic HCO3- will accompany increases in luminal Na+ entry. Realistic models of variable peritubular K+ permeability might include a functional dependence on flux through the Na(+)-K(+)-adenosinetriphosphatase, cytosolic pH, or cell volume. When K+ permeability is represented as a function of any of these variables, homeostatic control of cell volume and pH can be obtained over a physiological variation of Na+/H+ flux. However, when luminal Na+ entry is via Na(+)-glucose cotransport, volume homeostasis is best when peritubular K+ permeability depends on the rate of active Na+ transport. For any modulator of K+ permeability, realistic constraints on the value of this parameter suggest that peritubular K+ permeability is, by itself, not sufficient to maintain cell volume within narrow limits. Parallel activation of another exit pathway, such as peritubular Na(+)-3 HCO3- cotransport, may be required to achieve the necessary homeostasis.

Acid/base transport in a model of the proximal tubule brush border: impact of carbonic anhydrase

A mathematical model of the brush border of the proximal tubule (T. A. Krahn, P. S. Aronson, and A. M. Weinstein. Bull. Math. Biol, 56: 459-490, 1994) has been extended by the inclusion of CO2 and H2CO3 as diffusible species and by the inclusion of finite rate constants for the hydration of CO2. This permits the simulation of carbonic anhydrase (CA) activity and its inhibition. We confirm the result of our previous study, which is that, in the presence of CA, the unstirred layer has only a modest effect on the observed formic acid permeability. CA inhibition results in disequilibrium pH gradients, and the effect of these gradients on formic acid permeability depends on the presence of other membrane transport proteins. We also examined the impact of CA activity on the flux of total CO2 through the brush border. Under physiological conditions, CA inhibition depressed NaHCO3 reabsorption through the brush border by interfering with the HCO3(-)-facilitated diffusion of CO2. However, the determination of brush-border CO2 permeability, using an imposed CO2 gradient, was relatively uninfluenced by CA activity. Finally, we inserted a kinetic representation of the Na+/H+ exchanger into the brush-border model. Even when luminal and cytosolic diffusion coefficients were increased 1,000-fold, there was no effect on brush-border Na+ flux. This suggests that variations in the unstirred layer cannot be responsible for the flow dependence of Na+ reabsorption.

Cognitive processing in post-traumatic stress disorder

Recent research has suggested an abnormal attentional bias to threat in anxiety disorders. We have assessed the processing of thoughts of trauma, panic attacks, general fear and positive affect in a cohort of 15 war veterans with post-traumatic stress disorder (PTSD) and an age- and sex-matched normal control group. Subjects with PTSD showed delayed processing of self-referential sentences when the themes of the sentences were traumatic experiences or positive affect, compared with controls. However, they were more efficient than control subjects in the processing of sentences describing situations of panic attacks and general fear. It would therefore appear that in patients with PTSD, cognitive processing is hindered by personally relevant themes of past traumatic experiences, whereas it may be facilitated by information related to general threat or internal body sensations of panic.

Visual ERPs evidence for enhanced processing of threatening information in anxious university students

There is accumulating evidence that highly anxious individuals selectively attend to threatening information; however, contrary to expectations, there is no evidence of enhanced processing of threat stimuli in those individuals. We investigated this question by using a sample of 20 University students who were split into two groups consisting of 10 high-anxious and 10 low-anxious subjects according to Spielberger Trait Anxiety Inventory score (median STAI = 40). Without emphasizing speed, subjects were required to decide whether visually presented words (positive, neutral, or threat) matched semantically with previous priming sentences (threat or positive) displayed on a computer screen (altogether, two types of priming sentences and three types of probe words). There was a fixed interval of 1.1 seconds between priming sentences (SI) and probe words (S2) as well as between each priming sentence word. Response time and visual event-related potentials (ERPs) were recorded in both conditions. The results showed that, compared to the Low-Anxious group, the amplitude of N100 and P400 were enhanced for the High-Anxious group in the threat priming conditions. Low-anxious individuals showed almost identical processing of threat-related situations and positive situations. Furthermore, the P400 peak latency was shorter for emotional incongruous probes in high-anxious individuals. ERPs results of the experiment suggest that highly anxious individuals deploy more processing resources to threatening information. This bias in information processing occurs in the absence of any behavioral changes (indicated by reaction times). Attentional bias in anxiety therefore implies that threatening information is given a priority over other information and is more persistently activated in anxiety states.

A kinetically defined Na+/H+ antiporter within a mathematical model of the rat proximal tubule

The luminal membrane antiporter of the proximal tubule has been represented using the kinetic formulation of E. Heinz (1978. Mechanics and Engergetics of Biological Transport. Springer-Verlag, Berlin) with the assumption of equilibrium binding and 1:1 stoichiometry. Competitive binding and transport of NH+4 is included within this model. Ion affinities and permeation velocities were selected in a least-squares fit to the kinetic parameters determined experimentally in renal membrane vesicles (Aronson, P.S., M.A. Suhm, and J. Nee. 1983. Journal of Biological Chemistry. 258:6767-6771). The modifier role of internal H+ to enhance transport beyond the expected kinetics (Aronson, P.S., J. Nee, and M. A. Suhm. 1982. Nature. 299:161-163) is represented as a velocity effect of H+ binding to a single site. This kinetic formulation of the Na+/H+ antiporter was incorporated within a model of the rat proximal tubule (Weinstein, A. M. 1994. American Journal of Physiology. 267:F237-F248) as a replacement for the representation by linear nonequilibrium thermodynamics (NET). The membrane density of the antiporter was selected to yield agreement with the rate of tubular Na+ reabsorption. Simulation of 0.5 cm of tubule predicts that the activity of the Na+/H+ antiporter is the most important force for active secretion of ammonia. Model calculations of metabolic acid-base disturbances are performed and comparison is made among antiporter representations (kinetic model, kinetic model without internal modifier, and NET formulation). It is found that the ability to sharply turn off Na+/H+ exchange in cellular alkalosis substantially eliminates the cell volume increase associated with high HCO3- conditions. In the tubule model, diminished Na+/H+ exchange in alkalosis blunts the axial decrease in luminal HCO3- and thus diminishes paracellular reabsorption of Cl-. In this way, the kinetics of the Na+/H+ antiporter could act to enhance distal delivery of Na+, Cl-, and HCO3- in acute metabolic alkalosis.

A cognitive dysfunction in anxiety and its amelioration by effective treatment with SSRIs

There is extensive research suggesting an abnormal selective attention to threat in anxiety disorders. We assessed the processing of emotional cognitions of physical anxiety, psycho-social fears, depression and positive affect in a cohort of 15 patients with active anxiety disorder (mostly panic) in comparison with a group of 15 depressed patients and 15 recovered panic patients after treatment with antidepressants (all selective serotonin re-uptake inhibitors) and an age- and sex-matched normal control group. Anxious patients showed delayed processing of emotional words (both negative and positive) compared with depressed patients. The successfully treated group showed no such interference and their responses were indistinguishable from controls. It would therefore appear that anxious patients (panic and generalized anxiety disorder) are affected primarily (but not exclusively) by themes of self-harm and psycho-social fears, and that this cognitive dysfunction in pathological anxiety is a state rather than trait feature of the condition, which is responsive to pharmacological intervention.

Ammonia transport in a mathematical model of rat proximal tubule

Pathways for ammonia transport have been incorporated within a model of rat proximal tubule [A. M. Weinstein. Am. J. Physiol. 263 (Renal Fluid Electrolyte Physiol. 32): F784-F798, 1992]. The luminal membrane includes a Na+/NH4+ exchanger, while at the peritubular membrane there is uptake of NH4+ on the Na(+)-K(+)-adenosinetriphosphatase (Na(+)-K(+)-ATPase); both luminal and peritubular cell membranes contain conductive pathways for NH4+. The model equations have been expanded to include cellular ammoniagenesis. The principal focus of this study is the interplay of forces that can raise proximal tubule fluid total ammonia concentration 10-fold higher than in arterial plasma. Analysis of a cellular model reveals that luminal membrane Na+/NH4+ exchange, cellular production of ammonia, and peritubular membrane NH4+ uptake (via Na(+)-K(+)-ATPase or via K+ channel) all act in parallel to drive ammonia secretion. This derives from the cellular interconversion of NH4+ and NH3 and the free permeation of NH3 across cell membranes. It implies that inhibition of the luminal membrane transporter does not block the contribution of peritubular uptake to the overall active transport of ammonia. Conversely, when inhibition of the luminal membrane Na+/NH4+ entry (i.e., Na+/H+ inhibition) depresses transcellular Na+ flux, then the decrease of NH4+ flux through the peritubular Na+ pump enhances the apparent importance of the luminal membrane pathway. This analysis is confirmed in the numerical calculations and is a departure from the Ussing paradigm of series membrane Na+ transport. Although active secretion of ammonia by this tubule is substantial, the relative contribution of luminal Na+/NH4+ exchange and of peritubular uptake via the Na+ pump remains uncertain. The determination of peritubular capillary NH4+ concentration will be crucial to resolving this uncertainty, with lower concentration (i.e., closer to systemic arterial ammonia) obligating greater luminal membrane Na+/NH4+ exchange.

Weak acid permeability of a villous membrane: formic acid transport across rat proximal tubule

Chloride/formate exchange, in parallel with Na+/H+ exchange and nonionic diffusion of H2CO2, has been proposed as a mechanism of electroneutral transcellular Cl- reabsorption by the proximal tubule. However, the measured brush border H2CO2 permeability of the rat proximal tubule is at least an order of magnitude too low to support sufficient H2CO2 recycling. To investigate the possibility that an unstirred layer within the brush border might depress the measured H2CO2 permeability, we constructed a mathematical model of a villous membrane. Axial fluxes along villous and intervillous spaces were specified by Nernst-Planck diffusion equations. Model parameters were set to achieve agreement with ion and water fluxes measured in the rat proximal tubule. The equations were solved numerically to generate steady-state concentration profiles in the villous and intervillous spaces. An apparent brush border H2CO2 permeability was determined by perturbing luminal [H2CO2] and calculating the change in H2CO2 flux. Overall, the ratio of apparent brush border H2CO2 permeability to cell membrane H2CO2 permeability was greater than 90%. Contributing to the small decrease in apparent permeability are finite diffusion coefficients, folding of the membrane, and acidification of the luminal solution. An approximate analysis of this system shows the critical parameters of brush border formate transport to be the actual membrane H2CO2 permeability, and the diffusion coefficients of HCO2- and HCO3-. Nevertheless, decreasing the diffusion coefficients by one order of magnitude failed to depress apparent brush border H2CO2 permeability by more than an additional 25%. We conclude that although permeability is systematically underestimated across a villous membrane, unstirred layer effects in the brush border are still too small to resolve the discrepancy between the measured value of H2CO2 permeability and the value needed to allow recycling.

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.

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.

Chloride transport in a mathematical model of the rat proximal tubule

The proximal tubule model of this laboratory [Am. J. Physiol. 250 (Renal Fluid Electrolyte Physiol. 19): F860-F873, 1986] has been updated to examine proposed pathways for Cl- transport. Two additional buffer pairs have been added, i.e., HCO2-/H2CO2 and NH3/NH4+. At the luminal cell membrane Cl-/HCO2- and Cl-/HCO3- exchange are considered as pathways for Cl- entry, whereas at the peritubular membrane, Cl- exit occurs by either Na(+)-2HCO3-/Cl- exchange or K(+)-Cl- cotransport. Calculations with this model indicate that absolute proximal reabsorption of both Na+ and Cl- are critically dependent on the rate of luminal Na+/H+ exchange. In contrast, increases in the coefficient for Cl-/HCO2- exchange have little impact on overall Cl- flux, but, by enhancing base secretion, limit the depression of end-proximal HCO3-. Model calculations confirm those of Preisig and Alpern (J. Clin. Invest. 83: 1859-1867, 1989) showing that their measured value of luminal membrane H2CO2 permeability is inadequate to sustain the transcellular Cl- flux as Cl-/HCO2- exchange. Conversely, with sufficiently high H2CO2 permeability, luminal Cl- uptake is enhanced along the tubule, as HCO2- secretion and luminal acidification increase luminal H2CO2 to values severalfold greater than in glomerular filtrate. At the basolateral membrane, the thermodynamic driving force across the Na(+)-2HCO3-/Cl- exchanger is small. Although its contribution to steady-state Cl- exit may be less than the K(+)-Cl- cotransporter, the Na(+)-2HCO3-/Cl- exchanger can be a mechanism by which cytosolic acidification enhances peritubular Cl- transport, when luminal acidification enhances luminal Cl- uptake. A simulation is presented in which impermeant replacement of luminal Na+ leads to enhanced convective Cl- flux across the tight junction and alkalinization of the lateral interspace. In this setting, cytosolic Cl- depletion via the Na(+)-2HCO3-/Cl- exchanger may mimic luminal membrane Na(+)-Cl- cotransport.

Analysis of volume regulation in an epithelial cell model

An epithelial cell is modeled as a single compartment, bounded by apical and basolateral cell membranes, and containing two nonelectrolyte solute species, nominally NaCl and KCl. Membrane transport of these species may be metabolically driven, or it may follow the transmembrane concentration gradients, either singly (a channel) or jointly (a cotransporter). To represent the effect of stretch-activated channels or shrinkage-activated cotransporters, the membrane permeabilities and cotransport coefficients are permitted to be functions of cell volume. When this epithelium is considered as a dynamical system, conditions are indicated which guarantee the uniqueness and stability of equilibria. Experimentally, many epithelial cells can regulate their volume, and such volume regulatory capability is defined for this model. It is clearly distinct from dynamical stability of the equilibrium and requires more stringent conditions on the volume-dependent permeabilities and cotransporters. For a previously developed model of the toad urinary bladder (Strieter et al., 1990, J. gen. Physiol. 96, 319-344) the uniqueness and stability of its equilibria are indicated. The analysis also demonstrates that under some conditions a second stable equilibrium may appear, along with a saddle-node bifurcation. This is illustrated numerically in a modified model of the epithelium of the thick ascending limb of Henle.

Coupled water transport by rat proximal tubule

Simultaneous microperfusion of proximal tubules and peritubular capillaries in kidneys of rats anesthetized with Inactin was used to examine water reabsorption by this epithelium. Osmolality of the luminal solution was varied with changes in NaCl concentration and by the addition of raffinose. Capillary perfusates contained either low (2 g/dl) or high (16 g/dl) concentrations of albumin. We used low-bicarbonate perfusates for both lumen and capillary so that we might apply the nonequilibrium thermodynamic model of transport for a single solute (NaCl) to interpret our observations. Linear regression with the volume flux equation Jv = -Lp delta II - Lp sigma delta C + Jav (where Jv is volume flux, Lp is hydraulic conductance, delta II is oncotic force, sigma is osmotic reflection coefficient, delta C is salt concentration difference, and Jav is the component of Jv not attributed to transepithelial hydrostatic or osmotic forces) revealed a tubule water permeability (Pf = 0.11 +/- 0.01 cm/s) and a sigma (0.74 +/- 0.08) in agreement with previous determinations. These transport parameters were unaffected by changes in peritubular protein. We also found that Jav was substantial, approximately three-fourths of the rate of isotonic transport under these perfusion conditions. Further, this component of water transport nearly doubled with the transition from low- to high-protein peritubular capillary perfusion. When expressed as a capacity for water reabsorption against an osmotic gradient, the salt concentration differences required to null volume flux were 13.2 +/- 2.4 and 29.4 +/- 4.0 mosmol/kgH2O under low and high peritubular protein. Our data suggest that this protein effect is, most likely, an increase in solute transport by the tubule epithelial cells.

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.

Glomerulotubular balance in a mathematical model of the proximal nephron

A nonelectrolyte model of proximal tubule epithelium has been extended by the inclusion of a compliant tight junction. Here "compliance" signifies that both the junctional salt and water permeability increase and the salt reflection coefficient decreases in response to small pressure differences from lateral interspace to tubule lumen. In previous models of rat proximal tubule, there has been virtually no sensitivity of isotonic salt transport to changes in peritubular oncotic force. With the inclusion of junctional compliance, decreases in peritubular protein can open the junction and produce a secretory salt flux. Thus the model can represent the "backflux hypothesis," as it was originally put forth (J. E. Lewy and E. E. Windhager, Am. J. Physiol. 214: 943-954, 1968). Additional calculations, simulating a tight junction with negligible water permeability, reveal that the quantitative impact of peritubular protein can be realized whether or not there is substantial junctional water flux. The epithelial model of proximal tubule has also been incorporated into a model of the proximal nephron, complete with glomerulus, peritubular capillary, and interstitium. The interstitial compartment is well mixed and interstitial pressure and osmolality are determined iteratively to achieve balance between tubule reabsorption and capillary uptake. For this model, two domains of operation are identified. When interstitial pressures are low, junctions are closed, and filtration fraction has no effect on proximal reabsorption. When interstitial pressures are relatively elevated, epithelial junctions are open, and proximal salt reabsorption changes in proportion to changes in filtration fraction. In neither domain, however, does the model tubule augment salt flux with isolated increases in luminal flow rate (at constant filtration fraction). The absence of a separate effect of tubule fluid flow on salt transport precludes perfect glomerulotubular balance.

Osmotic water permeability of Necturus gallbladder epithelium

An electrophysiological technique that is sensitive to small changes in cell water content and has good temporal resolution was used to determine the hydraulic permeability (Lp) of Necturus gallbladder epithelium. The epithelial cells were loaded with the impermeant cation tetramethylammonium (TMA+) by transient exposure to the pore-forming ionophore nystatin in the presence of bathing solution TMA+. Upon removal of the nystatin a small amount of TMA+ is trapped within the cell. Changes in cell water content result in changes in intracellular TMA+ activity which are measured with intracellular ion-sensitive microelectrodes. We describe a method that allows us to determine the time course for the increase or decrease in the concentration of osmotic solute at the membrane surface, which allows for continuous monitoring of the difference in osmolality across the apical membrane. We also describe a new method for the determination of transepithelial hydraulic permeability (Ltp). Apical and basolateral membrane Lp's were assessed from the initial rates of change in cell water volume in response to anisosmotic mucosal or serosal bathing solutions, respectively. The corresponding values for apical and basolateral membrane Lp's were 0.66 x 10(-3) and 0.38 x 10(-3) cm/s.osmol/kg, respectively. This method underestimates the true Lp values because the nominal osmotic differences (delta II) cannot be imposed instantaneously, and because it is not possible to measure the true initial rate of volume change. A model was developed that allows for the simultaneous determination of both apical and basal membrane Lp's from a unilateral exposure to an anisosmotic bathing solution (mucosal). The estimates of apical and basal Lp with this method were 1.16 x 10(-3) and 0.84 x 10(-3) cm/s.osmol/kg, respectively. The values of Lp for the apical and basal cell membranes are sufficiently large that only a small (less than 3 mosmol/kg) transepithelial difference in osmolality is required to drive the observed rate of spontaneous fluid absorption by the gallbladder. Furthermore, comparison of membrane and transepithelial Lp's suggests that a large fraction of the transepithelial water flow is across the cells rather than across the tight junctions.

A canine composite femoral stem. An in vivo study

To evaluate a carbon fiber/polysulfone composite femoral stem, a press-fit unilateral hemiarthroplasty was performed in 17 greyhounds. The implant was designed to have strength and elastic properties commensurate with the proximal canine femur. The implant geometry was such that the naturally occurring internal cancellous structures of the proximal femur would be preserved and participate in load transfer from the implant to the bone. Animals were killed at one, five, ten, 16, and 24 months. At necropsy all the femoral stems were well fixed and functioning. All implants maintained their structural integrity. Radiographs and computed tomography scans showed a constructive bone remodeling response. Histologic analysis revealed a benign host tissue response, with few inflammatory cells observed. Both bone and fibrous tissue were observed at the implant-host tissue interface. Implants fabricated from carbon/polysulfone composites have the potential for use in load-bearing applications. An implant with appropriate elastic properties provides the opportunity for the natural bone remodeling response to enhance implant stability. Naturally occurring internal cancellous structures can be utilized for load transfer by femoral components. Press-fit devices with no physical or chemical bone-bonding mechanisms can attain long-term successful functional performance.

Modeling the proximal tubule: complications of the paracellular pathway

When the proximal tubule epithelium is represented as cellular and lateral intercellular (LIS) compartments, the presence of a paracellular pathway can render the overall phenomenologic equations quite an indirect representation of intraepithelial transport processes. 1) Active sodium transport into the LIS may create a hypertonic region that drives water movement from lumen to peritubular blood, i.e., a term for active water transport may appear in the overall transport equations. The correlate of this uphill water flux is a solute polarization effect, such that the measured epithelial water permeability is less than that of the cell membranes. 2) Basolateral uptake of potassium by the cell may lower the LIS concentration and promote diffusive entry of K across the tight junction. Even without cellular uptake of K from the lumen, the epithelial transport equations may contain a term for active K reabsorption. The solute polarization correlate is a low epithelial reflection coefficient that does not represent a convective flux of K through a specific channel. 3) When there is convective flux of Na and Cl through the tight junction but none through the cell, then a fluid circuit around junction and cell may be present, even when net epithelial volume flux is absent. In this case, part of the net epithelial Cl flux must be represented in the overall transport equations as electroneutral Na-Cl cotransport.

Convective paracellular solute flux. A source of ion-ion interaction in the epithelial transport equations

An electrolyte model of an epithelium (a cell and a tight junction in parallel, both in series with a lateral interspace basement membrane) is analyzed using the formalism of nonequilibrium thermodynamics. It is shown that if the parallel structures are heteroporous (i.e., reflection coefficients for two ion species differ between the components), then a cross-term will appear in the overall transport equations of the epithelium. Formally, this cross-term represents an ion-ion interaction. With respect to the rat proximal tubule, data indicating epithelial ionic reflection coefficients less than unity, together with the assumption of no transcellular solvent drag, imply the presence of convective paracellular solute flux. This means that a model applicable to a heteroporous structure must be used to represent the tubule, and, in particular, the cross-terms for ion-ion interaction must also be evaluated in permeability determinations. A series of calculations is presented that permits the estimation of the Na-Cl interaction for rat proximal tubule from available experimental data. One consequence of tubule heteroporosity is that an electrical potential may be substantially less effective than an equivalent concentration gradient in driving reabsorptive ion fluxes.

The regulation of cytosolic calcium in rat brain synaptosomes by sodium-dependent calcium efflux

1. When pinched-off presynaptic nerve endings (synaptosomes) isolated from rat brain are incubated in a low-Na (24-36 mM) medium, they take up 45Ca in a time-dependent manner. In a medium containing 1 mM-Ca, this Na-dependent 45Ca uptake amounts to approximately 10 nmol/mg protein at 1 min, and to approximately 40 nmol/mg protein at 20 min. The Na-dependent Ca uptake is not reduced when the synaptosomes are loaded with concentrations of quin 2 as high as 2 mM. 2. The increase in 45Ca uptake is paralleled by an increase in the free cytosolic Ca concentration [Ca]i, as monitored with the fluorescent Ca indicators quin 2 or fura 2. [Ca]i increases from the value of approximately 200 to approximately 500 nM within 3-5 min, and thereafter, remains at this elevated level. 3. When synaptosomes that have been loaded with 45Ca (for 1 min, in a low-Na medium) are diluted into an Na-containing medium, there is a rapid efflux of the Ca load. After correcting for Ca that is taken up during the efflux period, calculations show that the total Ca in the synaptosomes returns to the control level within 1 min. Measurements of total chemical Ca parallel the measurements made with radiotracer Ca, and confirm that the Ca loaded into the nerve terminals during a 5 min incubation in a low-Na medium is extruded from the nerve terminals within 1 min in a normal-Na medium. 4. The efflux of Ca from the synaptosomes is paralleled by a drop of [Ca]i to its basal level, also within 1 min. 5. The mitochondrial uncoupler, carbonyl cyanide p-trifluoromethyloxy-phenyl-hydrazone (FCCP, 1 microM), has no effect on either Na-dependent Ca uptake or efflux in synaptosomes. FCCP causes a slight (100-200 nM) increase in [Ca]i in synaptosomes resuspended in either a Na or a low-Na medium. This indicates that little of the Ca that is taken up by the synaptosomes in a low-Na medium is sequestered by the mitochondria. 6. These results suggest that Na-dependent Ca efflux (probably Na-Ca exchange) plays an important role in allowing nerve terminals to recover rapidly from a Ca load.

A mathematical model of the rat proximal tubule

The equations of mass conservation and electroneutrality are used to extend a nonequilibrium thermodynamic model of the rat proximal tubule epithelium to a representation of a 0.5-cm segment of tubule. The output of the tubule model includes the luminal profiles and absolute proximal reabsorption of Na, K, Cl, HCO3, HPO4, H2PO4, glucose, and urea, generated by the epithelial model. Transport rates and permeabilities, chosen in agreement with those of the rat, result in luminal glucose and bicarbonate depletion and a transition from an electronegative to positive lumen. Despite the development of significant transepithelial osmotic driving forces (a transepithelial glucose gradient and Cl-HCO3 asymmetry), intraepithelial solute-solvent coupling remains an important force for water reabsorption along the proximal tubule length. In particular, this means that when osmotic gradients that appear under free-flow conditions are used in the calculation of the epithelial water permeability, a substantial overestimate of this permeability will be obtained. A single first-order differential equation has been derived in conjunction with an approximate nonelectrolyte model of the proximal tubule that represents both coupled and gradient-driven water reabsorption. In the present work, this equation is shown to yield an accurate description of water transport by the comprehensive tubule model.

Osmotic diuresis in a mathematical model of the rat proximal tubule

Solute reabsorption in the presence of an osmotic load has been examined in a model of the rat proximal convoluted tubule. The model is a computer simulation of a 0.5-cm segment of tubule comprised of compliant cellular and paracellular compartments, which tracks the luminal profiles of Na, K, Cl, HCO3, phosphate, glucose, and urea. In one series of calculations, the peritubular and initial luminal glucose concentrations are varied from 1.0 to 50 mmol/liter. The resulting proximal reabsorption of glucose increases monotonically to 1.5 nmol X s-1 X cm-2. Sodium reabsorption increases with glucose perfusion concentrations between 1.0 and 10 mmol/liter and then declines with greater glucose loads. Above 10 mmol/liter glucose, there is progressive decline in mean luminal Na concentration so that diffusive paracellular backflux, as well as decreased convective reabsorption, are responsible for the natriuresis. Diuresis per se blunts reabsorption of species requiring the development of lumen-to-bath concentration gradients (i.e., K, Cl, and urea). Diminished bicarbonate reabsorption is also predicted with large glucose loads due to intraepithelial alkalinization. This derives both from cellular depolarization and bicarbonate trapping (interspace closure). It is also observed that when interspace closure occurs, a region of intraepithelial K depletion may be formed, promoting diffusive reabsorption of potassium across the tight junction. Thus a 'middle compartment model' for potassium may provide a means of achieving tubule fluid-to-plasma K ratios less than 1.0, in the absence of specific cellular uptake mechanisms.

Transport by epithelia with compliant lateral intercellular spaces: asymmetric oncotic effects across the rat proximal tubule

Mathematical models of the proximal tubule are considered in which the lateral intercellular spaces distend in response to increased interstitial pressures and basal outlet permeabilities increase as a result of interspace widening. An approximate analytical model of the interspace reveals the possibility that such compliance may introduce an asymmetry to the effect of protein oncotic forces on transepithelial volume flow. Peritubular oncotic forces close the interspace, enhance interspace hypertonicity, and thus substantially increase volume reabsorption (enhanced intraepithelial solute-solvent coupling). The model also predicts a decline in epithelial water permeability (Lp), salt reflection coefficient, and salt permeability, with the application of peritubular protein. When parameters are chosen so as to represent the rat proximal tubule, the predicted effect on solute permeability is comparable to the observed changes in electrical resistance of the epithelium. However, when the luminal solution is slightly hypotonic to blood and proximal reabsorption has become isosmotic, the models show relatively small protein effects, which are dependent upon cell and tight junction permeabilities and are little influenced by interspace compliance. The capability of such models to represent the peritubular protein enhancement of isosmotic salt and water reabsorption by the proximal tubule in vivo is questioned.

The overshoot phenomenon in cotransport

Based on simplified equations, the overshoot curve experimentally observed with Na+-linked cotransport of neutral substrate (sugars or amino acids) has been simulated by computer. The approach is in principle similar to that of previous approaches (Weiss, S.D., McNamara, P.D. and Segal, S. (1981) J. Theor. Biol. 91, 597-608), but more general; in particular, it includes the effect of electrical membrane potential difference, and the quantitative relationship between height of peak and certain transport parameters, such as maximum rate, dissociation constant of ternary complex, electric charge of translocator, respectively. In addition, it tests two alternative models with respect to the rate-determining step: the translocation, on the one hand, and the association/dissociation of the ligands at the translocator site, on the other. The major findings are the following: (1) An overshoot can be obtained similar to that usually found experimentally, provided that maximum rate and affinity between translocator and transport of solute exceed certain minimum values. (2) The overshoot effect with Na-linked cotransport is enhanced by a negative membrane potential (inside relative to outside) and decreased by a positive potential. In the first case, the peak is higher and occurs faster. In the latter case, the peak is lower and delayed. (3) The effect of an electric potential difference on the overshoot curve does not depend appreciably on the charge of the empty translocator, except if the translocation of the latter is strongly rate-limiting. (4) To obtain an overshoot curve, it is not necessary that the translocation step be rate-limiting, contrary to what has been postulated previously (Läuger, P. (1980) J. Membrane Biol. 57, 163-178).