In silico comparison of protein-bound uremic toxin removal by hemodialysis, hemodiafiltration, membrane adsorption, and binding competition.

Protein-bound uremic toxins (PBUTs) are poorly removed during hemodialysis (HD) due to their low free (dialyzable) plasma concentration. We compared PBUT removal between HD, hemodiafiltration (HDF), membrane adsorption, and PBUT displacement in HD. The latter involves infusing a binding competitor pre-dialyzer, which competes with PBUTs for their albumin binding sites and increases their free fraction. We used a mathematical model of PBUT/displacer kinetics in dialysis comprising a three-compartment patient model, an arterial/venous tube segment model, and a dialyzer model. Compared to HD, improvements in removal of prototypical PBUTs indoxyl sulfate (initial concentration 100 µM, 7% free) and p-cresyl sulfate (150 µM, 5% free) were: 5.5% and 6.4%, respectively, for pre-dilution HDF with 20 L replacement fluid; 8.1% and 9.1% for post-dilution HDF 20 L; 15.6% and 18.3% for pre-dilution HDF 60 L; 19.4% and 22.2% for complete membrane adsorption; 35.0% and 41.9% for displacement with tryptophan (2000 mg in 500 mL saline); 26.7% and 32.4% for displacement with ibuprofen (800 mg in 200 mL saline). Prolonged (one-month) use of tryptophan reduces the IS and pCS time-averaged concentration by 28.1% and 29.9%, respectively, compared to conventional HD. We conclude that competitive binding can be a pragmatic approach for improving PBUT removal.

A model of vascular refilling with inflammation.

Inflammation is prevalent in hemodialysis patients and is believed to significantly contribute to cardiovascular disease progression in end stage renal disease patients undergoing hemodialysis. Increased vascular permeability associated with inflammation is likely to influence the capillary wall properties, affecting vascular refilling during hemodialysis. In this paper, we present a model that incorporates inflammation into a vascular refilling model. We investigate how inflammation may affect the fluid volume and protein concentration dynamics in the plasma and interstitial spaces. In our work, we quantify inflammation by considering the concentration of the inflammatory biomarker C-reactive protein (CRP). Traditional sensitivity functions and subset selection based on asymptotic standard errors were used to aid in parameter identification. Estimates of the parameters were calculated from numerically generated measurements for fluid flux and hematocrit. Observations on the capillary wall properties, filtration and reflection coefficients, were done using data on mean CRP and serum albumin from a large population of European hemodialysis patients in their terminal two years before death and patients surviving for at least four years after dialysis initiation.

Prediction of hemoglobin levels in individual hemodialysis patients by means of a mathematical model of erythropoiesis.

Anemia commonly occurs in people with chronic kidney disease (CKD) and is associated with poor clinical outcomes. The management of patients with anemia in CKD is challenging, due to its severity, frequent hypo-responsiveness to treatment with erythropoiesis stimulating agents (ESA) and common hemoglobin cycling. Nonlinear dose-response curves and long delays in the effect of treatment on red blood cell population size complicate predictions of hemoglobin (Hgb) levels in individual patients. A comprehensive physiology based mathematical model for erythropoiesis was adapted individually to 60 hemodialysis patients treated with ESAs by identifying physiologically meaningful key model parameters from temporal Hgb data. Crit-Line® III monitors provided non-invasive Hgb measurements for every hemodialysis treatment. We used Hgb data during a 150-day baseline period together to estimate a patient's individual red blood cell lifespan, effects of the ESA on proliferation of red cell progenitor cells, endogenous erythropoietin production and ESA half-life. Estimated patient specific parameters showed excellent alignment with previously conducted clinical studies in hemodialysis patients. Further, the model qualitatively and quantitatively reflected empirical hemoglobin dynamics in demographically, anthropometrically and clinically diverse patients and accurately predicted the Hgb response to ESA therapy in individual patients for up to 21 weeks. The findings suggest that estimated model parameters can be used as a proxy for parameters that are clinically very difficult to quantify. The presented method has the potential to provide new insights into the individual pathophysiology of renal anemia and its association with clinical outcomes and can potentially be used to guide personalized anemia treatment.

The Virtual Anemia Trial: An Assessment of Model-Based In Silico Clinical Trials of Anemia Treatment Algorithms in Patients With Hemodialysis.

In silico approaches have been proposed as a novel strategy to increase the repertoire of clinical trial designs. Realistic simulations of clinical trials can provide valuable information regarding safety and limitations of treatment protocols and have been shown to assist in the cost-effective planning of clinical studies. In this report, we present a blueprint for the stepwise integration of internal, external, and ecological validity considerations in virtual clinical trials (VCTs). We exemplify this approach in the context of a model-based in silico clinical trial aimed at anemia treatment in patients undergoing hemodialysis (HD). Hemoglobin levels and subsequent anemia treatment were simulated on a per patient level over the course of a year and compared to real-life clinical data of 79,426 patients undergoing HD. The novel strategies presented here, aimed to improve external and ecological validity of a VCT, significantly increased the predictive power of the discussed in silico trial.

A novel mathematical model of protein-bound uremic toxin kinetics during hemodialysis.

Protein-bound uremic toxins (PBUTs) are difficult to remove by conventional hemodialysis; a high degree of protein binding reduces the free fraction of toxins and decreases their diffusion across dialyzer membranes. Mechanistic understanding of PBUT kinetics can open new avenues to improve their dialytic removal. We developed a comprehensive model of PBUT kinetics that comprises: (1) a three-compartment patient model, (2) a dialyzer model. The model accounts for dynamic equilibrium between protein, toxin, and the protein-toxin complex. Calibrated and validated using clinical and experimental data from the literature, the model predicts key aspects of PBUT kinetics, including the free and bound concentration profiles for PBUTs and the effects of dialysate flow rate and dialyzer size on PBUT removal. Model simulations suggest that an increase in dialysate flow rate improves the reduction ratio (and removal) of strongly protein-bound toxins, namely, indoxyl sulfate and p-cresyl sulfate, while for weakly bound toxins, namely, indole-3-acetic acid and p-cresyl glucuronide, an increase in blood flow rate is advantageous. With improved dialyzer performance, removal of strongly bound PBUTs improves gradually, but marginally. The proposed model can be used for optimizing the dialysis regimen and for in silico testing of novel approaches to enhance removal of PBUTs.

Control aspects of the human cardiovascular-respiratory system under a nonconstant workload.

The human cardiovascular system (CVS) and respiratory system (RS) work together in order to supply oxygen (O2) and other substrates needed for metabolism and to remove carbon dioxide (CO2). Global and local control mechanisms act on the CVS in order to adjust blood flow to the different parts of the body. This, in turn, affects the RS since the amount of O2 and CO2 transported, respectively to and away from the tissues depends on the cardiac output and blood flow in both the systemic and pulmonary circuits of the CVS. Local metabolic control is influenced by local concentrations of blood gases affecting systemic resistance, resulting to vasoconstriction/vasodilation. Thus, the exchange of blood gases demands a tight coordination between blood flow and ventilation of the lungs. In this work, a model of the cardiovascular-respiratory system (CVRS) is considered to obtain an optimal control for time-dependent ergometric workloads by using the Euler-Lagrange formulation of the optimal control problem. The essential controls in the CVRS model are variations in the heart rate and alveolar ventilation through which the central nervous system restricts the arterial partial pressure of CO2 ( [Formula: see text] ) close to 40  mmHg. Further, penalization terms in the cost functional are included to match the metabolic need for O2 and the metabolic production of CO2 with O2- and CO2-transport by blood.

Intradialytic Hypoxemia and Clinical Outcomes in Patients on Hemodialysis.

BACKGROUND AND OBJECTIVES: Intradialytic hypoxemia has been recognized for decades, but its associations with outcomes have not yet been assessed in a large patient cohort. DESIGN, SETTING, PARTICIPANTS, & MEASUREMENTS: Our retrospective cohort study was conducted between January of 2012 and January of 2015. We recorded blood oxygen saturation every minute during hemodialysis in patients with arteriovenous access. A 6-month baseline period with at least 10 treatments with oxygen saturation measurements preceded a 12-month follow-up. Patients were stratified by the presence or absence of prolonged intradialytic hypoxemia defined as oxygen saturation <90% for at least one third of the treatment time. Demographic, laboratory, and treatment data and hospitalization and mortality rates were compared between the groups. Multivariate Cox regression analysis was used to assess baseline predictors of all-cause mortality during follow-up. RESULTS: In total, 100 (10%) of 983 patients had prolonged intradialytic hypoxemia. These patients were older (+3.6 years; 95% confidence interval, 0.8 to 6.3), had longer dialysis vintage (+1.2 years; 95% confidence interval, 0.3 to 2.1), and had higher prevalence of congestive heart failure (+10.8%; 95% confidence interval, 1.6 to 20.7) and chronic obstructive pulmonary disease (+13%; 95% confidence interval, 5 to 21.2). They also resembled an inflammatory phenotype, with lower serum albumin levels (-0.1 g/dl; 95% confidence interval, -0.2 to 0) and higher neutrophil-to-lymphocyte ratios (+1; 95% confidence interval, 0.5 to 1.6). They had lower hemoglobin levels (-0.2 g/dl; 95% confidence interval, -0.4 to 0) and required more erythropoietin (+1374 U per hemodialysis treatment; 95% confidence interval, 343 to 2405). During follow-up, all-cause hospitalization (1113 hospitalizations; univariate hazard ratio, 1.46; 95% confidence interval, 1.22 to 1.73) and mortality (89 deaths; adjusted hazard ratio, 1.98; 95% confidence interval, 1.14 to 3.43) were higher in patients with prolonged intradialytic hypoxemia. CONCLUSIONS: Prolonged intradialytic hypoxemia was associated with laboratory indicators of inflammation, higher erythropoietin requirements, and higher all-cause hospitalization and mortality.

A physiologically based model of vascular refilling during ultrafiltration in hemodialysis.

An assessment of fluid status can be obtained by monitoring relative blood volume (RBV) during hemodialysis (HD) treatment. The dynamics of RBV is determined by fluid removal from the intravascular compartment by ultrafiltration (UF) and vascular refill from the interstitium. To characterize this dynamics, a two-compartment model describing the short-term dynamics of vascular refilling and UF is developed. Fluid movement between the compartments is governed by lymphatic and microvascular fluid shifts. Further, protein flux is described by convection, diffusion and the lymphatic protein flux. Patient specific parameters are identified based on hematocrit (Hct) measurements by the Crit-Line monitor (CLM). Different measurement frequencies and UF profiles are compared to determine data fidelity and influence on the quality of parameter estimates. This relevant information can be used to assess the (patho)physiological status of hemodialysis patients and could aid in individualizing therapy.

Estimation of arterio-venous access blood flow in hemodialysis patients using video image processing technique.

Assessment of arterio-venous fistula (AVF) blood flow (ABF) is vital in hemodialysis (HD) patients. Currently, no non-invasive and contact-free technique is available to accurately measure ABF in routine clinical practice. In this study, we developed a novel approach using video image processing (VIP) to measure the change in optic flow in the skin. We the tested the hypothesis that the change in optical flow, expressed as the change in pixels between consecutive frames, is related to ABF. We recorded AVF videos in 40 HD patients using a digital camera and processed them by VIP technique. We then compared the actual ABF as measured by routine online clearance (ABFOLC) and the amplitude (AMP) of optical flow. Technical and procedural errors rendered VIP invalid in 13 patients. In the remaining 27 patients the optical flow AMP was significantly lower in patients with low (<;900 ml/min) ABFOLC compared to patients with normal (≥900 ml/min) ABFOLC (AMP 3.4±1*103 vs 5.2±1.4 *103 [pixels], p<;0.01). In these 27 patients AMP correlated with ABFOLC (R2=0.71, p<;0.0001). While more extensive research is necessary, these preliminary results indicate the potential usefulness of the VIP technique to identify low ABF.

Accelerated or out of control: the final months on dialysis.

Mortality rates in dialysis patients are as high as 20% per year. Recent epidemiologic evidence indicates common patterns in biological and clinical indicators before death. Blood pressure, serum albumin levels, C-reactive protein, body weight, and other indicators change, at a population level, at an accelerated rate of change months before death. The escalation of inflammation (as indicated by a surge of C-reactive protein) appears to be a central event. The etiology of blood pressure decline before death is unclear. Although progressive heart failure is well documented in dialysis patients and a potential cause for blood pressure decline, adaptive functional changes need to be considered. In the general population, an inverse relationship between body weight and blood pressure is well described, and it is reasonable to hypothesize that the blood pressure decline before death is an adaptive response to a decline in body weight. Comparable trajectories of biological indicators before death are also documented in nonrenal illnesses, such as chronic obstructive pulmonary disease and certain malignancies. Descriptive analysis of clinical and laboratory variables clearly indicates an accelerated time course in most instances, pointing toward a loss of regulatory functions in a number of physiological subsystems. One can think of 2 reasons for that, (a) important control loops are damaged by the long-term effects of the disease, so that the system cannot react in a proper fashion to perturbations; and (b) the regulatory functions are still properly working, but are confronted with situations, which were of no relevance in the evolution of the system. More extensive research into qualitative and quantitative aspects of physiological control mechanisms is required to answer the question if the observed changes before death are indicative of failed control mechanisms and/or adaptive processes.

Stabilizing control for a pulsatile cardiovascular mathematical model.

In this paper, we develop a pulsatile model for the cardiovascular system which describes the reaction of this system to a submaximal constant workload imposed on a person at a bicycle ergometer test after a period of rest. Furthermore, the model should allow to use measurements for the pulsatile pressure in fingertips which provide information on the diastolic and the systolic pressure for parameter estimation. Based on the assumption that the baroreceptor loop is the essential control loop in this case, we design a stabilizing feedback control for the pulsatile model which is obtained by solving a linear-quadratic regulator problem for the linearization of a non-pulsatile counterpart of the pulsatile model. We also investigate the behavior of the model with respect to changes in the weight of the term in the cost functional for the linear-quadratic regulator problem which penalizes the deviation of the momentary pressure in the aorta from the pressure at the stationary situation which should be obtained.

Modeling of change in blood volume and extracellular fluid volume during hemodialysis.

Knowledge of dynamics of shift of fluid volume between intra- and extravascular compartments during hemodialysis (HD) is important for managing HD treatment to help patients approach dry weight without hypotension. The Relative blood volume (RBV) monitor indicates change in plasma volume based on the difference between ultrafiltration rate (UFR) and plasma refilling rate (PRR) during HD. However, the absolute value of PRR cannot be obtained from RBV. The aim of this study was to investigate whether fluid transport from the interstitial to blood spaces can be quantitatively analyzed with a two compartments model. 14 patients (30 measurements) were studied. RBV using a blood volume monitor (BVM, Fresenius) and calf extracellular volumes (ECV) by calf bioimpedance device (Hydra 4200, Xitron) were continuously measured during HD. A mathematic model was established with unknown transport coefficients (k1, k2, α, ß, γ, δ) and these coefficients were estimated using a Least Squares Optimization algorithm by fitting from experimental data. A high correlation (R(2)>0.8) between experimental data and calculation by the model were observed in both RBV and ECV measurements. Coefficients k1 and δ significantly differed with different degree of hydration. This model provides parameters which can used to understand relationships between degree of hydration and refilling rate.

Absolute blood volume in hemodialysis patients: why is it relevant, and how to measure it?.

Intradialytic hypotension (IDH) is the most common complication during hemodialysis and is associated with significant morbidity. It occurs as a consequence of a reduction in blood volume during ultrafiltration. Today, devices for monitoring relative blood volume (i.e. the intradialytic blood volume as a fraction of the blood volume at the start of the dialysis treatment) are routinely available and have been used to analyze the relationship between changes in relative blood volume and the occurrence of IDH in an attempt to derive critical thresholds that, when observed, would help avoid hypotensive episodes during the treatment. However, the results have been unsatisfactory in many patients. Here we illustrate the importance of absolute blood volume in hemodialysis patients, summarize the acute physiologic mechanisms involved in the preservation of adequate circulation during ultrafiltration, and outline why hemodialysis patients are often particularly vulnerable to reductions in blood volume. We then discuss the shortcomings of relative blood volume measurements, make a case for the superiority of absolute blood volume measurements, and introduce the reader to a mathematical concept that allows relative blood volume devices to be used for the estimation of absolute blood volume. Finally, we discuss the implications of absolute blood volume beyond IDH and propose a paradigm shift in the approach to dry weight attainment.

A model of erythropoiesis in adults with sufficient iron availability.

In this paper we present a model for erythropoiesis under the basic assumption that sufficient iron availability is guaranteed. An extension of the model including a sub-model for the iron dynamics in the body is topic of present research efforts. The model gives excellent results for a number of important situations: recovery of the red blood cell mass after blood donation, adaptation of the number of red blood cells to changes in the altitude of residence and, most important, the reaction of the body to different administration regimens of erythropoiesis stimulating agents, as for instance in the case of pre-surgical administration of Epoetin-α. The simulation results concerning the last item show that choosing an appropriate administration regimen can reduce the total amount of the administered drug considerably. The core of the model consists of structured population equations for the different cell populations which are considered. A key feature of the model is the incorporation of neocytolysis.

Bridging different perspectives of the physiological and mathematical disciplines.

The goal of this report is to discuss educational approaches for bridging the different perspectives of the physiological and mathematical disciplines. These approaches can enhance the learning experience for physiology, medical, and mathematics students and simultaneously act to stimulate mathematical/physiological/clinical interdisciplinary research. While physiology education incorporates mathematics, via equations and formulas, it does not typically provide a foundation for interdisciplinary research linking mathematics and physiology. Here, we provide insights and ideas derived from interdisciplinary seminars involving mathematicians and physiologists that have been conducted over the last decade. The approaches described here can be used as templates for giving physiology and medical students insights into how sophisticated tools from mathematics can be applied and how the disciplines of mathematics and physiology can be integrated in research, thereby fostering a foundation for interdisciplinary collaboration. These templates are equally applicable to linking mathematical methods with other life and health sciences in the educational process.

Time delay in physiological systems: analyzing and modeling its impact.

This article examines the functional and clinical impact of time delays that arise in human physiological systems, especially control systems. An overview of the mathematical and physiological contexts for considering time delays will be illustrated, from the system level to cell level, by examining models that incorporate time delays. This examination will highlight how such delays in combination with other system structures and parameters influence system dynamics. Model analysis that reveals the influence of delays can also reveal related physiological effects which may have medical consequences and clinical applications.

Comparison of Optimal Design Methods in Inverse Problems.

Typical optimal design methods for inverse or parameter estimation problems are designed to choose optimal sampling distributions through minimization of a specific cost function related to the resulting error in parameter estimates. It is hoped that the inverse problem will produce parameter estimates with increased accuracy using data collected according to the optimal sampling distribution. Here we formulate the classical optimal design problem in the context of general optimization problems over distributions of sampling times. We present a new Prohorov metric based theoretical framework that permits one to treat succinctly and rigorously any optimal design criteria based on the Fisher Information Matrix (FIM). A fundamental approximation theory is also included in this framework. A new optimal design, SE-optimal design (standard error optimal design), is then introduced in the context of this framework. We compare this new design criteria with the more traditional D-optimal and E-optimal designs. The optimal sampling distributions from each design are used to compute and compare standard errors; the standard errors for parameters are computed using asymptotic theory or bootstrapping and the optimal mesh. We use three examples to illustrate ideas: the Verhulst-Pearl logistic population model [13], the standard harmonic oscillator model [13] and a popular glucose regulation model [16, 19, 29].

Patterns of cardiovascular control during repeated tests of orthostatic loading.

To investigate patterns of cardiovascular control, a protocol of head up tilt (HUT) followed by lower body negative pressure (LBNP), which represents a significant cardiovascular control challenge, was employed. Linear regression of beat-to-beat heart rate (HR) and mean blood pressure (MBP) data collected over repeated tests was used to analyze control response during the LBNP phase of the combined HUT + LBNP protocol. Four runs for each of 10 healthy young males reaching presyncope were analyzed. Subjects were classified into 2 groups based on the consistency of MBP regulation in response to central hypovolemia induced by LBNP. The consistent group tended to exhibit consistent HR slope (rate of change of HR over time as calculated by linear regression) whereas subjects in the inconsistent group could not be easily classified. Subjects with consistent MBP maintenance exhibited patterns suggesting a consistency of response in cardiovascular control whereas subjects less successful in maintaining MBP exhibited less clearly defined patterns over four runs.

Receding horizon controller for the baroreceptor loop in a model for the cardiovascular system.

In this article, we discuss the design and implementation of a receding horizon control (RHC) which will be used to represent the control for the baroreceptor loop in the human cardiovascular system (CVS). This control will be applied to a model of the CVS developed in a previous work by Kappel and Peer. In that earlier work, a linear quadratic control strategy (LQR) was implemented to represent this baroreflex control which was designed to stabilize the system under an ergometric workload. The RHC approach will be examined as an alternate to the LQR implementation. The control parameters in the cost functional of the RHC will be estimated using the same experimental data as was used in the LQR study. The results of the RHQ implementation will be compared with the LQR implementation.