Mechanisms of hemoglobin cycling in anemia patients treated with erythropoiesis-stimulating agents.

Patients with renal anemia are frequently treated with erythropoiesis-stimulating agents (ESAs), which are dynamically dosed in order to stabilize blood hemoglobin levels within a specified target range. During typical ESA treatments, a fraction of patients experience hemoglobin 'cycling' periods during which hemoglobin levels periodically over- and undershoot the target range. Here we report a specific mechanism of hemoglobin cycling, whereby cycles emerge from the patient's delayed physiological response to ESAs and concurrent ESA dose adjustments. We introduce a minimal theoretical model that can explain dynamic hallmarks of observed hemoglobin cycling events in clinical time series and elucidates how physiological factors (such as red blood cell lifespan and ESA responsiveness) and treatment-related factors (such as dosing schemes) affect cycling. These results show that in general, hemoglobin cycling cannot be attributed to patient physiology or ESA treatment alone but emerges through an interplay of both, with consequences for the design of ESA treatment strategies.

Hypocalcemia-Induced Slowing of Human Sinus Node Pacemaking.

Each heartbeat is initiated by cyclic spontaneous depolarization of cardiomyocytes in the sinus node forming the primary natural pacemaker. In patients with end-stage renal disease undergoing hemodialysis, it was recently shown that the heart rate drops to very low values before they suffer from sudden cardiac death with an unexplained high incidence. We hypothesize that the electrolyte changes commonly occurring in these patients affect sinus node beating rate and could be responsible for severe bradycardia. To test this hypothesis, we extended the Fabbri et al. computational model of human sinus node cells to account for the dynamic intracellular balance of ion concentrations. Using this model, we systematically tested the effect of altered extracellular potassium, calcium, and sodium concentrations. Although sodium changes had negligible (0.15 bpm/mM) and potassium changes mild effects (8 bpm/mM), calcium changes markedly affected the beating rate (46 bpm/mM ionized calcium without autonomic control). This pronounced bradycardic effect of hypocalcemia was mediated primarily by ICaL attenuation due to reduced driving force, particularly during late depolarization. This, in turn, caused secondary reduction of calcium concentration in the intracellular compartments and subsequent attenuation of inward INaCa and reduction of intracellular sodium. Our in silico findings are complemented and substantiated by an empirical database study comprising 22,501 pairs of blood samples and in vivo heart rate measurements in hemodialysis patients and healthy individuals. A reduction of extracellular calcium was correlated with a decrease of heartrate by 9.9 bpm/mM total serum calcium (p < 0.001) with intact autonomic control in the cross-sectional population. In conclusion, we present mechanistic in silico and empirical in vivo data supporting the so far neglected but experimentally testable and potentially important mechanism of hypocalcemia-induced bradycardia and asystole, potentially responsible for the highly increased and so far unexplained risk of sudden cardiac death in the hemodialysis patient population.

A Multi-Compartment Model Capturing the Pharmacokinetics of the Calcimimetic Cinacalcet.

BACKGROUND/AIMS: Chronic kidney disease-mineral bone disorder is a major complication affecting the vast majority of chronic kidney disease patients. A hallmark of the disorder is an altered parathyroid gland biology resulting in secondary hyperparathyroidism. This condition is widely treated by calcimimetics like cinacalcet which act by allosteric activation of the calcium sensing receptor. METHODS: Here, we present a linear multi-compartment model based on physiological principles such as first-pass metabolism and protein binding, which captures all relevant pharmacokinetic parameters of cinacalcet. RESULTS: Due to the linear structure of the model, simulations are numerically stable and allow fast and accurate short or long-term predictions of cinacalcet concentrations in the body. CONCLUSION: The model compartments are physiological meaningful and can be easily adjusted to various conditions like impaired hepatic clearance or different drug administration regimens. Moreover, the model can be easily adapted to specific patient groups.

Association between intradialytic central venous oxygen saturation and ultrafiltration volume in chronic hemodialysis patients.

Background: Cardiac disease is highly prevalent in hemodialysis (HD) patients. Decreased tissue perfusion, including cardiac, due to high ultrafiltration volumes (UFVs) is considered to be one of the drivers of cardiac dysfunction. While central venous oxygen saturation (ScvO2) is frequently used as an indicator of cardiac output in non-uremic populations, the relationship of ScvO2 and UFV in HD patients remains unclear. Our aim was to determine how intradialytic ScvO2 changes associate with UFV. Methods: We conducted a 6-month retrospective cohort study in maintenance HD patients with central venous catheters as vascular access. Intradialytic ScvO2 was measured with the Critline monitor. We computed treatment-level slopes of intradialytic ScvO2 over time (ScvO2 trend) and applied linear mixed effects models to assess the association between patient-level ScvO2 trends and UFV corrected for body weight (cUFV). Results: We studied 6042 dialysis sessions in 232 patients. In about 62.4% of treatments, ScvO2 decreased. We observed in nearly 80% of patients an inverse relationship between cUFV and ScvO2 trend, indicating that higher cUFV is associated with steeper decline in ScvO2 during dialysis. Conclusions: In most patients, higher cUFV volumes are associated with steeper intradialytic ScvO2 drops. We hypothesize that in a majority of patients the intradialytic cardiac function is fluid dependent, so that in the face of high ultrafiltration rates or volume, cardiac pre-load and consequently cardiac output decreases. Direct measurements of cardiac hemodynamics are warranted to further test this hypothesis.

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.

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.

Proportional integral feedback control of ultrafiltration rate in hemodialysis.

BACKGROUND: Most hemodialysis patients without residual kidney function accumulate fluid between dialysis session that needs to be removed by ultrafiltration. Ultrafiltration usually results in a decline in relative blood volume (RBV). Recent epidemiological research has identified RBV ranges that were associated with significantly better survival. The objective of this work was to develop an ultrafiltration controller to steer a patient's RBV trajectory into these favorable RBV ranges. METHODS: We designed a proportional-integral feedback ultrafiltration controller that utilizes signals from a device that reports RBV. The control goal is to attain the RBV trajectory associated with improved patient survival. Additional constraints such as upper and lower bounds of ultrafiltration volume and rate were realized. The controller was evaluated in in silico and ex vivo bench experiments, and in a clinical proof-of-concept study in two maintenance dialysis patients. RESULTS: In all tests, the ultrafiltration controller performed as expected. In the in silico and ex vivo bench experiments, the controller showed robust reaction toward deliberate disruptive interventions (e.g. signal noise; extreme plasma refill rates). No adverse events were observed in the clinical study. CONCLUSIONS: The ultrafiltration controller can steer RBV trajectories toward desired RBV ranges while obeying to a set of constraints. Prospective studies in hemodialysis patients with diverse clinical characteristics are warranted to further explore the controllers impact on intradialytic hemodynamic stability, quality of life, and long-term outcomes.

Modeling osteoporosis to design and optimize pharmacological therapies comprising multiple drug types.

For the treatment of postmenopausal osteoporosis, several drug classes with different mechanisms of action are available. Since only a limited set of dosing regimens and drug combinations can be tested in clinical trials, it is currently unclear whether common medication strategies achieve optimal bone mineral density gains or are outperformed by alternative dosing schemes and combination therapies that have not been explored so far. Here, we develop a mathematical framework of drug interventions for postmenopausal osteoporosis that unifies fundamental mechanisms of bone remodeling and the mechanisms of action of four drug classes: bisphosphonates, parathyroid hormone analogs, sclerostin inhibitors, and receptor activator of NF-κB ligand inhibitors. Using data from several clinical trials, we calibrate and validate the model, demonstrating its predictive capacity for complex medication scenarios, including sequential and parallel drug combinations. Via simulations, we reveal that there is a large potential to improve gains in bone mineral density by exploiting synergistic interactions between different drug classes, without increasing the total amount of drug administered.

Our bones are constantly being renewed in a fine-tuned cycle of destruction and formation that helps keep them healthy and strong. However, this process can become imbalanced and lead to osteoporosis, where the bones are weakened and have a high risk of fracturing. This is particularly common post-menopause, with one in three women over the age of 50 experiencing a broken bone due to osteoporosis. There are several drug types available for treating osteoporosis, which work in different ways to strengthen bones. These drugs can be taken individually or combined, meaning that a huge number of drug combinations and treatment strategies are theoretically possible. However, it is not practical to test the effectiveness of all of these options in human trials. This could mean that patients are not getting the maximum potential benefit from the drugs available. Jörg et al. developed a mathematical model to predict how different osteoporosis drugs affect the process of bone renewal in the human body. The model could then simulate the effect of changing the order in which the therapies were taken, which showed that the sequence had a considerable impact on the efficacy of the treatment. This occurs because different drugs can interact with each other, leading to an improved outcome when they work in the right order. These results suggest that people with osteoporosis may benefit from altered treatment schemes without changing the type or amount of medication taken. The model could suggest new treatment combinations that reduce the risk of bone fracture, potentially even developing personalised plans for individual patients based on routine clinical measurements in response to different drugs.

A model-based analysis of phenytoin and carbamazepine toxicity treatment using binding-competition during hemodialysis.

Hemodialysis (HD) has limited efficacy towards treatment of drug toxicity due to strong drug-protein binding. In this work, we propose to infuse a competitor drug into the extracorporeal circuit that increases the free fraction of a toxic drug and thereby increases its dialytic removal. We used a mechanistic model to assess the removal of phenytoin and carbamazepine during HD with or without binding-competition. We simulated dialytic removal of (1) phenytoin, initial concentration 70 mg/L, using 2000 mg aspirin, (2) carbamazepine, initial concentration 35 mg/L, using 800 mg ibuprofen, in a 70 kg patient. The competitor drug was infused at constant rate. For phenytoin (~ 13% free at t = 0), HD brings the patient to therapeutic concentration in 460 min while aspirin infusion reduces that time to 330 min. For carbamazepine (~ 27% free at t = 0), the ibuprofen infusion reduces the HD time to reach therapeutic concentration from 265 to 220 min. Competitor drugs with longer half-life further reduce the HD time. Binding-competition during HD is a potential treatment for drug toxicities for which current recommendations exclude HD due to strong drug-protein binding. We show clinically meaningful reductions in the treatment time necessary to achieve non-toxic concentrations in patients poisoned with these two prescription drugs.

A mathematical model of the four cardinal acid-base disorders.

Precise maintenance of acid-base homeostasis is fundamental for optimal functioning of physiological and cellular processes. The presence of an acid-base disturbance can affect clinical outcomes and is usually caused by an underlying disease. It is, therefore, important to assess the acid-base status of patients, and the extent to which various therapeutic treatments are effective in controlling these acid-base alterations. In this paper, we develop a dynamic model of the physiological regulation of an HCO3-/CO2 buffering system, an abundant and powerful buffering system, using Henderson-Hasselbalch kinetics. We simulate the normal physiological state and four cardinal acidbase disorders: Metabolic acidosis and alkalosis and respiratory acidosis and alkalosis. We show that the model accurately predicts serum pH over a range of clinical conditions. In addition to qualitative validation, we compare the in silico results with clinical data on acid-base homeostasis and alterations, finding clear relationships between primary acid-base disturbances and the secondary adaptive compensatory responses. We also show that the predicted primary disturbances accurately resemble clinically observed compensatory responses. Furthermore, via sensitivity analysis, key parameters were identified which could be the most effective in regulating systemic pH in healthy individuals, and those with chronic kidney disease and distal and proximal renal tubular acidosis. The model presented here may provide pathophysiologic insights and can serve as a tool to assess the safety and efficacy of different therapeutic interventions to control or correct acid-base disorders.

A mathematical model of parathyroid gland biology.

Altered parathyroid gland biology in patients with chronic kidney disease (CKD) is a major contributor to chronic kidney disease-mineral bone disorder (CKD-MBD). This disorder is associated with an increased risk of bone disorders, vascular calcification, and cardiovascular events. Parathyroid hormone (PTH) secretion is primarily regulated by the ionized calcium concentration as well as the phosphate concentration in the extracellular fluid and vitamin D. The metabolic disturbances in patients with CKD lead to alterations in the parathyroid gland biology. A hallmark of CKD is secondary hyperparathyroidism, characterized by an increased production and release of PTH, reduced expression of calcium-sensing and vitamin D receptors on the surface of parathyroid cells, and hyperplasia and hypertrophy of these cells. These alterations happen on different timescales and influence each other, thereby triggering a cascade of negative and positive feedback loops in a highly complex manner. Due to this complexity, mathematical models are a useful tool to break down the patterns of the multidimensional cascade of processes enabling the detailed study of subsystems. Here, we introduce a comprehensive mathematical model that includes the major adaptive mechanisms governing the production, secretion, and degradation of PTH in patients with CKD on hemodialysis. Combined with models for medications targeting the parathyroid gland, it provides a ready-to-use tool to explore treatment strategies. While the model is of particular interest for use in hemodialysis patients with secondary hyperparathyroidism, it has the potential to be applicable to other clinical scenarios such as primary hyperparathyroidism or hypo- and hypercalcemia.

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.

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.

An in silico method to predict net calcium transfer during hemodialysis.

International guidelines for chronic hemodialysis patients suggest a dialysate calcium concentration between 1.25 and 1.5 mmol/L. However, it is not certain if these dialysate calcium levels result in net calcium transfer into the patient. With ubiquitous prevalence of vascular calcification in hemodialysis patients, it is pertinent to model the mass balance of calcium during dialysis. To this end, we developed a two compartmental patient model and spatiotemporal representation of dialyzer model to investigate and quantify the calcium mass balance during dialysis. The model accounts for calcium-albumin binding and varying protein concentration; the latter accounts for the Gibbs-Donnan effect. The model simulations suggest that despite a lower dialysate calcium concentration of 1.25 mmol/L, some of our patients may be loaded with calcium during dialysis. This net calcium flux from dialysate to blood side may be a potential contributor to vascular calcification, a primary cause of cardiovascular mortality in hemodialysis patients.

Intradialytic Central Venous Oxygen Saturation is Associated with Clinical Outcomes in Hemodialysis Patients.

Central venous oxygen saturation (ScvO2) in the superior vena cava is predominantly determined by cardiac output, arterial oxygen content, and oxygen consumption by the upper body. While abnormal ScvO2 levels are associated with morbidity and mortality in non-uremic populations, ScvO2 has received little attention in hemodialysis patients. From 1/2012 to 8/2015, 232 chronic hemodialysis patients with central venous catheters as vascular access had their ScvO2 monitored during a 6-month baseline period and followed for up to 36 months. Patients were stratified into upper and lower two tertiles by a ScvO2 of 61.1%. Survival analysis employed Kaplan-Meier curves and adjusted Cox proportional hazards models. Patients in the lower tertiles of ScvO2 were older, had longer hemodialysis vintage, lower systolic blood pressure, lower ultrafiltration rates, higher leukocyte counts and neutrophil-to-lymphocyte ratios. Kaplan-Meier analysis indicated a shorter survival time in the lower tertiles of ScvO2 (P = 0.005, log-rank test). In adjusted Cox analysis, a 1 percent point decrease in mean ScvO2 was associated with a 4% increase in mortality (HR 1.04 [95% CI 1.01-1.08], P = 0.044), indicating that low ScvO2 is associated with poor outcomes. Research on the relative contributions of cardiac output and other factors is warranted to further elucidate the pathophysiology underlying this novel finding.

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.