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

Effects of Individualized Anemia Therapy on Hemoglobin Stability: A Randomized Controlled Pilot Trial in Patients on Hemodialysis

Key Points

Background

Anemia is common among patients on hemodialysis. Maintaining stable hemoglobin levels within predefined target levels can be challenging, particularly in patients with frequent hemoglobin fluctuations both above and below the desired targets. We conducted a multicenter, randomized controlled trial comparing our anemia therapy assistance software against a standard population-based anemia treatment protocol. We hypothesized that personalized dosing of erythropoiesis-stimulating agents (ESAs) improves hemoglobin target attainment.

Methods

Ninety-six patients undergoing hemodialysis and receiving methoxy polyethylene glycol-epoetin beta were randomized 1:1 to the intervention group (personalized ESA dose recommendations computed by the software) or the standard-of-care group for 26 weeks. The therapy assistance software combined a physiology-based mathematical model and a model predictive controller designed to stabilize hemoglobin levels within a tight target range (10–11 g/dl). The primary outcome measure was the percentage of hemoglobin measurements within the target. Secondary outcome measures included measures of hemoglobin variability and ESA utilization.

Results

The intervention group showed an improved median percentage of hemoglobin measurements within target at 47% (interquartile range, 39–58), with a 10% point median difference between the two groups (95% confidence interval, 3 to 16; P = 0.008). The odds ratio of being within the hemoglobin target in the standard-of-care group compared with the group receiving the personalized ESA recommendations was 0.68 (95% confidence interval, 0.51 to 0.92). The variability of hemoglobin levels decreased in the intervention group, with the percentage of patients experiencing fluctuating hemoglobin levels being 45% versus 82% in the standard-of-care group. ESA usage was reduced by approximately 25% in the intervention group.

Conclusions

Our results demonstrated an improved hemoglobin target attainment and variability by using personalized ESA recommendations using the physiology-based anemia therapy assistance software.

Clinical Trial registration number:

NCT04360902.

Multi-head self-attention mechanism enabled individualized hemoglobin prediction and treatment recommendation systems in anemia management for hemodialysis patients

Anemia is a critical complication in hemodialysis patients, but the response to erythropoietin-stimulating agents (ESA) treatment varies from patient to patient and is not linear across different time points. The aim of this study was to develop deep learning algorithms for individualized anemia management. We retrospectively collected 36,677 data points from 623 hemodialysis patients, including clinical data, laboratory values, hemoglobin levels, and previous ESA doses. To reduce the computational complexity associated with recurrent neural networks (RNN) in processing time-series data, we developed neural networks based on multi-head self-attention mechanisms in an efficient and effective hemoglobin prediction model. Our proposed model achieved a more accurate hemoglobin prediction than the state-of-the-art RNN model, as shown by the smaller mean absolute error (MAE) of hemoglobin (0.451 vs. 0.593 g/dL, p = 0.014). In ESA (including darbepoetin and epoetin) dose recommendation, the simulation results by our model revealed a higher rate of achieved hemoglobin targets (physician prescription vs. model: 86.3 % vs. 92.7 %, p < 0.001), a lower rate of hemoglobin levels below 10 g/dL (13.7 % vs. 7.3 %, p < 0.001) and smaller change in hemoglobin levels (0.6 g/dL vs. 0.4 g/dL, p < 0.001) in all patients. Our model holds great potential for individualized anemia management as a computerized clinical decision support system for hemodialysis patients. Further external validation with other datasets and prospective clinical utility studies are warranted.

Recent Advances and Future Perspectives in the Use of Machine Learning and Mathematical Models in Nephrology

We reviewed some of the latest advancements in the use of mathematical models in nephrology. We looked over 2 distinct categories of mathematical models that are widely used in biological research and pointed out some of their strengths and weaknesses when applied to health care, especially in the context of nephrology. A mechanistic dynamical system allows the representation of causal relations among the system variables but with a more complex and longer development/implementation phase. Artificial intelligence/machine learning provides predictive tools that allow identifying correlative patterns in large data sets, but they are usually harder-to-interpret black boxes. Chronic kidney disease (CKD), a major worldwide health problem, generates copious quantities of data that can be leveraged by choice of the appropriate model; also, there is a large number of dialysis parameters that need to be determined at every treatment session that can benefit from predictive mechanistic models. Following important steps in the use of mathematical methods in medical science might be in the intersection of seemingly antagonistic frameworks, by leveraging the strength of each to provide better care.

A computational model for prediction of ferritin and haemoglobin levels in blood donors

Blood donors are at risk of iron deficiency anaemia. While this risk is decreased through ferritin-based deferral, ideally ferritin monitoring should also aid in optimising donation frequencies. We extended an existing model of haemoglobin (Hb) synthesis with iron homeostasis and validated the model on a cohort of 300 new donors whose ferritin levels were measured from stored blood samples collected over a 2-year period. We then used the donor's gender, body weight, height, and baseline Hb and ferritin levels to predict subsequent Hb and ferritin levels. The prediction error was within measurement variability in 88% of Hb level predictions and 64% of ferritin level predictions. A sensitivity analysis of the model revealed that baseline ferritin level was the most important in predicting future ferritin levels. Finally, we used the model to calculate the annual donation frequency at which donors would keep their ferritin level >15 ng/ml when measured after donating for 2 years. The mean annual donation frequency would then be 1.9 for women and 4.1 for men. The computational model, requiring baseline values only, can predict future Hb and ferritin levels remarkably well. This enables determination of optimal donation frequencies for individual donors at the start of their donation career.

Mathematical Models of Parathyroid Gland Biology: Complexity and Clinical Use

Altered parathyroid gland biology is a major driver of chronic kidney disease-mineral bone disorder (CKD-MBD) in patients with chronic kidney disease. CKD-MBD is associated with a high risk of vascular calcification and cardiovascular events. A hallmark of CKD-MBD is secondary hyperparathyroidism with increased parathyroid hormone (PTH) synthesis and release and reduced expression of calcium-sensing receptors on the surface of parathyroid cells and eventually hyperplasia of parathyroid gland cells. The KDIGO guidelines strongly recommend the control of PTH in hemodialysis patients. Due to the complexity of parathyroid gland biology, mathematical models have been employed to study the interaction of PTH regulators and PTH plasma concentrations. Here, we present an overview of various model approaches and discuss the impact of different model structures and complexities on the clinical use of these models.

The Role of Eryptosis in the Pathogenesis of Renal Anemia: Insights From Basic Research and Mathematical Modeling

Red blood cells (RBC) are the most abundant cells in the blood. Despite powerful defense systems against chemical and mechanical stressors, their life span is limited to about 120 days in healthy humans and further shortened in patients with kidney failure. Changes in the cell membrane potential and cation permeability trigger a cascade of events that lead to exposure of phosphatidylserine on the outer leaflet of the RBC membrane. The translocation of phosphatidylserine is an important step in a process that eventually results in eryptosis, the programmed death of an RBC. The regulation of eryptosis is complex and involves several cellular pathways, such as the regulation of non-selective cation channels. Increased cytosolic calcium concentration results in scramblase and floppase activation, exposing phosphatidylserine on the cell surface, leading to early clearance of RBCs from the circulation by phagocytic cells. While eryptosis is physiologically meaningful to recycle iron and other RBC constituents in healthy subjects, it is augmented under pathological conditions, such as kidney failure. In chronic kidney disease (CKD) patients, the number of eryptotic RBC is significantly increased, resulting in a shortened RBC life span that further compounds renal anemia. In CKD patients, uremic toxins, oxidative stress, hypoxemia, and inflammation contribute to the increased eryptosis rate. Eryptosis may have an impact on renal anemia, and depending on the degree of shortened RBC life span, the administration of erythropoiesis-stimulating agents is often insufficient to attain desired hemoglobin target levels. The goal of this review is to indicate the importance of eryptosis as a process closely related to life span reduction, aggravating renal anemia.

Enhanced prediction of hemoglobin concentration in a very large cohort of hemodialysis patients by means of deep recurrent neural networks

Erythropoiesis Stimulating Agents (ESAs) have become a standard anemia management tool for End Stage Renal Disease (ESRD) patients. However, dose optimization constitutes an extremely challenging task due to huge inter and intra-patient variability in the responses to ESA administration. Current data-based approaches to anemia control focus on learning accurate hemoglobin prediction models, which can be later utilized for testing competing treatment choices and choosing the optimal one. These methods, despite being proven effective in practice, present several shortcomings which this paper intends to tackle. Namely, they are limited to a small cohort of patients and, even then, they fail to provide suggestions when some strict requirements are not met (such as having a three month history prior to the prediction). Here, recurrent neural networks (RNNs) are used to model whole patient histories, providing predictions at every time step since the very first day. Furthermore, an unprecedented amount of data (∼110,000 patients from many different medical centers in twelve countries, without exclusion criteria) was used to train it, thus allowing it to generalize for every single patient. The resulting model outperforms state-of-the-art Hemoglobin prediction, providing excellent results even when tested on a prospective dataset. Simultaneously, it allows to bring the benefits of algorithmic anemia control to a very large group of patients.

A recurrent neural network approach to predicting hemoglobin trajectories in patients with End-Stage Renal Disease

The most severe form of kidney disease, End-Stage Renal Disease (ESRD) is treated with various forms of dialysis - artificial blood cleansing. Dialysis patients suffer many health burdens including high mortality and hospitalization rates, and symptomatic anemia: a low red blood cell count as indicated by a low hemoglobin (Hgb) level. ESRD-induced anemia is treated, with variable patient response, by erythropoiesis stimulating agents (ESAs): expensive injectable medications typically administered during dialysis sessions. The dosing protocol is typically a population level protocol based on original clinical trials, the use of which often results in Hgb cycling. This cycling phenomenon occurs primarily due to the mismatch in the time between dosing decisions and the time it takes for the effects of a dosing change to be fully realized. In this paper we develop a recurrent neural network approach that uses historic data together with future ESA and iron dosing data to predict the 1, 2, and 3 month Hgb levels of patients with ESRD-induced anemia. The results of extensive experimentation indicate that this approach generates predictions that are clinically relevant: the mean absolute error of the predictions is comparable to estimates of the intra-individual variability of the laboratory test for Hgb.

Optimal EPO dosing in hemodialysis patients using a non-linear model predictive control approach

Anemia management with erythropoiesis stimulating agents is a challenging task in hemodialysis patients since their response to treatment varies highly. In general, it is difficult to achieve and maintain the predefined hemoglobin (Hgb) target levels in clinical practice. The aim of this study is to develop a fully personalizable controller scheme to stabilize Hgb levels within a narrow target window while keeping drug doses low to mitigate side effects. First in-silico results of this framework are presented in this paper. Based on a model of erythropoiesis we formulate a non-linear model predictive control (NMPC) algorithm for the individualized optimization of epoetin alfa (EPO) doses. Previous to this work, model parameters were estimated for individual patients using clinical data. The optimal control problem is formulated for a continuous drug administration. This is currently a hypothetical form of drug administration for EPO as it would require a programmable EPO pump similar to insulin pumps used to treat patients with diabetes mellitus. In each step of the NMPC method the open-loop problem is solved with a projected quasi-Newton method. The controller is successfully tested in-silico on several patient parameter sets. An appropriate control is feasible in the tested patients under the assumption that the controlled quantity is measured regularly and that continuous EPO administration is adjusted on a daily, weekly or monthly basis. Further, the controller satisfactorily handles the following challenging problems in simulations: bleedings, missed administrations and dosing errors.