Rapid prototyping of multi-compartment models for urea kinetics in hemodialysis: a System Dynamics approach.

Models of urea kinetics facilitate a mechanistic understanding of urea transfer and provide a tool for optimizing dialysis efficacy. Dual-compartment models have largely replaced single-compartment models as they are able to accommodate the urea rebound on the cessation of dialysis. Modeling the kinetics of urea and other molecular species is frequently regarded as a rarefied academic exercise with little relevance at the bedside. We demonstrate the utility of System Dynamics in creating multi-compartment models of urea kinetics by developing a dual-compartment model that is efficient, intuitive, and widely accessible to a range of practitioners. Notwithstanding its simplicity, we show that the System Dynamics model compares favorably with the performance of a more complex volume-average model in terms of calibration to clinical data and parameter estimation. Its intuitive nature, ease of development/modification, and excellent performance with real-world data may make System Dynamics an invaluable tool in widening the accessibility of hemodialysis modeling.

Nephron morphometry in mice and rats using tomographic microscopy.

The aim was to quantify the glomerular capillary surface area, the segmental tubular radius, length, and area of single nephrons in mouse and rat kidneys. Multiple 2.5-µm-thick serial Epon sections were obtained from three mouse and three rat kidneys for three-dimensional reconstruction of the nephron tubules. Micrographs were aligned for each kidney, and 359 nephrons were traced and their segments localized. Thirty mouse and thirty rat nephrons were selected for further investigation. The luminal radius of each segment was determined by two methods. The luminal surface area was estimated from the radius and length of each segment. High-resolution micrographs were recorded for five rat glomeruli, and the capillary surface area determined. The capillary volume and surface area were corrected for glomerular shrinkage. A positive correlation was found between glomerular capillary area and proximal tubule area. The thickest part of the nephron, i.e., the proximal tubule, was followed by the thinnest part of the nephron, i.e., the descending thin limb, and the diameters of the seven identified nephron segments share the same rank in the two species. The radius and length measurements from mouse and rat nephrons generally share the same pattern; rat tubular radius-to-mouse tubular radius ratio ≈ 1.47, and rat tubular length-to-mouse tubular length ratio ≈ 2.29, suggesting relatively longer tubules in the rat. The detailed tables of mouse and rat glomerular capillary area and segmental radius, length, and area values may be used to enhance understanding of the associated physiology, including existing steady-state models of the urine-concentrating mechanism.

Thermodynamic considerations in renal separation processes.

BACKGROUND: Urine production in the kidney is generally thought to be an energy-intensive process requiring large amounts of metabolic activity to power active transport mechanisms. This study uses a thermodynamic analysis to evaluate the minimum work requirements for urine production in the human kidney and provide a new perspective on the energy costs of urine production. In this study, black-box models are used to compare the Gibbs energy inflow and outflow of the overall kidney and physiologically-based subsections in the kidney, to calculate the work of separation for urine production. RESULTS: The results describe the work done during urine production broadly and for specific scenarios. Firstly, it shows glomerular filtration in both kidneys requires work to be done at a rate of 5 mW under typical conditions in the kidney. Thereafter, less than 54 mW is sufficient to concentrate the filtrate into urine, even in the extreme cases considered. We have also related separation work in the kidney with the excretion rates of individual substances, including sodium, potassium, urea and water. Lastly, the thermodynamic calculations indicate that plasma dilution significantly reduces the energy cost of separating urine from blood. CONCLUSIONS: A comparison of these thermodynamic results with physiological reference points, elucidates how various factors affect the energy cost of the process. Surprisingly little energy is required to produce human urine, seeing that double the amount of work can theoretically be done with all the energy provided through pressure drop of blood flow through the kidneys, while the metabolic energy consumption of the kidneys could possibly drive almost one hundred times more separation work. Nonetheless, the model's outputs, which are summarised graphically, show the separation work's nuances, which can be further analysed in the context of more empirical evidence.

Facilitating Understanding, Modeling and Simulation of Infectious Disease Epidemics in the Age of COVID-19.

Interest in the mathematical modeling of infectious diseases has increased due to the COVID-19 pandemic. However, many medical students do not have the required background in coding or mathematics to engage optimally in this approach. System dynamics is a methodology for implementing mathematical models as easy-to-understand stock-flow diagrams. Remarkably, creating stock-flow diagrams is the same process as creating the equivalent differential equations. Yet, its visual nature makes the process simple and intuitive. We demonstrate the simplicity of system dynamics by applying it to epidemic models including a model of COVID-19 mutation. We then discuss the ease with which far more complex models can be produced by implementing a model comprising eight differential equations of a Chikungunya epidemic from the literature. Finally, we discuss the learning environment in which the teaching of the epidemic modeling occurs. We advocate the widespread use of system dynamics to empower those who are engaged in infectious disease epidemiology, regardless of their mathematical background.

Glomerular protein separation as a mechanism for powering renal concentrating processes.

Various models have been proposed to explain the urine concentrating mechanism in mammals, however uncertainty remains regarding the origin of the energy required for the production of concentrated urine. We propose a novel mechanism for concentrating urine. We postulate that the energy for the concentrating process is derived from the osmotic potentials generated by the separation of afferent blood into protein-rich efferent blood and protein-deplete filtrate. These two streams run in mutual juxtaposition along the length of the nephron and are thus suitably arranged to provide the osmotic potential to concentrate the urine. The proposed model is able to qualitatively explain the production of various urine concentrations under different clinical conditions. An approach to testing the feasibility of the hypothesis is proposed.

Towards Automated Three-Dimensional Tracking of Nephrons through Stacked Histological Image Sets.

An automated approach for tracking individual nephrons through three-dimensional histological image sets of mouse and rat kidneys is presented. In a previous study, the available images were tracked manually through the image sets in order to explore renal microarchitecture. The purpose of the current research is to reduce the time and effort required to manually trace nephrons by creating an automated, intelligent system as a standard tool for such datasets. The algorithm is robust enough to isolate closely packed nephrons and track their convoluted paths despite a number of nonideal, interfering conditions such as local image distortions, artefacts, and interstitial tissue interference. The system comprises image preprocessing, feature extraction, and a custom graph-based tracking algorithm, which is validated by a rule base and a machine learning algorithm. A study of a selection of automatically tracked nephrons, when compared with manual tracking, yields a 95% tracking accuracy for structures in the cortex, while those in the medulla have lower accuracy due to narrower diameter and higher density. Limited manual intervention is introduced to improve tracking, enabling full nephron paths to be obtained with an average of 17 manual corrections per mouse nephron and 58 manual corrections per rat nephron.