Mathematical models for kidney function focusing on clinical interest

Mathematical models of cystic fibrosis as a systemic disease

Cystic fibrosis (CF) is widely known as a disease of the lung, even though it is in truth a systemic disease, whose symptoms typically manifest in gastrointestinal dysfunction first. CF ultimately impairs not only the pancreas and intestine but also the lungs, gonads, liver, kidneys, bones, and the cardiovascular system. It is caused by one of several mutations in the gene of the epithelial ion channel protein CFTR. Intense research and improved antimicrobial treatments during the past eight decades have steadily increased the predicted life expectancy of a person with CF (pwCF) from a few weeks to over 50 years. Moreover, several drugs ameliorating the sequelae of the disease have become available in recent years, and notable treatments of the root cause of the disease have recently generated substantial improvements in health for some but not all pwCF. Yet, numerous fundamental questions remain unanswered. Complicating CF, for instance in the lung, is the fact that the associated insufficient chloride secretion typically perturbs the electrochemical balance across epithelia and, in the airways, leads to the accumulation of thick, viscous mucus and mucus plaques that cannot be cleared effectively and provide a rich breeding ground for a spectrum of bacterial and fungal communities. The subsequent infections often become chronic and respond poorly to antibiotic treatments, with outcomes sometimes only weakly correlated with the drug susceptibility of the target pathogen. Furthermore, in contrast to rapidly resolved acute infections with a single target pathogen, chronic infections commonly involve multi-species bacterial communities, called "infection microbiomes," that develop their own ecological and evolutionary dynamics. It is presently impossible to devise mathematical models of CF in its entirety, but it is feasible to design models for many of the distinct drivers of the disease. Building upon these growing yet isolated modeling efforts, we discuss in the following the feasibility of a multi-scale modeling framework, known as template-and-anchor modeling, that allows the gradual integration of refined sub-models with different granularity. The article first reviews the most important biomedical aspects of CF and subsequently describes mathematical modeling approaches that already exist or have the potential to deepen our understanding of the multitude aspects of the disease and their interrelationships. The conceptual ideas behind the approaches proposed here do not only pertain to CF but are translatable to other systemic diseases. This article is categorized under: Congenital Diseases > Computational Models.

Navigating Between Right, Wrong, and Relevant: The Use of Mathematical Modeling in Preclinical Decision Making

The goal of this mini-review is to summarize the collective experience of the authors for how modeling and simulation approaches have been used to inform various decision points from discovery to First-In-Human clinical trials. The article is divided into a high-level overview of the types of problems that are being aided by modeling and simulation approaches, followed by detailed case studies around drug design (Nektar Therapeutics, Genentech), feasibility analysis (Novartis Pharmaceuticals), improvement of preclinical drug design (Pfizer), and preclinical to clinical extrapolation (Merck, Takeda, and Amgen).

Quantitative renal magnetic resonance imaging: magnetic resonance urography

The goal of functional renal imaging is to identify and quantitate irreversible renal damage and nephron loss, as well as potentially reversible hemodynamic changes. MR urography has evolved into a comprehensive evaluation of the urinary tract that combines anatomical imaging with functional evaluation in a single test without ionizing radiation. Quantitative functional MR imaging is based on dynamic contrast-enhanced MR acquisitions that provide progressive, visible enhancement of the renal parenchyma and urinary tract. The signal changes related to perfusion, concentration and excretion of the contrast agent can be evaluated using both quantitative and qualitative measures. Functional evaluation with MR has continued to improve as a result of significant technical advances allowing for faster image acquisition as well as the development of new tracer kinetic models of renal function. The most common indications for MR urography in children are the evaluation of congenital anomalies of the kidney and urinary tract including hydronephrosis and renal malformations, and the identification of ectopic ureters in children with incontinence. In this paper, we review the underlying acquisition schemes and techniques used to generate quantitative functional parameters including the differential renal function (DRF), asymmetry index, mean transit time (MTT), signal intensity versus time curves as well as the calculation of individual kidney glomerular filtration rate (GFR). Visual inspection and semi-quantitative assessment using the renal transit time (RTT) and calyceal transit times (CTT) are fundamental to accurate diagnosis and are used as a basis for the interpretation of the quantitative data. The importance of visual assessment of the images cannot be overstated when analyzing the quantitative measures of renal function.