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.

Identification of arterial oxygen intermittency in oximetry data.

In patients with kidney failure treated by hemodialysis, intradialytic arterial oxygen saturation (SaO2) time series present intermittent high-frequency high-amplitude oximetry patterns (IHHOP), which correlate with observed sleep-associated breathing disturbances. A new method for identifying such intermittent patterns is proposed. The method is based on the analysis of recurrence in the time series through the quantification of an optimal recurrence threshold ([Formula: see text]). New time series for the value of [Formula: see text] were constructed using a rolling window scheme, which allowed for real-time identification of the occurrence of IHHOPs. The results for the optimal recurrence threshold were confronted with standard metrics used in studies of obstructive sleep apnea, namely the oxygen desaturation index (ODI) and oxygen desaturation density (ODD). A high correlation between [Formula: see text] and the ODD was observed. Using the value of the ODI as a surrogate to the apnea-hypopnea index (AHI), it was shown that the value of [Formula: see text] distinguishes occurrences of sleep apnea with great accuracy. When subjected to binary classifiers, this newly proposed metric has great power for predicting the occurrences of sleep apnea-related events, as can be seen by the larger than 0.90 AUC observed in the ROC curve. Therefore, the optimal threshold [Formula: see text] from recurrence analysis can be used as a metric to quantify the occurrence of abnormal behaviors in the arterial oxygen saturation time series.

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.

Sample pooling: burden or solution?

BACKGROUND: Pool-testing strategies combine samples from multiple people and test them as a group. A pool-testing approach may shorten the screening time and increase the test rate during times of limited test availability and inadequate reporting speed. Pool testing has been effectively used for a wide variety of infectious disease screening settings. Historically, it originated from serological testing in syphilis. During the current coronavirus disease 2019 (COVID-19) pandemic, pool testing is considered across the globe to inform opening strategies and to monitor infection rates after the implementation of interventions. AIMS: This narrative review aims to provide a comprehensive overview of the global efforts to implement pool testing, specifically for COVID-19 screening. SOURCES: Data were retrieved from a detailed search for peer-reviewed articles and preprint reports using Medline/PubMed, medRxiv, Web of Science, and Google up to 21st March 2021, using search terms "pool testing", "viral", "serum", "SARS-CoV-2" and "COVID-19". CONTENT: This review summarizes the history and theory of pool testing. We identified numerous peer-reviewed articles that describe specific details and practical implementation of pool testing. Successful examples as well as limitations of pool testing, in general and specifically related to the detection of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) RNA and antibodies, are reviewed. While promising, significant operational, pre-analytical, logistical, and economic challenges need to be overcome to advance pool testing. IMPLICATIONS: The theory of pool testing is well understood and numerous successful examples from the past are available. Operationalization of pool testing requires sophisticated processes that can be adapted to the local medical circumstances. Special attention needs to be paid to sample collection, sample pooling, and strategies to avoid re-sampling.

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.

Analysis of Lauffenburger-Kennedy bacterial infection model for tissue inflammation dynamics.

In this paper, we analyze a mathematical model for an inflammatory response to bacterial infection of homogeneous tissues. Specifically, we provide a detailed analysis of the Lauffenburger-Kennedy bacterial infection model and show that the model exhibits three possible equilibria corresponding to a bacteria-free and two endemic compromised steady states. Asymptotic results of the steady states along with the existences of saddle-node connection Hopf bifurcations are shown under certain conditions of the parameters. Within the biological ranges of the parameter values, we observe that the system can exhibit both forward and backward bifurcation. In addition, in both cases, the larger compromise bacterial infection steady state can either approach an equilibrium or can oscillate around it via Hopf bifurcation depending on the value of the ratio of leukocyte mortality to phagocytosis rates. Numerical results are used to provide illustrative examples of these different dynamical patterns observed in the model.

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.

Homo-psychologicus: Reactionary behavioural aspects of epidemics.

We formulate an in silico model of pathogen avoidance mechanism and investigate its impact on defensive behavioural measures (e.g., spontaneous social exclusions and distancing, crowd avoidance and voluntary vaccination adaptation). In particular, we use SIR(B)S (e.g., susceptible-infected-recovered with additional behavioural component) model to investigate the impact of homo-psychologicus aspects of epidemics. We focus on reactionary behavioural changes, which apply to both social distancing and voluntary vaccination participations. Our analyses reveal complex relationships between spontaneous and uncoordinated behavioural changes, the emergence of its contagion properties, and mitigation of infectious diseases. We find that the presence of effective behavioural changes can impede the persistence of disease. Furthermore, it was found that under perfect effective behavioural change, there are three regions in the response factor (e.g., imitation and/or reactionary) and behavioural scale factor (e.g., global/local) factors ρ-α behavioural space. Mainly, (1) disease is always endemic even in the presence of behavioural change, (2) behavioural-prevalence plasticity is observed and disease can sometimes be eradication, and (3) elimination of endemic disease under permanence of permanent behavioural change is achieved. These results suggest that preventive behavioural changes (e.g., non-pharmaceutical prophylactic measures, social distancing and exclusion, crowd avoidance) are influenced by individual differences in perception of risks and are a salient feature of epidemics. Additionally, these findings indicates that care needs to be taken when considering the effect of adaptive behavioural change in predicting the course of epidemics, and as well as the interpretation and development of the public health measures that account for spontaneous behavioural changes.

Mathematical analysis of a multiple strain, multi-locus-allele system for antigenically variable infectious diseases revisited.

Many important pathogens such as HIV/AIDS, influenza, malaria, dengue and meningitis generally exist in phenotypically distinct serotypes that compete for hosts. Models used to study these diseases appear as meta-population systems. Herein, we revisit one of the multiple strain models that have been used to investigate the dynamics of infectious diseases with co-circulating serotypes or strains, and provide analytical results underlying the numerical investigations. In particular, we establish the necessary conditions for the local asymptotic stability of the steady states and for the existence of oscillatory behaviors via Hopf bifurcation. In addition, we show that the existence of discrete antigenic forms among pathogens can either fully or partially self-organize, where (i) strains exhibit no strain structures and coexist or (ii) antigenic variants sort into non-overlapping or minimally overlapping clusters that either undergo the principle of competitive exclusion exhibiting discrete strain structures, or co-exist cyclically.

Cliophysics: socio-political reliability theory, polity duration and African political (in)stabilities.

Quantification of historical sociological processes have recently gained attention among theoreticians in the effort of providing a solid theoretical understanding of the behaviors and regularities present in socio-political dynamics. Here we present a reliability theory of polity processes with emphases on individual political dynamics of African countries. We found that the structural properties of polity failure rates successfully capture the risk of political vulnerability and instabilities in which , , , and of the countries with monotonically increasing, unimodal, U-shaped and monotonically decreasing polity failure rates, respectively, have high level of state fragility indices. The quasi-U-shape relationship between average polity duration and regime types corroborates historical precedents and explains the stability of the autocracies and democracies.