Deep brain stimulation pulse sequences to optimally modulate frequency-specific neural activity.

OBJECTIVE: Precise neuromodulation systems are needed to identify the role of neural oscillatory dynamics in brain function and to advance the development of brain stimulation therapies tailored to each patient's signature of brain dysfunction. Low-frequency, local field potentials (LFPs) are of increasing interest for the development of these systems because they can reflect the synaptic inputs to a recorded neuronal population and can be chronically recorded in humans. In this computational study, we aim to identify stimulation pulse patterns needed to optimally maximize the suppression or amplification of frequency-specific neural activity. Approach: We derived DBS pulse patterns to minimize or maximize the 2-norm of frequency-specific neural oscillations using a generalized mathematical model of spontaneous and stimulation-evoked LFP activity, and a subject-specific model of neural dynamics in the pallidum of a Parkinson's disease patient. We leveraged convex and mixed-integer optimization tools to identify these pulse patterns, and employed constraints on the pulse frequency and amplitude that are required to keep electrical stimulation within its safety envelope. Main results: Our analysis revealed that a combination of phase, amplitude, and frequency pulse modulation is needed to attain optimal suppression or amplification of the targeted oscillations. Phase modulation is sufficient to modulate oscillations with a constant amplitude envelope. To attain optimal modulation for oscillations with a time-varying envelope, a trade-off between frequency and amplitude pulse modulation is needed. The optimized pulse sequences were invariant to changes in the dynamics of stimulation-evoked neural activity, including changes in damping and natural frequency or complexity (i.e., generalized vs. patient-specific model). Significance: Our results provide insight into the structure of pulse patterns for future closed-loop brain stimulation strategies aimed at controlling neural activity precisely and in real-time.

Mathematical modeling of brain metastases growth and response to therapies: A review.

Brain metastases (BMs) are the most common intracranial tumor type and a significant health concern, affecting approximately 10% to 30% of all oncological patients. Although significant progress is being made, many aspects of the metastatic process to the brain and the growth of the resulting lesions are still not well understood. There is a need for an improved understanding of the growth dynamics and the response to treatment of these tumors. Mathematical models have been proven valuable for drawing inferences and making predictions in different fields of cancer research, but few mathematical works have considered BMs. This comprehensive review aims to establish a unified platform and contribute to fostering emerging efforts dedicated to enhancing our mathematical understanding of this intricate and challenging disease. We focus on the progress made in the initial stages of mathematical modeling research regarding BMs and the significant insights gained from such studies. We also explore the vital role of mathematical modeling in predicting treatment outcomes and enhancing the quality of clinical decision-making for patients facing BMs.

Utilization of diffusion-weighted derived mathematical models to predict prognostic factors of resectable rectal cancer.

PURPOSE: This study explored models of monoexponential diffusion-weighted imaging (DWI), diffusion kurtosis imaging (DKI), stretched exponential (SEM), fractional-order calculus (FROC), and continuous-time random-walk (CTRW) as diagnostic tools for assessing pathological prognostic factors in patients with resectable rectal cancer (RRC). METHODS: RRC patients who underwent radical surgery were included. The apparent diffusion coefficient (ADC), the mean kurtosis (MK) and mean diffusion (MD) from the DKI model, the distributed diffusion coefficient (DDC) and α from the SEM model, D, ß and u from the FROC model, and D, α and ß from the CTRW model were assessed. RESULTS: There were a total of 181 patients. The area under the receiver operating characteristic (ROC) curve (AUC) of CTRW-α for predicting histology type was significantly higher than that of FROC-u (0.780 vs. 0.671, p = 0.043). The AUC of CTRW-α for predicting pT stage was significantly higher than that of FROC-u and ADC (0.786 vs.0.683, p = 0.043; 0.786 vs. 0.682, p = 0.030), the difference in predictive efficacy of FROC-u between ADC and MK was not statistically significant [0.683 vs. 0.682, p = 0.981; 0.683 vs. 0.703, p = 0.720]; the difference between the predictive efficacy of MK and ADC was not statistically significant (p = 0.696). The AUC of CTRW (α + ß) (0.781) was significantly higher than that of FROC-u (0.781 vs. 0.625, p = 0.003) in predicting pN stage but not significantly different from that of MK (p = 0.108). CONCLUSION: The CTRW and DKI models may serve as imaging biomarkers to predict pathological prognostic factors in RRC patients before surgery.

Prediction and control of cholera outbreak: Study case of Cameroon.

This paper deals with the problem of the prediction and control of cholera outbreak using real data of Cameroon. We first develop and analyze a deterministic model with seasonality for the cholera, the novelty of which lies in the incorporation of undetected cases. We present the basic properties of the model and compute two explicit threshold parameters R¯0 and R_0 that bound the effective reproduction number R0, from below and above, that is R_0≤R0≤R¯0. We prove that cholera tends to disappear when R¯0≤1, while when R_0>1, cholera persists uniformly within the population. After, assuming that the cholera transmission rates and the proportions of newly symptomatic are unknown, we develop the EnKf approach to estimate unmeasurable state variables and these unknown parameters using real data of cholera from 2014 to 2022 in Cameroon. We use this result to estimate the upper and lower bound of the effective reproduction number and reconstructed active asymptomatic and symptomatic cholera cases in Cameroon, and give a short-term forecasts of cholera in Cameroon until 2024. Numerical simulations show that (i) the transmission rate from free Vibrio cholerae in the environment is more important than the human transmission and begin to be high few week after May and in October, (ii) 90% of newly cholera infected cases that present the symptoms of cholera are not diagnosed and (iii) 60.36% of asymptomatic are detected at 14% and 86% of them recover naturally. The future trends reveals that an outbreak appeared from July to November 2023 with the number of cases reported monthly peaked in October 2023. An impulsive control strategy is incorporated in the model with the aim to avoid or prevent the cholera outbreak. In the first year of monitoring, we observed a reduction of more than 75% of incidences and the disappearance of the peaks when no control are available in Cameroon. A second monitoring of control led to a further reduction of around 60% of incidences the following year, showing how impulse control could be an effective means of eradicating cholera.

Clinical implications of a mathematical-geometrical model to predict changes in the anterior arch dimension.

PURPOSE: Anterior arch length (AL) and the alterations in its dimension following incisor movements were shown to be predictable for an individual patient using a mathematical-geometrical model based on a third-degree parabola. Although the model has been validated previously, it is hard to apply in daily orthodontic routine. Thus, the aim of this study was to modify the model using different approaches to allow its establishment in daily routine. METHODS: This retrospective study was based on a study collective, which was described previously and consisted of 50 randomly chosen dental casts and lateral cephalograms taken before (T0) and after (T1) orthodontic treatment with fixed appliances. A JAVA computer program (Oracle, Austin, TX, USA) was developed to predict AL changes following therapeutic changes of arch width, depth or incisor inclination/position, taking the type of tooth movement into account. Performing exemplary AL calculations with the computer program, general rules and nomograms were set up, followed by multiple linear regression analyses to establish easy-to-use regression equations. RESULTS: The JAVA computer program is available for download. Sagittal changes showed more effect on AL than transverse modifications. Protruding incisors increased AL, but also reduced overbite. The extent of alteration in AL depended on the initial depth, width, incisor inclination, tooth movement type and distance between the incisal edge and the centre of rotation. CONCLUSIONS: The computer program precisely predicts individual changes in AL but is time-consuming. The presented regression equations and nomograms, considering metric variables, are easier to apply clinically and the differences compared to the AL calculated by the computer program are negligible.

Relationship between body weight and hip width in dairy buffaloes (Bubalus bubalis).

The objective of the present study was to evaluate the relationship between body weight (BW) and hip width (HW) in dairy buffaloes (Bubalus bubalis). HW was measured in 215 Murrah buffaloes with a BW of 341 ± 161.6 kg, aged between three months and five years, and raised in southeastern Mexico. Linear and non-linear regressions were used to construct the prediction models. The goodness of fit of the models was evaluated using the Akaike information criterion (AIC), Bayesian information criterion (BIC), coefficient of determination (R2), mean squared error (MSE), and root MSE (RMSE). Additionally, the developed models were evaluated through internal and external cross-validation (k-folds) using independent data. The ability of the fitted models to predict the observed values was assessed based on the root mean square error of prediction (RMSEP), R2, and mean absolute error (MAE). The relationship between BW and HW showed a high correlation coefficient (r = 0.96, P < 0.001). The chosen fitted model to predict BW was: -176.33 (± 40.83***) + 8.74 (± 1.79***) × HW + 0.04 (± 0.01*) × HW2, because it presented the lowest MSE, RMSE, and AIC values, which were 1228.64, 35.05 and 1532.41, respectively. Therefore, with reasonable accuracy, the quadratic model using hip width may be suitable for predicting body weight in buffaloes.

Mathematical models and analysis tools for risk assessment of unnatural epidemics: a scoping review.

Predicting, issuing early warnings, and assessing risks associated with unnatural epidemics (UEs) present significant challenges. These tasks also represent key areas of focus within the field of prevention and control research for UEs. A scoping review was conducted using databases such as PubMed, Web of Science, Scopus, and Embase, from inception to 31 December 2023. Sixty-six studies met the inclusion criteria. Two types of models (data-driven and mechanistic-based models) and a class of analysis tools for risk assessment of UEs were identified. The validation part of models involved calibration, improvement, and comparison. Three surveillance systems (event-based, indicator-based, and hybrid) were reported for monitoring UEs. In the current study, mathematical models and analysis tools suggest a distinction between natural epidemics and UEs in selecting model parameters and warning thresholds. Future research should consider combining a mechanistic-based model with a data-driven model and learning to pursue time-varying, high-precision risk assessment capabilities.

Mosquito species identity matters: unraveling the complex interplay in vector-borne diseases.

BACKGROUND: Research on vector-borne diseases has traditionally centred on a limited number of vertebrate hosts and their associated pathogens, often neglecting the broader array of vectors within communities. Mosquitoes, with their vast species diversity, hold a central role in disease transmission, yet their capacity to transmit specific pathogens varies considerably among species. Quantitative modelling of mosquito-borne diseases is essential for understanding transmission dynamics and requires the necessity of incorporating the identity of vector species into these models. Consequently, understanding the role of different species of mosquitoes in modelling vector-borne diseases is crucial for comprehending pathogen amplification and spill-over into humans. This comprehensive overview highlights the importance of considering mosquito identity and emphasises the essential need for targeted research efforts to gain a complete understanding of vector-pathogen specificity. METHODS: Leveraging the recently published book, 'Mosquitoes of the World', I identified 19 target mosquito species in Europe, highlighting the diverse transmission patterns exhibited by different vector species and the presence of 135 medically important pathogens. RESULTS: The review delves into the complexities of vector-pathogen interactions, with a focus on specialist and generalist strategies. Furthermore, I discuss the importance of using appropriate diversity indices and the challenges associated with the identification of correct indices. CONCLUSIONS: Given that the diversity and relative abundance of key species within a community significantly impact disease risk, comprehending the implications of mosquito diversity in pathogen transmission at a fine scale is crucial for advancing the management and surveillance of mosquito-borne diseases.

Current examining methods and mathematical models of horizontal transfer of antibiotic resistance genes in the environment.

The increasing prevalence of antibiotic resistance genes (ARGs) in the environment has garnered significant attention due to their health risk to human beings. Horizontal gene transfer (HGT) is considered as an important way for ARG dissemination. There are four general routes of HGT, including conjugation, transformation, transduction and vesiduction. Selection of appropriate examining methods is crucial for comprehensively understanding characteristics and mechanisms of different HGT ways. Moreover, combined with the results obtained from different experimental methods, mathematical models could be established and serve as a powerful tool for predicting ARG transfer dynamics and frequencies. However, current reviews of HGT for ARG spread mainly focus on its influencing factors and mechanisms, overlooking the important roles of examining methods and models. This review, therefore, delineated four pathways of HGT, summarized the strengths and limitations of current examining methods, and provided a comprehensive summing-up of mathematical models pertaining to three main HGT ways of conjugation, transformation and transduction. Finally, deficiencies in current studies were discussed, and proposed the future perspectives to better understand and assess the risks of ARG dissemination through HGT.

Smart Algorithms for Efficient Insulin Therapy Initiation in Individuals With Type 2 Diabetes: An in Silico Study.

BACKGROUND: Insulin-naive subjects with type 2 diabetes (T2D) start basal insulin titration from a low initial insulin dose (IID), which is adjusted weekly or twice per week based on fasting plasma glucose (FPG) measurement as recommended by the American Diabetes Association (ADA). The procedure to reach the optimal insulin dose (OID) is time-consuming, especially in subjects with high insulin needs (HIN). The aim of this study is to provide a fast and effective, but still safe, insulin titration algorithm in insulin-naive T2D subjects with HIN. METHOD: To do that, we in silico cloned 300 subjects, matching a real population of insulin-naive T2D and used a logistic regression model to classify them as subjects with HIN or subjects with low insulin needs (LIN). Then, we applied to the subjects with HIN both a more aggressive insulin dose initiation (SMART-IID) and two newly developed titration algorithms (continuous glucose monitoring [CGM]-BASED and SMART-CGM-BASED) in which CGM was used to guide the decision-making process. RESULTS: The new titration algorithm applied to HIN-classified individuals guaranteed a faster reaching of OID, with significant improvements in time in range (TIR) and reduction in time above range (TAR) in the first months of the trial, without any clinically significant increase in the risk of hypoglycemia. CONCLUSIONS: Smart basal insulin titration algorithms enable insulin-naive T2D individuals to achieve OID and improve their glycemic control faster than standard guidelines, without jeopardizing patient safety.

A computational model of Alzheimer's disease at the nano, micro, and macroscales.

Introduction: Mathematical models play a crucial role in investigating complex biological systems, enabling a comprehensive understanding of interactions among various components and facilitating in silico testing of intervention strategies. Alzheimer's disease (AD) is characterized by multifactorial causes and intricate interactions among biological entities, necessitating a personalized approach due to the lack of effective treatments. Therefore, mathematical models offer promise as indispensable tools in combating AD. However, existing models in this emerging field often suffer from limitations such as inadequate validation or a narrow focus on single proteins or pathways. Methods: In this paper, we present a multiscale mathematical model that describes the progression of AD through a system of 19 ordinary differential equations. The equations describe the evolution of proteins (nanoscale), cell populations (microscale), and organ-level structures (macroscale) over a 50-year lifespan, as they relate to amyloid and tau accumulation, inflammation, and neuronal death. Results: Distinguishing our model is a robust foundation in biological principles, ensuring improved justification for the included equations, and rigorous parameter justification derived from published experimental literature. Conclusion: This model represents an essential initial step toward constructing a predictive framework, which holds significant potential for identifying effective therapeutic targets in the fight against AD.

Predictive Models of Life Span in Old Female Mice Based on Immune, Redox, and Behavioral Parameters.

The development of mathematical models capable of predicting the lifespan of animals is growing. However, there are no studies that compare the predictive power of different sets of parameters depending on the age of the animals. The aim of the present study is to test whether mathematical models for life span prediction developed in adult female mice based on immune, redox, and behavioral parameters can predict life span in old animals and to develop new models in old mice. For this purpose, 29 variables, including parameters of immune function, redox state, and behavioral ones, were evaluated in old female Swiss mice (80 ± 4 weeks). Life span was registered when they died naturally. Firstly, we observed that the models developed in adults were not able to accurately predict the life span of old mice. Therefore, the immunity (adjusted R2 = 73.6%), redox (adjusted R2 = 46.5%), immunity-redox (adjusted R2 = 96.4%), and behavioral (adjusted R2 = 67.9%) models were developed in old age. Finally, the models were validated in another batch of mice. The developed models in old mice show certain similarities to those in adults but include different immune, redox, and behavioral markers, which highlights the importance of age in the prediction of life span.

New Tools and Nuanced Interventions to Accelerate Achievement of the 2030 Roadmap for Neglected Tropical Diseases.

The World Health Organization roadmap for neglected tropical diseases (NTDs) sets out ambitious targets for disease control and elimination by 2030, including 90% fewer people requiring interventions against NTDs and the elimination of at least 1 NTD in 100 countries. Mathematical models are an important tool for understanding NTD dynamics, optimizing interventions, assessing the efficacy of new tools, and estimating the economic costs associated with control programs. As NTD control shifts to increased country ownership and programs progress toward disease elimination, tailored models that better incorporate local context and can help to address questions that are important for decision-making at the national level are gaining importance. In this introduction to the supplement, New Tools and Nuanced Interventions to Accelerate Achievement of the 2030 Roadmap for Neglected Tropical Diseases, we discuss current challenges in generating more locally relevant models and summarize how the articles in this supplement present novel ways in which NTD modeling can help to accelerate achievement and sustainability of the 2030 targets.

A simplified longitudinal model for the development of Type 2 Diabetes Mellitus.

Obesity and diabetes are a progressively more and more deleterious hallmark of modern, well fed societies. In order to study the potential impact of strategies designed to obviate the pathological consequences of detrimental lifestyles, a model for the development of Type 2 diabetes geared towards large population simulations would be useful. The present work introduces such a model, representing in simplified fashion the interplay between average glycemia, average insulinemia and functional beta-cell mass, and incorporating the effects of excess food intake or, conversely, of physical activity levels. Qualitative properties of the model are formally established and simulations are shown as examples of its use.

Accelerating Progress Towards the 2030 Neglected Tropical Diseases Targets: How Can Quantitative Modeling Support Programmatic Decisions?

Over the past decade, considerable progress has been made in the control, elimination, and eradication of neglected tropical diseases (NTDs). Despite these advances, most NTD programs have recently experienced important setbacks; for example, NTD interventions were some of the most frequently and severely impacted by service disruptions due to the coronavirus disease 2019 (COVID-19) pandemic. Mathematical modeling can help inform selection of interventions to meet the targets set out in the NTD road map 2021-2030, and such studies should prioritize questions that are relevant for decision-makers, especially those designing, implementing, and evaluating national and subnational programs. In September 2022, the World Health Organization hosted a stakeholder meeting to identify such priority modeling questions across a range of NTDs and to consider how modeling could inform local decision making. Here, we summarize the outputs of the meeting, highlight common themes in the questions being asked, and discuss how quantitative modeling can support programmatic decisions that may accelerate progress towards the 2030 targets.

Four-compartment muscle fatigue model to predict metabolic inhibition and long-lasting nonmetabolic components.

Introduction: Computational muscle force models aim to mathematically represent the mechanics of movement and the factors influencing force generation. These tools allow the prediction of the nonlinear and task-related muscle behavior, aiding biomechanics, sports science, and rehabilitation. Despite often overlooking muscle fatigue in low-force scenarios, these simulations are crucial for high-intensity activities where fatigue and force loss play a significant role. Applications include functional electrical stimulation, motor control, and ergonomic considerations in diverse contexts, encompassing rehabilitation and the prevention of injuries in sports and workplaces. Methods: In this work, the authors enhance the pre-existing 3CCr muscle fatigue model by introducing an additional component of force decay associated with central fatigue and a long-term fatigue state. The innovative four-compartment model distinguishes between the short-term fatigued state (related to metabolic inhibition) and the long-term fatigued state (emulating central fatigue and potential microtraumas). Results: Its validation process involved experimental measurements during both short- and long-duration exercises, shedding light on the limitations of the traditional 3CCr in addressing dynamic force profiles.

Monitoring progress towards the elimination of hepatitis C as a public health threat in Norway: a modelling study among people who inject drugs and immigrants.

BACKGROUND: The global incidence target for the elimination of hepatitis C among people who inject drugs (PWID) is <2/100. In Norway, the hepatitis C epidemic is concentrated in PWID. Immigrants are the second most important risk group for chronic infection. We modelled the incidence of hepatitis C among active PWID, and the prevalence of chronic infection among active PWID, ex-PWID and immigrants in Norway until 2022. METHODS: We built a stochastic compartmental model, which was informed using data from national data sources, literature, and expert opinion. We report median values with 95% credible intervals (CrI). RESULTS: The model estimated 30 (95% Crl: 13-52) new infections among active PWID in 2022, or 0.37/100 (95% Crl: 0.17-0.65), down from a peak of 726 (95% Crl: 506-1,067) in 2000. Across all groups, the model estimated 3,202 (95% Crl: 1,273-6,601) chronically infected persons in 2022. Results were robust in sensitivity analyses. CONCLUSIONS: Norway provides an example of the feasibility of hepatitis C elimination in a setting with a concentrated epidemic, high coverage of harm reduction services and no treatment restrictions. Continued momentum is needed to further reduce the transmission and burden of hepatitis C in Norway.

Predicting the long-term collective behaviour of fish pairs with deep learning.

Modern computing has enhanced our understanding of how social interactions shape collective behaviour in animal societies. Although analytical models dominate in studying collective behaviour, this study introduces a deep learning model to assess social interactions in the fish species Hemigrammus rhodostomus. We compare the results of our deep learning approach with experiments and with the results of a state-of-the-art analytical model. To that end, we propose a systematic methodology to assess the faithfulness of a collective motion model, exploiting a set of stringent individual and collective spatio-temporal observables. We demonstrate that machine learning (ML) models of social interactions can directly compete with their analytical counterparts in reproducing subtle experimental observables. Moreover, this work emphasizes the need for consistent validation across different timescales, and identifies key design aspects that enable our deep learning approach to capture both short- and long-term dynamics. We also show that our approach can be extended to larger groups without any retraining, and to other fish species, while retaining the same architecture of the deep learning network. Finally, we discuss the added value of ML in the context of the study of collective motion in animal groups and its potential as a complementary approach to analytical models.

Efficient Estimates of Surface Diffusion Parameters for Spatio-Temporally Resolved Virus Replication Dynamics.

Advanced methods of treatment are needed to fight the threats of virus-transmitted diseases and pandemics. Often, they are based on an improved biophysical understanding of virus replication strategies and processes in their host cells. For instance, an essential component of the replication of the hepatitis C virus (HCV) proceeds under the influence of nonstructural HCV proteins (NSPs) that are anchored to the endoplasmatic reticulum (ER), such as the NS5A protein. The diffusion of NSPs has been studied by in vitro fluorescence recovery after photobleaching (FRAP) experiments. The diffusive evolution of the concentration field of NSPs on the ER can be described by means of surface partial differential equations (sufPDEs). Previous work estimated the diffusion coefficient of the NS5A protein by minimizing the discrepancy between an extended set of sufPDE simulations and experimental FRAP time-series data. Here, we provide a scaling analysis of the sufPDEs that describe the diffusive evolution of the concentration field of NSPs on the ER. This analysis provides an estimate of the diffusion coefficient that is based only on the ratio of the membrane surface area in the FRAP region to its contour length. The quality of this estimate is explored by a comparison to numerical solutions of the sufPDE for a flat geometry and for ten different 3D embedded 2D ER grids that are derived from fluorescence z-stack data of the ER. Finally, we apply the new data analysis to the experimental FRAP time-series data analyzed in our previous paper, and we discuss the opportunities of the new approach.