scholarly journals Understanding virtual patients efficiently and rigorously by combining machine learning with dynamical modelling

2022 ◽  
Author(s):  
Tongli Zhang ◽  
John J. Tyson
Keyword(s):  
Machine Learning ◽  
Mathematical Model ◽  
Bifurcation Analysis ◽  
Sensitivity Analyses ◽  
Model Parameters ◽  
Virtual Patients ◽  
Multiple Model ◽  
Systems Pharmacology ◽  
Fixed Structure ◽  
Parameter Values

AbstractIndividual biological organisms are characterized by daunting heterogeneity, which precludes describing or understanding populations of ‘patients’ with a single mathematical model. Recently, the field of quantitative systems pharmacology (QSP) has adopted the notion of virtual patients (VPs) to cope with this challenge. A typical population of VPs represents the behavior of a heterogeneous patient population with a distribution of parameter values over a mathematical model of fixed structure. Though this notion of VPs is a powerful tool to describe patients’ heterogeneity, the analysis and understanding of these VPs present new challenges to systems pharmacologists. Here, using a model of the hypothalamic–pituitary–adrenal axis, we show that an integrated pipeline that combines machine learning (ML) and bifurcation analysis can be used to effectively and efficiently analyse the behaviors observed in populations of VPs. Compared with local sensitivity analyses, ML allows us to capture and analyse the contributions of simultaneous changes of multiple model parameters. Following up with bifurcation analysis, we are able to provide rigorous mechanistic insight regarding the influences of ML-identified parameters on the dynamical system’s behaviors. In this work, we illustrate the utility of this pipeline and suggest that its wider adoption will facilitate the use of VPs in the practice of systems pharmacology.

scholarly journals Phase i trials in melanoma: A framework to translate preclinical findings to the clinic

2015 ◽  
Author(s):  
Eunjung Kim ◽  
Vito W. Rebecca ◽  
Keiran S.M. Smalley ◽  
Alexander R.A. Anderson
Keyword(s):  
Mathematical Model ◽  
Clinical Trial ◽  
Combination Therapy ◽  
Phase I ◽  
Phase 1 ◽  
Cell Populations ◽  
Model Parameters ◽  
Phase I Trials ◽  
Virtual Patients ◽  
Akt Inhibitor

We present a, mathematical model driven, framework to implement virtual or imaginary clinical trials (phase i trials) that can be used to bridge the gap between preclinical studies and the clinic. The trial implementation process includes the development of an experimentally validated mathematical model, generation of a cohort of heterogeneous virtual patients, an assessment of stratification factors, and optimization of treatment strategy. We show the detailed process through application to melanoma treatment, using a combination therapy of chemotherapy and an AKT inhibitor, which was recently tested in a phase 1 clinical trial. We developed a mathematical model, composed of ordinary differential equations, based on experimental data showing that such therapies differentially induce autophagy in melanoma cells. Model parameters were estimated using an optimization algorithm that minimizes differences between predicted cell populations and experimentally measured cell numbers. The calibrated model was validated by comparing predicted cell populations with experimentally measured melanoma cell populations in twelve different treatment scheduling conditions. By using this validated model as the foundation for a genetic algorithm, we generated a cohort of virtual patients that mimics the heterogeneous combination therapy responses observed in a companion clinical trial. Sensitivity analysis of this cohort defined parameters that discriminated virtual patients having more favorable versus less favorable outcomes. Finally, the model predicts optimal therapeutic approaches across all virtual patients.  

Validation of a Mathematical Model for Road Cycling Power

1998 ◽  
Vol 14 (3) ◽  
pp. 276-291 ◽  
Author(s):  
James C. Martin ◽  
Douglas L. Milliken ◽  
John E. Cobb ◽  
Kevin L. McFadden ◽  
Andrew R. Coggan
Keyword(s):  
Mathematical Model ◽  
Measurement System ◽  
Standard Error ◽  
Power Measurement ◽  
Model Parameters ◽  
Model Parameter ◽  
Road Cycling ◽  
Highly Correlated ◽  
Parameter Values ◽  
Measured Power

This investigation sought to determine if cycling power could be accurately modeled. A mathematical model of cycling power was derived, and values for each model parameter were determined. A bicycle-mounted power measurement system was validated by comparison with a laboratory ergometer. Power was measured during road cycling, and the measured values were compared with the values predicted by the model. The measured values for power were highly correlated (R2= .97) with, and were not different than, the modeled values. The standard error between the modeled and measured power (2.7 W) was very small. The model was also used to estimate the effects of changes in several model parameters on cycling velocity. Over the range of parameter values evaluated, velocity varied linearly (R2> .99). The results demonstrated that cycling power can be accurately predicted by a mathematical model.

scholarly journals A mathematical investigation of different growth rates in simultaneous tumors at two distant sites

2021 ◽  
Author(s):  
Farjana Aktar
Keyword(s):  
Mathematical Model ◽  
Growth Rate ◽  
Simulated Annealing Algorithm ◽  
The Other ◽  
Sensitivity Analyses ◽  
Small Tumour ◽  
System A ◽  
Set Up ◽  
Parameter Values ◽  
The Mathematical Model

Experimental data demonstrates that simultaneous injection of cancer cells at two distinct sites often results in one large and one small tumour. Unbalanced tumour-stimulating inflammation is hypothesized to be the cause of this growth rate separation, causing one tumour to grow faster than the other. Here, a mathematical model for immune recruitment and competition between two cancer sites is developed to explore the role of tumour-promoting inflammation in the observed growth rate separation. Due to the experimental set-up, immune predation may be neglected, focusing the model on tumour-promoting immune actions. A new mathematical model with localized immune recruitment and competition between the two cancer sites is developed using a multi-compartment ODE system. A simulated annealing algorithm is used to fit the model to control data (one tumour burden). Stability and parameter sensitivity analyses are used to explore the mathematical model and parameter space. Next, the two-tumour scenario is predicted by testing parameter values tied to possible biological mechanisms of action. The model predicts that indeed inflammation may be a contributor to growth rate separation observed in simultaneous tumour growth, if one site is pre-inflamed compared to the other.

scholarly journals Combining Physiology-Based Modeling and Evolutionary Algorithms for Personalized, Noninvasive Cardiovascular Assessment Based on Electrocardiography and Ballistocardiography

2022 ◽  
Vol 12 ◽  
Author(s):  
Nicholas Mattia Marazzi ◽  
Giovanna Guidoboni ◽  
Mohamed Zaid ◽  
Lorenzo Sala ◽  
Salman Ahmad ◽  
...  
Keyword(s):  
Blood Pressure ◽  
Mathematical Model ◽  
Blood Pressure Measurement ◽  
Model Parameters ◽  
Cardiovascular Monitoring ◽  
Cardiovascular Parameters ◽  
Physiological Variables ◽  
Novel Approach ◽  
Cardiovascular Assessment ◽  
Parameter Values

Purpose: This study proposes a novel approach to obtain personalized estimates of cardiovascular parameters by combining (i) electrocardiography and ballistocardiography for noninvasive cardiovascular monitoring, (ii) a physiology-based mathematical model for predicting personalized cardiovascular variables, and (iii) an evolutionary algorithm (EA) for searching optimal model parameters.Methods: Electrocardiogram (ECG), ballistocardiogram (BCG), and a total of six blood pressure measurements are recorded on three healthy subjects. The R peaks in the ECG are used to segment the BCG signal into single BCG curves for each heart beat. The time distance between R peaks is used as an input for a validated physiology-based mathematical model that predicts distributions of pressures and volumes in the cardiovascular system, along with the associated BCG curve. An EA is designed to search the generation of parameter values of the cardiovascular model that optimizes the match between model-predicted and experimentally-measured BCG curves. The physiological relevance of the optimal EA solution is evaluated a posteriori by comparing the model-predicted blood pressure with a cuff placed on the arm of the subjects to measure the blood pressure.Results: The proposed approach successfully captures amplitudes and timings of the most prominent peak and valley in the BCG curve, also known as the J peak and K valley. The values of cardiovascular parameters pertaining to ventricular function can be estimated by the EA in a consistent manner when the search is performed over five different BCG curves corresponding to five different heart-beats of the same subject. Notably, the blood pressure predicted by the physiology-based model with the personalized parameter values provided by the EA search exhibits a very good agreement with the cuff-based blood pressure measurement.Conclusion: The combination of EA with physiology-based modeling proved capable of providing personalized estimates of cardiovascular parameters and physiological variables of great interest, such as blood pressure. This novel approach opens the possibility for developing quantitative devices for noninvasive cardiovascular monitoring based on BCG sensing.

Use of Machine Learning algorithms in evaluating the WRF model parameter sensitivity for the simulation of tropical cyclones

2021 ◽  
Author(s):  
Baki Harish ◽  
Sandeep Chinta ◽  
Chakravarthy Balaji ◽  
Balaji Srinivasan
Keyword(s):  
Machine Learning ◽  
Sensitivity Analysis ◽  
Tropical Cyclones ◽  
Surrogate Model ◽  
Learning Algorithms ◽  
Wrf Model ◽  
Machine Learning Algorithms ◽  
Model Parameters ◽  
Model Parameter ◽  
Parameter Values

<p>The Indian subcontinent is prone to tropical cyclones that originate in the Indian Ocean and cause widespread destruction to life and property. Accurate prediction of cyclone track, landfall, wind, and precipitation are critical in minimizing damage. The Weather Research and Forecast (WRF) model is widely used to predict tropical cyclones. The accuracy of the model prediction depends on initial conditions, physics schemes, and model parameters. The parameter values are selected empirically by scheme developers using the trial and error method, implying that the parameter values are sensitive to climatological conditions and regions. The number of tunable parameters in the WRF model is about several hundred, and calibrating all of them is highly impossible since it requires thousands of simulations. Therefore, sensitivity analysis is critical to screen out the parameters that significantly impact the meteorological variables. The Sobol’ sensitivity analysis method is used to identify the sensitive WRF model parameters. As this method requires a considerable amount of samples to evaluate the sensitivity adequately, machine learning algorithms are used to construct surrogate models trained using a limited number of samples. They could help generate a vast number of required pseudo-samples. Five machine learning algorithms, namely, Gaussian Process Regression (GPR), Support Vector Machine, Regression Tree, Random Forest, and K-Nearest Neighbor, are considered in this study. Ten-fold cross-validation is used to evaluate the surrogate models constructed using the five algorithms and identify the robust surrogate model among them. The samples generated from this surrogate model are then used by the Sobol’ method to evaluate the WRF model parameter sensitivity.</p>

scholarly journals Forecasting the Bladder Tumor Size and Immune Response of a Patient Over the Time Using a Dynamic Mathematical Model

2018 ◽  
Author(s):  
Clara Burgos ◽  
Noemí García-Medina ◽  
David Martínez-Rodríguez ◽  
José-Luis Pontones ◽  
David Ramos ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Immune Response ◽  
Tumor Size ◽  
Model Calibration ◽  
Bladder Tumor ◽  
Tumor Evolution ◽  
Model Parameters ◽  
Single Patient ◽  
Dynamic Mathematical Model ◽  
Parameter Values

Bladder cancer is one of the most common malignant diseases in the urinary system and a highly aggressive neoplasm. The prognosis is not favourable usually and its evolution for particular patients is very difficult to find out. In this paper we propose a dynamic mathematical model that describes the bladder tumor growth and the immune response evolution. This model is customized for a single patient, determining appropriate model parameter values via model calibration. Due to the uncertainty of the tumor evolution, using the calibrated model parameters, we predict the tumor size and the immune response evolution over the next few months assuming three different scenarios: favourable, neutral and unfavourable. In the former, the cancer disappears; in the second a 5mm tumor is expected around the middle of August 2018; in the worst scenario, a 5mm tumor is expected around the end of May 2018. The patient has been cited around June 15th, 2018, to check the tumor size, if it exists.

Modeling Heart Rate Dynamics in Response to Changes in Exercise Intensity

2015 ◽  
Author(s):  
Michael J. Mazzoleni ◽  
Claudio L. Battaglini ◽  
Brian P. Mann
Keyword(s):  
Genetic Algorithm ◽  
Mathematical Model ◽  
Heart Rate ◽  
Heart Rate Response ◽  
Synthetic Data ◽  
Model Parameters ◽  
Nonlinear Mathematical Model ◽  
Heart Rate Dynamics ◽  
Parameter Values ◽  
Good Agreement

This paper develops a nonlinear mathematical model to describe the heart rate response of an individual during cycling. The model is able to account for the fluctuations of an individual’s heart rate while they participate in exercise that varies in intensity. A method for estimating the model parameters using a genetic algorithm is presented and implemented, and the results show good agreement between the actual parameter values and the estimated values when tested using synthetic data.

scholarly journals Intelligent Prediction of The Equivalent Circulating Density From Surface Data Sensors During Drilling By Employing Machine Learning Techniques

2021 ◽  
Author(s):  
Hany Gamal ◽  
Ahmed Abdelaal ◽  
Salaheldin Elkatatny
Keyword(s):  
Machine Learning ◽  
Prediction Models ◽  
Machine Learning Techniques ◽  
Sensitivity Analyses ◽  
Percentage Error ◽  
Model Parameters ◽  
Data Set ◽  
Inference System ◽  
Mathematical Correlation ◽  
Drilling Parameters

Abstract The precise control for the equivalent circulating density (ECD) will lead to evade well control issues like loss of circulation, formation fracturing, underground blowout, and surface blowout. Predicting the ECD from the drilling parameters is a new horizon in drilling engineering practices and this is because of the drawbacks of the cost of downhole ECD tools and the low accuracy of the mathematical models. Machine learning methods can offer a superior prediction accuracy over the traditional and statistical models due to the advanced computing capacity. Hence, the objective of this paper is to use the artificial neural network (ANN) and adaptive neuro-fuzzy inference system (ANFIS) techniques to develop ECD prediction models. The novel contribution for this study is predicting the downhole ECD without any need for downhole measurements but only the available surface drilling parameters. The data in this study covered the drilling data for a horizontal section with 3,570 readings for each input after data preprocessing. The data covered the mud rate, rate of penetration, drill string speed, standpipe pressure, weight on bit, and the drilling torque. The data used to build the model with a 77:23 training to testing ratio. Another data set (1,150 data points) from the same field was used for models` validation. Many sensitivity analyses were done to optimize the ANN and ANFIS model parameters. The prediction of the developed machine learning models provided a high performance and accuracy level with a correlation coefficient (R) of 0.99 for the models' training and testing data sets, and an average absolute percentage error (AAPE) less than 0.24%. The validation results showed R of 0.98 and 0.96 and AAPE of 0.30% and 0.69% for ANN and ANFIS models respectively. Besides, a mathematical correlation was developed for estimating ECD based on the inputs as a white-box model.

scholarly journals A mathematical investigation of different growth rates in simultaneous tumors at two distant sites

2021 ◽  
Author(s):  
Farjana Aktar
Keyword(s):  
Mathematical Model ◽  
Growth Rate ◽  
Simulated Annealing Algorithm ◽  
The Other ◽  
Sensitivity Analyses ◽  
Small Tumour ◽  
System A ◽  
Set Up ◽  
Parameter Values ◽  
The Mathematical Model

Experimental data demonstrates that simultaneous injection of cancer cells at two distinct sites often results in one large and one small tumour. Unbalanced tumour-stimulating inflammation is hypothesized to be the cause of this growth rate separation, causing one tumour to grow faster than the other. Here, a mathematical model for immune recruitment and competition between two cancer sites is developed to explore the role of tumour-promoting inflammation in the observed growth rate separation. Due to the experimental set-up, immune predation may be neglected, focusing the model on tumour-promoting immune actions. A new mathematical model with localized immune recruitment and competition between the two cancer sites is developed using a multi-compartment ODE system. A simulated annealing algorithm is used to fit the model to control data (one tumour burden). Stability and parameter sensitivity analyses are used to explore the mathematical model and parameter space. Next, the two-tumour scenario is predicted by testing parameter values tied to possible biological mechanisms of action. The model predicts that indeed inflammation may be a contributor to growth rate separation observed in simultaneous tumour growth, if one site is pre-inflamed compared to the other.

scholarly journals Bifurcation and sensitivity analysis reveal key drivers of multistability in a model of macrophage polarization

2020 ◽  
Author(s):  
Anna-Simone Josefine Frank ◽  
Kamila Larripa ◽  
Hwayeon Ryu ◽  
Ryan Snodgrass ◽  
Susanna Röblitz
Keyword(s):  
Mathematical Model ◽  
Sensitivity Analysis ◽  
Complex Dynamics ◽  
Macrophage Polarization ◽  
Regulatory Mechanisms ◽  
Sensitivity Analyses ◽  
Multiple Phenotypes ◽  
Key Drivers ◽  
Parameter Values

AbstractIn this paper, we present and analyze a mathematical model for polarization of a single macrophage which, despite its simplicity, exhibits complex dynamics in terms of multistability. In particular, we demonstrate that an asymmetry in the regulatory mechanisms and parameter values is important for observing multiple phenotypes. Bifurcation and sensitivity analyses show that external signaling cues are necessary for macrophage commitment and emergence to a phenotype, but that the intrinsic macrophage metabolism is equally important. Based on our numerical results, we formulate hypotheses that could be further investigated by in vitro experiments to deepen our understanding of macrophage polarization.2010 MSC93A30, 34C23, 49Q12, 92C42, 37N25

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