Stability of a model of human granulopoiesis using continuous maturation

A class of mathematical models involving a convection-reaction partial differential equation (PDE) is introduced with reference to recovering human granulopoiesis after high dose chemotherapy with stem cell support. The stability properties of the model are addressed by means of numerical investigations and analysis. A simplified model with proliferation rate and mobilization rate independent of maturity shows that the model is stable as the maturation rate grows without bounds, but may go through stable and non-stable regimens as the maturation rate varies. It is also shown that the system is stable when parameters are chosen to approximate a real physiological situation. System characteristics do not change profoundly by introduction of a maturity-dependent proliferation and mobilization rate, as is necessary to make the model operate more in accordance with hematological observations. However, by changing the system mitotic responsiveness with respect to changes in cytokine level, the system is still stable but may show persistent oscillations much resembling clinical observations of cyclic neutropenia. Furthermore, in these cases, changes in the model feedback signal caused by, for instance, an impaired effective cytokine elimination by cell receptors may enforce these oscillations markedly.     

Using Networks To Understand Medical Data: The Case of Class III Malocclusions

A system of elements that interact or regulate each other can be represented by a mathematical object called a network. While network analysis has been successfully applied to high-throughput biological systems, less has been done regarding their application in more applied fields of medicine; here we show an application based on standard medical diagnostic data. We apply network analysis to Class III malocclusion, one of the most difficult to understand and treat orofacial anomaly. We hypothesize that different interactions of the skeletal components can contribute to pathological disequilibrium; in order to test this hypothesis, we apply network analysis to 532 Class III young female patients. The topology of the Class III malocclusion obtained by network analysis shows a strong co-occurrence of abnormal skeletal features. The pattern of these occurrences influences the vertical and horizontal balance of disharmony in skeletal form and position. Patients with more unbalanced orthodontic phenotypes show preponderance of the pathological skeletal nodes and minor relevance of adaptive dentoalveolar equilibrating nodes. Furthermore, by applying Power Graphs analysis we identify some functional modules among orthodontic nodes. These modules correspond to groups of tightly inter-related features and presumably constitute the key regulators of plasticity and the sites of unbalance of the growing dentofacial Class III system. The data of the present study show that, in their most basic abstraction level, the orofacial characteristics can be represented as graphs using nodes to represent orthodontic characteristics, and edges to represent their various types of interactions. The applications of this mathematical model could improve the interpretation of the quantitative, patient-specific information, and help to better targeting therapy. Last but not least, the methodology we have applied in analyzing orthodontic features can be applied easily to other fields of the medical science.     

Precision Medicine with Imprecise Therapy: Computational Modeling for Chemotherapy in Breast Cancer

Medical oncology is in need of a mathematical modeling toolkit that can leverage clinically-available measurements to optimize treatment selection and schedules for patients. Just as the therapeutic choice has been optimized to match tumor genetics, the delivery of those therapeutics should be optimized based on patient-specific pharmacokinetic/pharmacodynamic properties. Under the current approach to treatment response planning and assessment, there does not exist an efficient method to consolidate biomarker changes into a holistic understanding of treatment response. While the majority of research on chemotherapies focus on cellular and genetic mechanisms of resistance, there are numerous patient-specific and tumor-specific measures that contribute to treatment response. New approaches that consolidate multimodal information into actionable data are needed. Mathematical modeling offers a solution to this problem. In this perspective, we first focus on the particular case of breast cancer to highlight how mathematical models have shaped the current approaches to treatment. Then we compare chemotherapy to radiation therapy. Finally, we identify opportunities to improve chemotherapy treatments using the model of radiation therapy. We posit that mathematical models can improve the application of anticancer therapeutics in the era of precision medicine. By highlighting a number of historical examples of the contributions of mathematical models to cancer therapy, we hope that this contribution serves to engage investigators who may not have previously considered how mathematical modeling can provide real insights into breast cancer therapy.     

Estimating compliance to study medication from serum drug levels: application to an AIDS clinical trial of zidovudine.

This paper examines the use of serum drug levels to assess compliance to study medication in a clinical trial. We discuss problems of false-positivity, false-negativity, and bias that arise because of experimental errors in the drug assays, pharmacokinetic variations of the drug, and differential dosing levels. Basic concepts in probability are applied to derive a simple model that quantifies these problems. This model is used to obtain an estimate of compliance rate that corrects for these problems. However, derivation of this estimate requires additional information about false-positive and false-negative rates of the assay as well as some knowledge of the pharmacokinetic properties of the drug. We illustrate the evaluation of such a compliance estimate in the setting of an AIDS clinical trial of zidovudine (ZDV), in which some accessory data are available on the properties of ZDV serum assays and on the pharmacokinetic behavior of ZDV. We also describe a method that uses the accessory data to provide the additional information needed for computing the compliance estimate.     

Using adaptive model predictive control to customize maintenance therapy chemotherapeutic dosing for childhood acute lymphoblastic leukemia

Acute lymphoblastic leukemia (ALL) is a common childhood cancer in which nearly one-quarter of patients experience a disease relapse. However, it has been shown that individualizing therapy for childhood ALL patients by adjusting doses based on the blood concentration of active drug metabolite could significantly improve treatment outcome. An adaptive model predictive control (MPC) strategy is presented in which maintenance therapy for childhood ALL is personalized using routine patient measurements of red blood cell mean corpuscular volume as a surrogate for the active drug metabolite concentration. A clinically relevant mathematical model is developed and used to describe the patient response to the chemotherapeutic drug 6-mercaptopurine, with some model parameters being patient-specific. During the course of treatment, the patient-specific parameters are adaptively identified using recurrent complete blood count measurements, which sufficiently constrain the patient parameter uncertainty to support customized adjustments of the drug dose. While this work represents only a first step toward a quantitative tool for clinical use, the simulated treatment results indicate that the proposed mathematical model and adaptive MPC approach could serve as valuable resources to the oncologist toward creating a personalized treatment strategy that is both safe and effective.     

BrainSignals Revisited: Simplifying a Computational Model of Cerebral Physiology

Multimodal monitoring of brain state is important both for the investigation of healthy cerebral physiology and to inform clinical decision making in conditions of injury and disease. Near-infrared spectroscopy is an instrument modality that allows non-invasive measurement of several physiological variables of clinical interest, notably haemoglobin oxygenation and the redox state of the metabolic enzyme cytochrome c oxidase. Interpreting such measurements requires the integration of multiple signals from different sources to try to understand the physiological states giving rise to them. We have previously published several computational models to assist with such interpretation. Like many models in the realm of Systems Biology, these are complex and dependent on many parameters that can be difficult or impossible to measure precisely. Taking one such model, BrainSignals, as a starting point, we have developed several variant models in which specific regions of complexity are substituted with much simpler linear approximations. We demonstrate that model behaviour can be maintained whilst achieving a significant reduction in complexity, provided that the linearity assumptions hold. The simplified models have been tested for applicability with simulated data and experimental data from healthy adults undergoing a hypercapnia challenge, but relevance to different physiological and pathophysiological conditions will require specific testing. In conditions where the simplified models are applicable, their greater efficiency has potential to allow their use at the bedside to help interpret clinical data in near real-time.     

Tracking the Sleep Onset Process: An Empirical Model of Behavioral and Physiological Dynamics

The sleep onset process (SOP) is a dynamic process correlated with a multitude of behavioral and physiological markers. A principled analysis of the SOP can serve as a foundation for answering questions of fundamental importance in basic neuroscience and sleep medicine. Unfortunately, current methods for analyzing the SOP fail to account for the overwhelming evidence that the wake/sleep transition is governed by continuous, dynamic physiological processes. Instead, current practices coarsely discretize sleep both in terms of state, where it is viewed as a binary (wake or sleep) process, and in time, where it is viewed as a single time point derived from subjectively scored stages in 30-second epochs, effectively eliminating SOP dynamics from the analysis. These methods also fail to integrate information from both behavioral and physiological data. It is thus imperative to resolve the mismatch between the physiological evidence and analysis methodologies. In this paper, we develop a statistically and physiologically principled dynamic framework and empirical SOP model, combining simultaneously-recorded physiological measurements with behavioral data from a novel breathing task requiring no arousing external sensory stimuli. We fit the model using data from healthy subjects, and estimate the instantaneous probability that a subject is awake during the SOP. The model successfully tracked physiological and behavioral dynamics for individual nights, and significantly outperformed the instantaneous transition models implicit in clinical definitions of sleep onset. Our framework also provides a principled means for cross-subject data alignment as a function of wake probability, allowing us to characterize and compare SOP dynamics across different populations. This analysis enabled us to quantitatively compare the EEG of subjects showing reduced alpha power with the remaining subjects at identical response probabilities. Thus, by incorporating both physiological and behavioral dynamics into our model framework, the dynamics of our analyses can finally match those observed during the SOP.     

Population statistical methodology for determining the mechanisms of physiological regulation of concentrations of some biochemical substances in blood

The population statistical methodology has been considered in terms of its application to determining the physiological mechanisms providing constant concentrations in blood for different groups of biochemical substances. As applied to the group of substances with asymmetric statistical distributions, a mathematical model has been developed for breaking down such distribution into two components: normal distributions conditioned by the independent rates of substance inflow to the blood (production) and clearance, i.e., the blood volume from which all this substance is removed per time unit. The mathematical treatment of data sets (46155 subjects) made it possible to assess the parameters of this regulation at the population level. It is concluded that the mathematical treatment of biometric data based on the probability theory followed by the factual analysis of the results may be a useful tool for obtaining valuable physiological information not only on the case under study.     

Modeling of cardiac growth and remodeling of myofiber orientation

The heart has the ability to respond to long-term changes in its environment through changes in mass (growth), shape (morphogenesis) and tissue properties (remodeling). For improved quantitative understanding of cardiac growth and remodeling (G&R) experimental studies need to be complemented by mathematical models. This paper reviews models for cardiac growth and remodeling of myofiber orientation, as induced by mechanical stimuli. A distinction is made between optimization models, that focus on the end stage of G&R, and adaptation models, that aim to more closely describe the mechanistic relation between stimulus and effect. While many models demonstrate qualitatively promising results, a lot of questions remain, e.g. with respect to the choice of the stimulus for G&R or the long-term stability of the outcome of the model. A continued effort combining information on mechanotransduction at the cellular level, experimental observations on G&R at organ level, and testing of hypotheses on stimulus-effect relations in mathematical models is needed to answer these questions on cardiac G&R. Ultimately, models of cardiac G&R seem indispensable for patient-specific modeling, both to reconstruct the actual state of the heart and to assess the long-term effect of potential interventions.     

Linking flux network measurements to continental scale simulations: ecosystem carbon dioxide exchange capacity under non-water-stressed conditions

This paper examines long‐term eddy covariance data from 18 European and 17 North American and Asian forest, wetland, tundra, grassland, and cropland sites under non‐water‐stressed conditions with an empirical rectangular hyperbolic light response model and a single layer two light‐class carboxylase‐based model. Relationships according to ecosystem functional type are demonstrated between empirical and physiological parameters, suggesting linkages between easily estimated parameters and those with greater potential for process interpretation. Relatively sparse documentation of leaf area index dynamics at flux tower sites is found to be a major difficulty in model inversion and flux interpretation. Therefore, a simplification of the physiological model is carried out for a subset of European network sites with extensive ancillary data. The results from these selected sites are used to derive a new parameter and means for comparing empirical and physiologically based methods across all sites, regardless of ancillary data. The results from the European analysis are then compared with results from the other Northern Hemisphere sites and similar relationships for the simplified process‐based parameter were found to hold for European, North American, and Asian temperate and boreal climate zones. This parameter is useful for bridging between flux network observations and continental scale spatial simulations of vegetation/atmosphere carbon dioxide exchange.     

Expert systems for clinical pathology reporting

* Conventional automated interpretative reporting systems use standard or "canned" comments for patient reports. These are result-specific and do not generally refer to the patient context. * Laboratory information systems (LIS) are limited in their application of patient-specific content of reporting. * Patient-specific interpretation requires extensive cross-referencing to other information contained in the LIS such as previous test results, other related tests, and clinical notes, both current and previous. * Expert systems have the potential to improve reporting quality by enabling patient-specific reporting in clinical laboratories.     

A Quantitative Model of Early Atherosclerotic Plaques Parameterized Using In Vitro Experiments

There are a growing number of studies that model immunological processes in the artery wall that lead to the development of atherosclerotic plaques. However, few of these models use parameters that are obtained from experimental data even though data-driven models are vital if mathematical models are to become clinically relevant. We present the development and analysis of a quantitative mathematical model for the coupled inflammatory, lipid and macrophage dynamics in early atherosclerotic plaques. Our modeling approach is similar to the biologists’ experimental approach where the bigger picture of atherosclerosis is put together from many smaller observations and findings from in vitro experiments. We first develop a series of three simpler submodels which are least-squares fitted to various in vitro experimental results from the literature. Subsequently, we use these three submodels to construct a quantitative model of the development of early atherosclerotic plaques. We perform a local sensitivity analysis of the model with respect to its parameters that identifies critical parameters and processes. Further, we present a systematic analysis of the long-term outcome of the model which produces a characterization of the stability of model plaques based on the rates of recruitment of low-density lipoproteins, high-density lipoproteins and macrophages. The analysis of the model suggests that further experimental work quantifying the different fates of macrophages as a function of cholesterol load and the balance between free cholesterol and cholesterol ester inside macrophages may give valuable insight into long-term atherosclerotic plaque outcomes. This model is an important step toward models applicable in a clinical setting.     

THE VALUE OF BLOOD OXYGEN DETERMINATIONS

The blood oxygen determination is of great value in the diagnosis of congenital cardiovascular anomalies, evaluation of the relative influence between pulmonary and cardiac diseases, study of blood pigments, and in many physiological investigations. The recent popularization of the intravascular catheter and the advent of accurate and simplified methods for determining blood oxygen content have enhanced the clinical usage of the determinations. The correct interpretation of the data with regard to the clinical status of the patient is most essential. While the blood oxygen value is merely a laboratory determination, proper employment of the findings may afford crucial information for the clinician.     

Towards the Personalized Treatment of Glioblastoma: Integrating Patient-Specific Clinical Data in a Continuous Mechanical Model

Glioblastoma multiforme (GBM) is the most aggressive and malignant among brain tumors. In addition to uncontrolled proliferation and genetic instability, GBM is characterized by a diffuse infiltration, developing long protrusions that penetrate deeply along the fibers of the white matter. These features, combined with the underestimation of the invading GBM area by available imaging techniques, make a definitive treatment of GBM particularly difficult. A multidisciplinary approach combining mathematical, clinical and radiological data has the potential to foster our understanding of GBM evolution in every single patient throughout his/her oncological history, in order to target therapeutic weapons in a patient-specific manner. In this work, we propose a continuous mechanical model and we perform numerical simulations of GBM invasion combining the main mechano-biological characteristics of GBM with the micro-structural information extracted from radiological images, i.e. by elaborating patient-specific Diffusion Tensor Imaging (DTI) data. The numerical simulations highlight the influence of the different biological parameters on tumor progression and they demonstrate the fundamental importance of including anisotropic and heterogeneous patient-specific DTI data in order to obtain a more accurate prediction of GBM evolution. The results of the proposed mathematical model have the potential to provide a relevant benefit for clinicians involved in the treatment of this particularly aggressive disease and, more importantly, they might drive progress towards improving tumor control and patient’s prognosis.     

Reverse-engineering of gene networks for regulating early blood development from single-cell measurements

Background

Recent advances in omics technologies have raised great opportunities to study large-scale regulatory networks inside the cell. In addition, single-cell experiments have measured the gene and protein activities in a large number of cells under the same experimental conditions. However, a significant challenge in computational biology and bioinformatics is how to derive quantitative information from the single-cell observations and how to develop sophisticated mathematical models to describe the dynamic properties of regulatory networks using the derived quantitative information.

Methods

This work designs an integrated approach to reverse-engineer gene networks for regulating early blood development based on singel-cell experimental observations. The wanderlust algorithm is initially used to develop the pseudo-trajectory for the activities of a number of genes. Since the gene expression data in the developed pseudo-trajectory show large fluctuations, we then use Gaussian process regression methods to smooth the gene express data in order to obtain pseudo-trajectories with much less fluctuations. The proposed integrated framework consists of both bioinformatics algorithms to reconstruct the regulatory network and mathematical models using differential equations to describe the dynamics of gene expression.

Results

The developed approach is applied to study the network regulating early blood cell development. A graphic model is constructed for a regulatory network with forty genes and a dynamic model using differential equations is developed for a network of nine genes. Numerical results suggests that the proposed model is able to match experimental data very well. We also examine the networks with more regulatory relations and numerical results show that more regulations may exist. We test the possibility of auto-regulation but numerical simulations do not support the positive auto-regulation. In addition, robustness is used as an importantly additional criterion to select candidate networks.

Conclusion

The research results in this work shows that the developed approach is an efficient and effective method to reverse-engineer gene networks using single-cell experimental observations.

     

Effect of misreported family history on Mendelian mutation prediction models

People with familial history of disease often consult with genetic counselors about their chance of carrying mutations that increase disease risk. To aid them, genetic counselors use Mendelian models that predict whether the person carries deleterious mutations based on their reported family history. Such models rely on accurate reporting of each member's diagnosis and age of diagnosis, but this information may be inaccurate. Commonly encountered errors in family history can significantly distort predictions, and thus can alter the clinical management of people undergoing counseling, screening, or genetic testing. We derive general results about the distortion in the carrier probability estimate caused by misreported diagnoses in relatives. We show that the Bayes factor that channels all family history information has a convenient and intuitive interpretation. We focus on the ratio of the carrier odds given correct diagnosis versus given misreported diagnosis to measure the impact of errors. We derive the general form of this ratio and approximate it in realistic cases. Misreported age of diagnosis usually causes less distortion than misreported diagnosis. This is the first systematic quantitative assessment of the effect of misreported family history on mutation prediction. We apply the results to the BRCAPRO model, which predicts the risk of carrying a mutation in the breast and ovarian cancer genes BRCA1 and BRCA2.     

Intermittent Androgen Suppression: Estimating Parameters for Individual Patients Based on Initial PSA Data in Response to Androgen Deprivation Therapy

When a physician decides on a treatment and its schedule for a specific patient, information gained from prior patients and experience in the past is taken into account. A more objective way to make such treatment decisions based on actual data would be useful to the clinician. Although there are many mathematical models proposed for various diseases, so far there is no mathematical method that accomplishes optimization of the treatment schedule using the information gained from past patients or “rapid learning” technology. In an attempt to use this approach, we integrate the information gained from patients previously treated with intermittent androgen suppression (IAS) with that from a current patient by first fitting the time courses of clinical data observed from the previously treated patients, then constructing the prior information of the parameter values of the mathematical model, and finally, maximizing the posterior probability for the parameters of the current patient using the prior information. Although we used data from prostate cancer patients, the proposed method is general, and thus can be applied to other diseases once an appropriate mathematical model is established for that disease.     

Determinants of biventricular cardiac function: a mathematical model study on geometry and myofiber orientation

In patient-specific mathematical models of cardiac electromechanics, usually a patient-specific geometry and a generic myofiber orientation field are used as input, upon which myocardial tissue properties are tuned to clinical data. It remains unclear to what extent deviations in myofiber orientation and geometry between model and patient influence model predictions on cardiac function. Therefore, we evaluated the sensitivity of cardiac function for geometry and myofiber orientation in a biventricular (BiV) finite element model of cardiac mechanics. Starting out from a reference geometry in which myofiber orientation had no transmural component, two new geometries were defined with either a 27 % decrease in LV short- to long-axis ratio, or a 16 % decrease of RV length, but identical LV and RV cavity and wall volumes. These variations in geometry caused differences in both local myofiber and global pump work below 6 %. Variation of fiber orientation was induced through adaptive myofiber reorientation that caused an average change in fiber orientation of \({\sim }8^\circ \) predominantly through the formation of a component in transmural direction. Reorientation caused a considerable increase in local myofiber work \(({\sim }18\,\%)\) and in global pump work \(({\sim }17\,\%)\) in all three geometries, while differences between geometries were below 5 %. The findings suggest that implementing a realistic myofiber orientation is at least as important as defining a patient-specific geometry. The model for remodeling of myofiber orientation seems a useful approach to estimate myofiber orientation in the absence of accurate patient-specific information.