Mathematics for Understanding Disease

Abstract

The application of mathematical models to reflect the organization and activity of biological systems can be viewed as a continuum of purpose. The far left of the continuum is solely the prediction of biological parameter values, wherein an understanding of the underlying biological processes is irrelevant to the purpose. At the far right of the continuum are mathematical models, the purposes of which are a precise understanding of those biological processes. No models in present use fall at either end of the continuum. Without question, however, the emphasis in regards to purpose has been on prediction, e.g., clinical trial simulation and empirical disease progression modeling. Clearly the model that ultimately incorporates a universal understanding of biological organization will also precisely predict biological events, giving the continuum the logical form of a tautology. Currently that goal lies at an immeasurable distance. Nonetheless, the motive here is to urge movement in the direction of that goal. The distance traveled toward understanding naturally depends upon the nature of the scientific question posed with respect to comprehending and/or predicting a particular disease process. A move toward mathematical models implies a move away from static empirical modeling and toward models that focus on systems biology, wherein modeling entails the systematic study of the complex pattern of organization inherent in biological systems.

Integrated Pharmacometrics and Systems Pharmacology Model‐Based Analyses to Guide GnRH Receptor Modulator Development for Management of Endometriosis

“…Ideally, this modeling provides a platform for future simulations, that could include compound‐specific kinetic and dynamic considerations, to evaluate candidate drug and dosing selection scenarios. Overall, this integrated approach represents a synergy of multiscale systems pharmacology modeling and more traditional pharmacometrics analyses; this could serve as a case study for recent efforts to promote model‐based drug development 8 , 17 , 18 , 19 , 20 , 21 …”

Pharmacometrics as a Discipline Is Entering the “Industrialization” Phase: Standards, Automation, Knowledge Sharing, and Training Are Critical for Future Success

“…Similarly, CAMD pools data from publicly available sources like ADNI and precompetitive proprietary data from member companies (patient‐level data from control arms and active treatment groups from failed trials), which are being remapped to existing and newly developed CDISC standards 16 , 17 . The deliverables from the work will be made publicly available by CAMD itself and also through collaborations like http://OpenDiseaseModels.org and through peer‐reviewed publications.…”

“…Critical Path Institute, in collaboration with the Engelberg Center for Health Care Reform at the Brookings Institution, formed CAMD in September 2008 16 . This coalition includes the FDA, the European Medicines Agency (EMA), 2 branches of the US National Institutes of Health (NIH), academic scientists, patient groups, and leading global companies representing the medical product industry 17 …”

The Coalition Against Major Diseases: Developing Tools for an Integrated Drug Development Process for Alzheimer’s and Parkinson’s Diseases

“…These models can increase efficiency in making drug development decisions because many variables that influence outcomes can be considered simultaneously through the use of simulations. Also, the weight of knowledge and data gaps may be more systematically ranked and prioritized 1 , 3 . For additional references on modeling and simulation, please see the online.…”

“…In the specific case of Parkinson's and Alzheimer's diseases, given the incomplete understanding of the molecular and physiological chains that govern disease progression, a top‐down approach may be preferred initially. Satellite modeling efforts (e.g., models borrowing from in vitro or in vivo studies and scaling up to human, molecular‐marker kinetic models in various body compartments, and model‐based imaging scaling from animals to patients) may be used to indirectly support the top‐down approach 1 , 3 …”