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Project Title: Validate mathematical models of AD treatments

Scientific Abstract:
Background: Personalized medicine is an emerging approach for disease prevention, early detection, and treatment that takes into account individual variability in genes, environment, demographic factors, and lifestyle [1]. The tools of mathematical modeling will allow integration of this large amount of data with current disease models, based on experimental data, to create quantitative averaged disease models [2]. It also enables personalization, based on individualized data to yield personal risk profiles and suggest possible prevention/treatment strategies. By combining insights from a causal model-based approach with that of a data-driven approach, computational systems biology will provide a more comprehensive characterization of the complex pathogenesis of AD [3,4]. Moreover, it will provide a powerful and new means to personalize averaged models of disease with individual data, yielding personal predictions of biomarker trajectories and potential individualized prevention strategies.

Objectives: The overall objective of this project is to use the clinical trial data to develop a personalized multifactorial mathematical model of AD progression that identifies patient-specific triggers, predicts disease trajectory, and simulates therapeutic responses.

Study Design: Aim 1: Validate a newly developed mathematical model of AD by using the clinical trail dataset. A sparse model of AD, based on a system of ordinary differential equations (ODEs), has been developed by PI to include all the essential AD clinical biomarkers [4]. We will validate the personalized AD model by serial clinical and scalar clinical measures for each patient.

Aim 2: Study personalized therapeutic plans for AD patients via mathematical modeling. We will introduce control functions in our model to mimic current therapies, such as anti-amyloid, anti-tau, and neuro-protective therapies, and provide an optimal personalized treatment plan for each patient. We will also simulate the effect of treatment on the spatial patterns of biomarker pathology to mimic the in vivo brain environment.

Participants: the entire trial study population

Primary and Secondary Outcome Measure: At the end of the funding period, we will have a personalized, data-driven quantitative mathematical model that we expect will greatly enhance our ability to predict AD trajectory at an individual level and accelerate drug discovery and personalized treatment. This model is expected to yield future personal biomarker trajectory predictions with estimates of predictive accuracy, based on patient follow-up data, as well as model-optimized single or combination therapeutic strategies.

Statistical Analysis: We will use the requested clinical trial data to validate our model and calibrate the personalized parameters by using clinical data fro each individual.

Brief Project Background and Statement of Project Significance:
Taking into account individual variability among these clinical biomarkers to provide the different disease progression for different patients is so-called personalized medicine which is an emerging approach for disease prevention, early detection, and treatment. It is the cornerstone of the national Precision Medicine Initiative, a research effort launched by the White House in 2015, with significant implications for AD research. Two components are necessary to realize this idea: first, there needs to be an abundance of longitudinal data to cover many physiological aspects of individuals when they are healthy and possibly into disease [5]. Such data, for example, might combine genomics with data from other technologies that enable longitudinal monitoring of molecular components that reflect real-time physiological states, such as clinical biomarkers. Second, there needs to be computational methods and models capable of analyzing and integrating the data on a large scale [6].

The tools of data-driven modeling and artificial intelligence are capable of integrating large-scale data with current causal models of disease to create quantitative generalized disease models, applicable to a population. It also enables personalization of the models, based on individualized data, to yield personal risk profiles and suggest possible prevention/treatment strategies. This data-driven modeling approach has already been highlighted by systems biology researchers to AD pathophysiology using tools such as genomics, transcriptomics, and proteomics[20-24]. It is likely that all forms of AD evolve through the convergence of failures in several ?systems? networks, signaling pathways, or pathophysiological processes. By combining insights from a causal model-based approach with that of a data-driven approach, computational modeling will provide a more comprehensive characterization of the complex pathogenesis of AD. Moreover, it can provide a powerful and innovative way to personalize averaged models of disease with individual data, yielding personal predictions of biomarker trajectories and potential individualized prevention strategies.

Upon successful completion of the proposed research, we expect to have a data-driven personalizable multifactorial causal model of AD progression that identifies patient-specific triggers, predicts biomarker trajectory, and simulates therapeutic responses to single and/or combination therapies, all at the level of the individual subject. This contribution is expected to be significant because it will help accurately forecast a patient?s natural history years before significant symptoms become apparent, as well as aid in enriching samples in clinical trials with pre-symptomatic or early symptom subjects who are most likely to benefit from particular interventions. For example, some patients may benefit more from anti-amyloid, anti-tau, or neuroprotective agents, or combinations thereof. Because of the significant expense of large-phase clinical trials, targeted enrichment of patient samples will be critical for streamlining the drug discovery process and accelerating the search for methods to prevent, slow, or cure AD.

Specific Aims of the Project:
Aim 1: Validate a newly developed mathematical model of AD by using the clinical trial dataset. . A sparse model of AD, based on a system of ordinary differential equations (ODEs), has been developed by PI to include all the essential AD clinical biomarkers. We will validate the personalized AD model by serial clinical and scalar clinical measures for each patient.

Aim 2: Study personalized therapeutic plans for AD patients via mathematical modeling. We will introduce control functions in our model to mimic current therapies, such as anti-amyloid, anti-tau, and neuro-protective therapies, and provide an optimal personalized treatment plan for each patient. We will also simulate the effect of treatment on the spatial patterns of biomarker pathology to mimic the in vivo brain environment.

Study Design: Methodological research

What is the purpose of the analysis being proposed? Please select all that apply.:

Software Used:

Data Source and Inclusion/Exclusion Criteria to be used to define the patient sample for your study: CSF beta-amyloid peptide (A?42), total tau, and phosphorylated tau levels. Volumetrics such as hippocampal volume and neuropsychological tests, such as the Alzheimer's Disease Assessment Scale (ADAS) score.

Primary and Secondary Outcome Measure(s) and how they will be categorized/defined for your study: Upon successful completion of the proposed research, we expect to have a basic personalizable multifactorial causal model of AD progression that identifies patient-specific triggers, predicts biomarker trajectory, and simulates therapeutic responses to single and/or combination therapies, all at the level of the individual subject.

Main Predictor/Independent Variable and how it will be categorized/defined for your study: CSF beta-amyloid peptide (A?42), total tau, and phosphorylated tau levels. Volumetrics such as hippocampal volume and neuropsychological tests, such as the Alzheimer's Disease Assessment Scale (ADAS) score.

Other Variables of Interest that will be used in your analysis and how they will be categorized/defined for your study: none

Statistical Analysis Plan:
We will use the requested clinical trial data to validate our model. First, we will analyze the data based on the different disease groups such as CN, LMCI and AD. Then we will perform the data normalization across the dataset. More specifically, data Normalization will be performed by rescaling biomarker data such that the mean in the different groups is mapped to a value of zero and the mean in the AD group to a value of one. An average group model will initially be estimated for use as initial parameter and biomarker values in the optimization of the personalized model using baseline patient data in the clinical database.

Once the data is normalized, we will conduct an optimization procedure to fit the parameters in our model by using the requested clinical dataset. More specifically, personalized parametrization will be performed for each patient by solving an optimization problem on the normalized dataset. We will extend this personalized parameterization for tau, neuronal degeneration, and cognitive impairment. Despite just 12 personalized parameters in the sparse model, it is still a highly non-convex optimization problem, which is influenced by the optimization algorithm. Thus we will develop an optimization based on the ?equation-by-equation? (EBE) setup [7] which fits A_? concertation first, the tau biomarker second, the neuron degeneration third, and cognitive impairment last.

Narrative Summary: We have developed a new mathematical model, based on AD cognitive, cerebrospinal fluid (CSF) and MRI biomarkers, to provide a personalized optimal treatment plan for individuals. We want to parameterize this model by clinical trial datasets so we can use the validated mathematical model to do some AD treatment studies.

Project Timeline:
Month 0-6: Analyze clinical biomarker data from the clinical trial database, design, parameterize and optimize the math model;

Month 6-12: Test potential AD treatments on the validated math model to suggest an optimal personalized treatment plan and compare the efficacy in the clinical dataset.

Dissemination Plan:
The project?s most notable deliverable will be an open-source software, which we will

design for workstations and Linux clusters. This software will incorporate all of the algorithms developed

by this project and will be housed on GitHub for public access. Additionally, we will develop some flexible

modules that will make these computational models accessible to researchers in a variety of other areas,

so that these individuals can advance their own research and contribute directly to the development of the

software. In other words, the software that will be developed with the support of this grant has the potential

for continued growth across many research areas, long after the term of the grant concludes. This opensource

software will have broad-spectrum applications in Alzheimer's disease.

potentially suitable journals for submission of the completed research project: npj digital medicine, plos computational biology

Bibliography:

1. Villain, N., G. Chetelat, B. Grassiot, P. Bourgeat, G. Jones, K. A. Ellis, D. Ames, R. N. Martins, F. Eustache, O. Salvado, C. L. Masters, C. C. Rowe, V. L. Villemagne and A. R. Group (2012). Regional dynamics of amyloid-? deposition in healthy elderly, mild cognitive impairment and Alzheimer’s disease: a voxelwise PiB-PET longitudinal study. Brain. Jul;135(Pt 7):2126-39.

2. Jack, C. R., Jr., D. A. Bennett, K. Blennow, M. C. Carrillo, H. H. Feldman, G. B. Frisoni, H. Hampel, W. J. Jagust, K. A. Johnson, D. S. Knopman, R. C. Petersen, P. Scheltens, R. A. Sperling and B. Dubois (2016). A/T/N: An unbiased descriptive classification scheme for Alzheimer disease biomarkers. Neurology 87(5): 539-547.

3. Hao, W. and A. Friedman (2016). Mathematical model on Alzheimer?s disease. BMC Systems Biology 10: 108.

4. Petrella, J., Hao, W., Rao, A., and Doraiswamy M (2019). Computational Causal Modeling of the Dynamic Biomarker Cascade Theory in Alzheimer?s Disease. Comput Math Methods Med. 2019:6216530.

5. Batool, A, Kamal, MA, Rizvi, SMD, Rashid, S (2018). Topical Discoveries on Multi-Target Approach to Manage Alzheimer’s Disease. Curr. Drug Metab., 19, 8:704-713.

6. Scahill, R. I., J. M. Schott, J. M. Stevens, M. N. Rossor and N. C. Fox (2002). Mapping the evolution of regional atrophy in Alzheimer’s disease: unbiased analysis of fluid-registered serial MRI. Proc Natl Acad Sci U S A 99(7): 4703-4707.

7. Hao, W. and Harlim, J. (2018) An Equation-By-Equation Method for Solving the Multidimensional Moment Constrained Maximum Entropy Problem, Communications in Applied Mathematics and Computational Science, Vol. 13, pp. 189?214.