I investigate biomedical problems using a variety of mathematical tools, such as ODE and PDE modeling, sensitivity analysis, parameter estimation, uncertainty quantification, linear stability and bifurcation analysis, and optimal control. My research focuses on immune-mediated conditions and explores the mechanisms involved in 1) autoimmunity, immune privilege, hair growth and disorders, and 2) immune dysregulation, which leads to cardiovascular, brain and vision damage.
1) Autoimmunity: My case study is the autoimmune hair loss disease alopecia areata (AA), affecting people of different ethnic groups from both genders and all ages. There is no cure for AA, and available treatments fail in most patients. During my PhD at Florida State University, I created the first mathematical model for AA development, which has helped to obtain insights not accessible before. Selecting this thesis topic was my initiative as my advisor had never heard of AA, but he got intrigued, encouraged the project, and we established collaboration with Dr. Ralf Paus, a prominent dermatologist and Professor at University of Manchester and University of Miami. The AA model captures the key disease progression events, namely immune cells attack and destroy the cells producing hair. Via model simulations and analysis, I discovered that the AA autoimmune response alters the impact of different hair growth processes, which has implications for the investigation of novel therapeutic options. My research aims to improve assessment and treatment of AA patients. The disease development is heterogeneous, and clinicians are unable to forecast how fast hairless lesions will progress and how a patient will respond to therapy. Such prognostics require time course information about the key immune components, but this cannot be collected from the affected skin, as multiple biopsies would inflict more damage and exacerbate the AA condition. My AA research has very important translational relevance to the study of autoimmune disorders which damage organs not as accessible for investigation, such as the eye, the brain and internal organs.
2) Immune dysregulation: As a postdoc at NC State University (NCSU), I expand my previous work by studying more fundamental mechanisms guiding the immune system and how it interacts with the cardiovascular, cerebrovascular and other physiological functions. The overarching goal of this research is to cast light on unresolved questions regarding the development and treatment of vascular dysfunction induced by severe infection and inflammation. My efforts include developing a model that captures how the inflammatory response to bacterial endotoxin in healthy adults affects the dynamics of physiological signals, such as heart rate (HR), blood pressure (BP), temperature, and pain perception. This involves interconnecting dynamical equations for the behavior of key elements in the immune, thermal and pain response to an endotoxin challenge with a cardiovascular system module from which HR and BP can be predicted. This coupled model is able to reflect the qualitative behavior exhibited by HR, BP, and temperature data from two independent studies in which healthy adults were given a single injection of E. coli-derived endotoxin. Using simulation analysis, we also explore the model’s response to a sustained level of endotoxin and different therapeutic interventions.
In addition, I am involved in a project that aims to enhance the understanding and explore ways for better treatment of age-related macular degeneration (AMD), a condition leading to vision impairment. AMD has no cure and involves degeneration of photoreceptors, the cells converting light into electrical signals sent to the brain via the optic nerve. AMD has been associated with inefficient lactate transport inside the retina. I contribute to the development of a model for photoreceptor metabolic mechanisms and apply sensitivity analysis to determine the processes with greatest impact on the output. The project was initiated at the 2019 Workshop for Women in Mathematical Biology, and I collaborate on it with five female biomathematicians outside NCSU. We received funding to participate in the summer program of the Mathematical Sciences Research Institute in Berkley, CA in order to further develop the investigation. Each of us will take on a related but separate topic, and I will lead the line of research where mathematical modeling and analysis will be used to explore the role of inflammation in vision loss.
A. Dobreva, R. Paus, and N. G. Cogan (2020). Toward predicting the spatio-temporal dynamics of alopecia areata lesions using partial differential equation analysis, Bulletin of Mathematical Biology, 82(3), Article number: 34.
A. Dobreva, R. Paus, and N. G. Cogan (2017). Analyzing the dynamics of a model for alopecia areata as an autoimmune disorder of hair follicle cycling, Mathematical Medicine and Biology, 35(3): 387-407.
A. Dobreva, R. Paus, and N. G. Cogan (2015). Mathematical model for alopecia areata. Journal of Theoretical Biology, 380, 332-345.
A. Dobreva, R. Brady, K. Larripa, C. Puelz, J. Mehlsen, and M. S. Olufsen. A physiological model of the inflammatory-thermal-pain-cardiovascular interactions during an endotoxin challenge, In revision, Mar. 2020. Preprint available on arXiv:1908.07611 [q-bio.TO].
E. Camacho, A. Dobreva, K. Larripa, A. Radulescu, D. Schmidt, and I. Trejo. Mathematical modeling of retinal degeneration, In revision May 2020 for publication in a Springer volume for research generated at the 2019 Collaborative Workshop for Women in Mathematical Biology.
N. G. Cogan, F. Bao, R. Paus, and A. Dobreva. Data assimilation of synthetic data as a novel strategy for predicting disease progression in alopecia areata, Submitted Apr. 2020.