Ardith El-Kareh Fox

Dr. El-Kareh’s research is primarily focused on mathematical modeling of cancer treatment and growth, with the aim of using these models to discover ways to optimize treatment, particularly chemotherapy and chemoimmunotherapy. Other research interests have included applying mathematical modeling to fluid mechanics, blood flow in the microcirculation, and human memory. Her undergraduate degree from the University of Colorado is in chemical engineering, as is her PhD from the California Institute of Technology, where her research studies were in theoretical fluid mechanics. Her work in cancer-related areas is motivated by the potential for mathematical modeling to contribute to cancer research, notably in several key ways: (1) through the ability of such models to consider a wide range of possible treatment combinations, schedules, and doses to to optimize therapy, while experimental studies are more limited in the number of possibilities they can test; (2) through the ability of models to perform virtual “experiments” examining the effects of adding, removing, or quantitatively changing certain system variables, parameters, or mechanisms in ways that might not even be feasible experimentally, to better understand which factors are most important, and (3) through the fact that mathematical models can help test hypotheses and contribute to a better understanding of the mechanisms behind tumor growth, response to treatment, and the interaction of tumors with the host. Dr. El-Kareh began her work in cancer research with an interest in modeling tumor response to treatment, including drug transport and effects of the tumor microenvironment. However, she soon realized that a major limitation to such studies was a lack of adequate mathematical models for describing cellular response to drugs, and multidrug or drug-radiation combinations. She found that model predictions could vary widely according to which model was used to describe cellular response, and this led to her interest in cellular pharmacology. With her collaborators she developed more realistic models for the response of cells to widely-used chemotherapy drugs such as cisplatin, doxorubicin, and paclitaxel, and then pioneered the “additive damage model” as a way to describe cellular pharmacology of drug and drug-radiation combinations. The additive damage model has been very successful in describing experimental data for a wide range of drug and drug-radiation combinations, and she has extended it to include schedule-dependence. A 2007 paper on paclitaxel-platinum drug combinations introduced a new model, the “cell cycle checkpoint model,” that built on the additive damage concept to include cell cycle effects on drug response. The key point of these models has been to consider cellular damage as a separate variable that changes over time in response to exposure and cellular uptake, efflux, binding, metabolism, and repair processes, and to then consider cell kill as determined by peak damage at a critical point in the cell cycle. This separation of cellular response into damage and response to damage has proven essential for explaining delayed responses (cell death often occurs well after exposure has ended) and responses to combinations, where the kinetics of damage formation from each agent is different, and where perturbations, such as to the cell cycle, caused by one agent can influence response to a second agent. Taken together, these cellular pharmacodynamics models provide a very useful framework for more realistically assessing and predicting cellular response to combinations, and they are an important building block for larger-scale models predicting response to therapy. Work in this area is continuing, including the development of models for response to drug-radiation combinations with fractionation. Another focus of research that evolved from Dr. El-Kareh’s modeling of response to cancer treatment has been the driving question: how does chemotherapy actually cause tumor regression? While chemotherapy does not lead to long-term survival for many cancer patients, it remains an important part of standard-of-care treatment for a substantial fraction of patients, at least functioning to prolong survival or to give palliative relief, and for some cancers such as testicular it is in fact curative. In a number of cases it can lead to partial or even total clinical regression of tumors. The traditional, textbook explanation has been these regressions occur because it kills rapidly growing cells. Yet this explanation is generally inadequate, as has increasingly been realized in recent years. Dr. El-Kareh found in her modeling work that explaining regression with only direct cell kill would require assuming a much larger fraction of actively proliferating cells in a tumor than is substantiated by experiment. This then leaves the very important question: what effects other than direct cell kill are causing tumor regression? The most promising explanations are that chemotherapy alters the tumor microenvironment, that it affects host stromal cells in addition to tumor cells, and that it somehow stimulates the immune system or alters the balance in tumor-immune interactions. Dr. El-Kareh has primarily focused on modeling tumor-immune interactions to seek an answer to the question of the actual mechanisms of chemotherapy action. Two papers with Mark Robertson-Tessi and Alain Goriely from 2012 and 2015 examine tumor-immune interactions of only the adaptive immune system; the latter also considers chemotherapy and chemoimmunotherapy. These studies point to potential for models to guide the design of such therapies to maximally exploit the immune system’s potential and to thus optimize therapy. More recently, Dr. El-Kareh worked with Applied Math graduate student Victoria Gershuny to develop models of tumor-immune interactions that included the innate as well as the adaptive immune system, and that were particularly aimed at examining the role of the immune system in the FOLFOX treatment regimen, which is widely used for colorectal cancer. This work is still in progress, and has now led to a re-examination of the role of intratumoral T cells. These efforts at modeling tumor-immune interactions have significance beyond understanding chemotherapy, as immune treatments are currently the most promising area of development of new anti-cancer therapies, and chemotherapy is likely to still be used in combination with such treatments at least for a sizeable fraction of patients. An understanding of tumor-immune interactions is sure to have clinical relevance for many years ahead. Most cancers kill patients not by the primary tumor but through widely disseminated metastatic disease, yet most mathematical models do not consider growth or treatment of metastatic tumors. This has led to another area of Dr. El-Kareh’s research. One key question she is investigating is: how does the per-cell rate of metastasis change over time as a tumor develops? She has been using data from the NIH’s SEER database along with mathematical models for metastatic growth to address this question. Another question is how considering the nature of a tumor as a large number of separate nodules rather than a single mass affects predictions for optimal treatment. These studies will also lead to integration of the previously developed immune models with models for metastatic disease, as the immune system not only affects growth and response of individual tumor nodules, but also affects the ability of cells to move to distant locations and colonize. Survival of cancer patients, even for the same tumor size and stage at diagnosis, is adversely affected by age, even when corrected for other age-related factors. While there are a number of possible explanations for this, including under-treatment of older populations or their decreased tolerance for treatment, it appears very likely that age-related changes to the immune system may lie behind this statistical survival difference. Dr. El-Kareh is currently using data from the NIH’s SEER database and extending previously-developed models for tumor-immune interactions to address the question: can age-related changes in the immune system explain decreased survival times for older patients? As a by-product of this work, the models for the immune system that include age effects have the potential to be useful to researchers in other areas, such as those studying how age affects response to infections. In the area of cancer research, these models are aimed ultimately at studying how immunotherapies might be used to improve cancer survival. Dr. El-Kareh’s interests in modeling cancer growth and treatment have also led to developing a mathematical model for the mammalian cell cycle, work that initiated as she advised Dr. Katherine Williams during her doctoral studies in Applied Math. The cell cycle is important for understanding both cancer growth and anti-cancer treatment, as cancer is a disease of cell cycle dysregulation, and numerous widely-used anti-cancer treatments perturb the cell cycle, or are affected in their efficacy by it. As mentioned above in connection with developing models for cellular pharmacodynamics, these perturbations are particularly relevant for optimizing combination treatment, including optimization of schedules of administration. While several models of the cell cycle have previously been proposed, this new model has the desirable feature of involving continuous ordinary differential equations, and of linking cell cycle progression to completion of cell cycle tasks such as licensing, DNA replication, or nuclear envelope breakdown. This linkage is essential, as regardless of levels of cell cycle controllers, the cycle is designed to not progress if a key task remains unfulfilled. A manuscript on this model is currently in progress, and a follow-up study that will extend the model to include coupling with metabolism is planned. The current model explains S phase control (while DNA is replicated) through the inhibition of additional origin firing by currently active origins (areas of replication), which has led to preliminary work on explaining S phase in more detail, with the aim of improving on previous models that explain DNA origin firing in stochastic terms. A seeming conundrum of origin firing is local promotion simultaneous with global inhibition, and the model in development will include this as a new feature to explain how the length of S phase is determined. A final area of interest of Dr. El-Kareh’s is mathematical modeling of human memory, particular the forgetting function. Dr. El-Kareh came upon this accidentally through an interest in online chess problem solving. By using publicly-available data from a chess problem website, she was able to deduce information about the forgetting function, and test various mathematical forms that have been proposed to describe it. This work is ongoing.