(549f) Markov Process Model for Cancer Growth Elucidates Tumor Escape of Immune Surveillance and Treatment

Cancer is a disease whose patient outcomes are difficult to predict. In particular, patients occasionally appear to recover, only to suffer a recurrence of the disease after a few years or even decade or more. In melanoma, for example, the disease reappears in patients 10 years or more after treatment at a 7% rate. This recurrence after a long period of dormancy (during which the disease is medically undetectable) is a feature in many cancers including breast cancer and metastatic melanoma. One interpretation of long-time recurrences is the possibility that tumors somehow enter a dormant state at sub-detectable sizes. They revive from their dormant state through genetic adaptations such as ones that promote angiogenesis or counter immune surveillance. Traditional approaches to modeling cancer growth solve for the median outcome and are less adept at predicting unlikely but important events such as recurrence.

The causes - and even the true nature - of dormancy and recurrence are poorly understood, though the fact that cancers evolve over time is an important factor. Tumors can grow via cell division, can shrink via the attack of chemotherapy, radiation or the immune system, and can spawn metastases via the breakoff and implantation of cells from existing tumors. Different tumors inside an individual patient each have elements of statistical variation in how they undergo these processes due to the complex tumor microenvironments and the occurrence of random mutations. However, these processes are still rate processes.

We consider a model in which we model cancer growth, shrinkage, and metastasis each as a Markov process, with size-dependent Poisson parameters, whose results predict the time evolution of all initial and expected metastasized tumors in patients. This new model is built to mirror the results of an existing population balance (partial differential equation) model and takes its parameters from the fit of the continuum model to experimental tumor data. The new model augments the old, in that the new model simulates a discrete number of tumors in individual patients, and thus more closely resembles nature, as opposed to the abstraction of a continuous number of tumors from a very large patient population. This discrete process allows the properties of tumors to spontaneously change due to genetic adaptation on an individual basis, which captures the effect of the appearance of well-adapted tumor cell subpopulations that often appear in metastatic cancer and confer properties that promote tumor escape.

We present simulation results of changing tumor populations and show how apparent dormancy and recurrence can occur. The implied mechanism differ from the classic dormancy idea above. We show how such long-time recovery can arise after successful surgery and we investigate its likelihood by related realization from a given initial tumor size distributions. The goal is to predict both the likelihood of recurrence and the expected time to recurrence. Should this expected time be longer than the patient's expected remaining lifetime, doctors may reconsider employing side-effect laden prophylactic treatments that, in any case, may provoke a host response that is tumorigenic. This model will help grant foresight into the expected time for detectable metastases to appear after surgeries or other treatments, and help physicians better decide on treatment plans given these prognostic predictions.