Seminar: Harrison H. Barrett

    Tuesday, January 24, 2017 - 3:30pm - 5:00pm
    Radiology Research Laboratory, Conference Room

    1609 N Warren Ave. (Building 211, Room 101)

    Just north of the construction site for the new Banner Hospital. Best approach is via the Ring Road.


    Physiological Random Processes: Mathematical and statistical basics, computational methods and applications to precision cancer therapy.


    Many different physiological processes affect the growth of malignant lesions and their response to therapy.  Each of these processes is spatially and genetically heterogeneous; dynamically evolving in time; controlled by many other physiological processes, and intrinsically random and unpredictable.  It is the premise of this talk that all of these properties of cancer physiology can be treated in a unified, mathematically rigorous way by the use of the theory of random processes.  In this approach, each physiological process is treated as a random function of time and position within a tumor.  The statistical properties of this function are quantified by the characteristic functional, which can be regarded as the infinite-dimensional extension of the more familiar characteristic function, commonly used to specify the statistics of scalar random variables and finite-dimensional random vectors.  If the characteristic functional for a random process is known, any desired statistical properties of the process can be computed. 

    In this talk we show how these concepts can be extended to multiple physiological random processes as they interact with each other and evolve in time.  The new theory is illustrated by analyzing various models of tumor growth and response to therapy.  Application of the theory to precision cancer therapy requires information about physiological random processes in individual patients.  We show how maximum-likelihood estimation can be applied to Emission Computed Tomography (ECT) images to estimate important unknown parameters in the characteristic functional and ultimately to predict the probability of tumor control for an individual patient undergoing a proposed therapeutic regimen.  Methods for quantifying the uncertainties in these estimates are also discussed.