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Clinical Oncological imaging is performed with various modalities, CT, MRI and F-18-FDG-PET. Recently,
investigators have used diffusion-advective-reaction tumor-growth models for registration to brain-atlas for MRI braintumor
datasets. We wish to extract model parameters from clinical time series scans of tumors (e.g. CT or MRI of brain
or lung tumors) to see if some of the parameters, tumor growth rate and/or diffusion-coefficient, could potentially serve
as predictive markers for monitoring disease and treatment response. We can then correlate with disease history and/or
PET SUV to assess the viability of the model parameters as markers. One hurdle to performing this is that for majority
of patients only 1 or 2 scans would be available for a specific tumor. We first take an existing diffusion-advectionreaction
dynamic tumor growth model and generate series of synthetic tumors. Then we try to invert the model and
recover the coefficient for one or multiple target scans, minimizing the sum-squared-error using APPSPACK. We find
that for this idealized case we could recover the diffusion-coefficient and growth-rate parameters with ~2%-3% error
whether we used the entire time series or a single time point. However, in general, for either case (multiple or single time
scan) some additional parameters such the tumor time scan and starting locations maybe necessary in the minimization.
In a second (novel) approach, we hypothesize that over a short time scale the tumor density/volume change is small (or
undetectable). Thus the cell birth and death and diffusion terms are in near-equilibrium. This steady-state model
diffusion-coefficient and growth parameters may then be extracted from even a single CT or MRI scan available for each
patient. Our steady state forward simulation and inversion could recover steady-state diffusion and growth-rate
parameters with near-perfect (~0.6% ) error for no-noise case and ~(0,7%) error for a high-noise case. The steady-state
model fitted excellently to a lung-tumor (1-d) profile of an (anonymized) patient with only 1.74% fitting error in a sumsquared
sense.
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