Experimental method and statistical analysis to fit tumor growth model using SPECT/CT imaging: a preclinical study.

Background: Over the last decade, several theoretical tumor-models have been developed to describe tumor growth. Oncology imaging is performed using various modalities including computed tomography (CT), magnetic resonance imaging (MRI), single-photon emission computed tomography (SPECT) and fluorodeoxyglucose-positron emission tomography (FDG-PET). Our goal is to extract useful, otherwise hidden, quantitative biophysical parameters (such as growth-rate, tumor-necrotic-factor, etc.) from these serial images of tumors by fitting mathematical models to images. These biophysical features are intrinsic to the tumor types and specific to the study-subject, and expected to add valuable information on the tumor containment or spread and help treatment plans. Thus, fitting realistic but practical models and assessing parameter-errors and degree of fit is important.

Methods: We implemented an existing theoretical ode-compartment model and variants and applied them for the first time, . We developed an inversion algorithm to fit the models for tumor growth for simulated as well as experimental data. Serial SPECT/CT scans of mice breast-tumors were acquired, and SPECT data was used to segment the proliferating-layers of tumors.

Results: Results of noisy data simulation and inversion show that 5 out of 7 parameters were recovered to within 4.3% error. In particular, tumor "growth-rate" parameter was recovered to 0.07% error. For model fitting to mice-tumors, regression analysis on the P-layer volume showed R of 0.99 for logistic and Gompertzian while surface area model yielded R=0.96. For the necrotic layer the R values were 0.95, 0.93 and 0.94 respectively for surface-area, logistic and Gompertzian. The Akaike Information Criterion (AIC) weights of the models (giving their relative probability of being the best Kullback-Leibler (K-L) model among the set of candidate models) were ~0, 0.43 and 0.57 for surface-area, logistic and Gompertzian models.

Conclusions: Model-fitting to mice tumor studies demonstrates feasibility of applying the models to imaging data to extract features. Akaike information criterion (AIC) evaluations show Gompertzian or logistic growth model fits breast-tumors better than surface-area based growth model.