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, in vivo. We developed an inversion algorithm to fit the models for tumor growth for simulated as well as in vivo 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 in vivo mice-tumors, regression analysis on the P-layer volume showed R2 of 0.99 for logistic and Gompertzian while surface area model yielded R2=0.96. For the necrotic layer the R2 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 in vivo imaging data to extract features. Akaike information criterion (AIC) evaluations show Gompertzian or logistic growth model fits in vivo breast-tumors better than surface-area based growth model

Neutron Interferometry Using a Single Modulated Phase Grating

Neutron grating interferometry provides information on phase and small-angle scatter in addition to attenuation. Previously, phase grating moiré interferometers (PGMI) with two or three phase gratings have been developed. These phase-grating systems use the moiré far-field technique to avoid the need for high-aspect absorption gratings used in Talbot-Lau interferometers (TLI) which reduce the neutron flux reaching the detector. We demonstrate through simulations a novel phase grating interferometer system for cold neutrons that requires a single modulated phase grating (MPG) for phase-contrast imaging, as opposed to the two or three phase gratings in previously employed PGMI systems. We compare the MPG system to experiments in the literature that use a two-phase-grating-based PGMI with a best-case visibility of around 39% by Pushin et al. 2017. The simulations of the MPG system show improved visibility in comparison to that two-phase-grating-based PGMI. For example, an MPG with a modulation period 120 µm, pitch of 1 µm, and grating heights with a phase modulation of (pi,pi/4), illuminated by a monochromatic beam, produces a visibility of 85% with a comparable source-to-detector distance (SDD) as the two-phase-grating-based PGMI. Phase sensitivity, another important performance metric of the grating interferometer was compared to values available in the literature, viz. the conventional TLI with phase sensitivity of 4.5 x 103 for a SDD of 3.5 m and a beam wavelength of 0.44 nm (Kim et al. 2014). For a range of modulation periods, the MPG system provides comparable or greater theoretical maximum phase sensitivity of 4.1 x 103 to 10.0 x 103 for SDD of up to 3.5 m. This proposed MPG system appears capable of providing high-performance PGMI that obviates the need for the alignment of 2 phase gratings