IMPROVING QUANTITATIVE TREATMENT RESPONSE MONITORING WITH DEFORMABLE IMAGE REGISTRATION

Quantitative imaging with 18F-FDG PET/CT has the potential to provide an in vivo assessment of response to radiotherapy (RT). However, comparing tissue tracer uptake in longitudinal studies is often confounded by variations in patient setup and potential treatment induced gross anatomic changes. These variations make true response monitoring for the same anatomic volume a challenge, not only for tumors, but also for normal organs-at-risk (OAR). The central hypothesis of this study is that more accurate image registration will lead to improved quantitation of tissue response to RT with 18F-FDG PET/CT. Employing an in-house developed “demons” based deformable image registration algorithm, pre-RT tumor and parotid gland volumes can be more accurately mapped to serial functional images. To test the hypothesis, specific aim 1 was designed to analyze whether deformably mapping tumor volumes rather than aligning to bony structures leads to superior tumor response assessment. We found that deformable mapping of the most metabolically avid regions improved response prediction (P<0.05). The positive predictive power for residual disease was 63% compared to 50% for contrast enhanced post-RT CT. Specific aim 2 was designed to use parotid gland standardized uptake value (SUV) as an objective imaging biomarker for salivary toxicity. We found that relative change in parotid gland SUV correlated strongly with salivary toxicity as defined by the RTOG/EORTC late effects analytic scale (Spearman’s ρ = -0.96, P<0.01). Finally, the goal of specific aim 3 was to create a phenomenological dose-SUV response model for the human parotid glands. Utilizing only baseline metabolic function and the planned dose distribution, predicting parotid SUV change or salivary toxicity, based upon specific aim 2, became possible. We found that the predicted and observed parotid SUV relative changes were significantly correlated (Spearman’s ρ = 0.94, P<0.01). The application of deformable image registration to quantitative treatment response monitoring with 18F-FDG PET/CT could have a profound impact on patient management. Accurate and early identification of residual disease may allow for more timely intervention, while the ability to quantify and predict toxicity of normal OAR might permit individualized refinement of radiation treatment plan designs.

NONLINEAR TIME SERIES/SYSTEM ANALYSIS (STATE-SPACE, DYNAMICS, INTERVENTION, RESILIENCE, KALMAN)

A discussion of nonlinear dynamics, demonstrated by the familiar automobile, is followed by the development of a systematic method of analysis of a possibly nonlinear time series using difference equations in the general state-space format. This format allows recursive state-dependent parameter estimation after each observation thereby revealing the dynamics inherent in the system in combination with random external perturbations.^ The one-step ahead prediction errors at each time period, transformed to have constant variance, and the estimated parametric sequences provide the information to (1) formally test whether time series observations y(,t) are some linear function of random errors (ELEM)(,s), for some t and s, or whether the series would more appropriately be described by a nonlinear model such as bilinear, exponential, threshold, etc., (2) formally test whether a statistically significant change has occurred in structure/level either historically or as it occurs, (3) forecast nonlinear system with a new and innovative (but very old numerical) technique utilizing rational functions to extrapolate individual parameters as smooth functions of time which are then combined to obtain the forecast of y and (4) suggest a measure of resilience, i.e. how much perturbation a structure/level can tolerate, whether internal or external to the system, and remain statistically unchanged. Although similar to one-step control, this provides a less rigid way to think about changes affecting social systems.^ Applications consisting of the analysis of some familiar and some simulated series demonstrate the procedure. Empirical results suggest that this state-space or modified augmented Kalman filter may provide interesting ways to identify particular kinds of nonlinearities as they occur in structural change via the state trajectory.^ A computational flow-chart detailing computations and software input and output is provided in the body of the text. IBM Advanced BASIC program listings to accomplish most of the analysis are provided in the appendix. ^