Mistiming Death: Modeling the Time-Domain Variability of Tumor Apoptosis and Implications for Molecular Imaging of Cell Death

Purpose: Apoptosis, in the context of cancer, is a form of programmed cell death induced by chemotherapy, radiotherapy, and immunotherapy. As this is a central pathway in treatment response, considerable effort has been expended on the development of molecular imaging agents to non-invasively measure tumor apoptosis prior to quantitative changes in tumor dimensions. Despite these efforts, clinical trials directed at imaging apoptosis by PET, SPECT, and MRI have failed to robustly predict response to treatment with high sensitivity and specificity. Although these shortcomings may be linked to probe design, we propose that the combination of variability in the timing of maximal in vivo tumor apoptosis and sub-optimal sampling times fundamentally limits the predictive power of PET/SPECT apoptosis imaging. Procedures: Herein, we surveyed the literature describing the time course of therapy-induced tumor apoptosis in vivo and used these data to construct a mathematical model describing the onset, duration, amplitude, and variability of the apoptotic response. Uncertainty in the underlying time of initiation of tumor apoptosis was simulated by Gaussian, uniform, and Landau distributions centered at the median time-to-maximum apoptotic rate derived from the literature. We then computationally sampled these models for various durations to simulate PET/SPECT imaging agents with variable effective half-lives. Results: Models with a narrow Gaussian distribution of initiation times for tumor apoptosis predicted high contrast ratios and strong predictive values for all effective tracer half-lives. However, when uncertainty in apoptosis initiation times were simulated with uniform and Landau distributions, high contrast ratios and predictive values were only obtained with extremely long imaging windows (days). The imaging contrast ratios predicted in these models were consistent with those seen in pre-clinical apoptosis PET/SPECT imaging studies and suggest that uncertainty in the timing of tumor cell death plays a significant role in the maximal contrast obtainable. Moreover, when uncertainty in both apoptosis initiation and imaging start times were simulated, the predicted contrast ratios were dramatically reduced for all tracer half-lives. Conclusions: These studies illustrate the effect of uncertainty of apoptosis initiation on the predictive power of PET/SPECT apoptosis imaging agents and suggest that long integration times are required to surmount uncertainty in the time domain of this biological process.