Development of a mathematical model to estimate intra-tumor oxygen concentrations through multi-parametric imaging

Background Tumor hypoxia is involved in every stage of solid tumor development: formation, progression, metastasis, and apoptosis. Two types of hypoxia exist in tumors—chronic hypoxia and acute hypoxia. Recent studies indicate that the regional hypoxia kinetics is closely linked to metastasis and therapeutic responses, but regional hypoxia kinetics is hard to measure. We propose a novel approach to determine the local pO2 by fusing the parameters obtained from in vivo functional imaging through the use of a modified multivariate Krogh model. Methods To test our idea and its potential to translate into an in vivo setting through the use of existing imaging techniques, simulation studies were performed comparing the local partial oxygen pressure (pO2) from the proposed multivariate image fusion model to the referenced pO2 derived by Green’s function, which considers the contribution from every vessel segment of an entire three-dimensional tumor vasculature to profile tumor oxygen with high spatial resolution. Results pO2 derived from our fusion approach were close to the referenced pO2 with regression slope near 1.0 and an r2 higher than 0.8 if the voxel size (or the spatial resolution set by functional imaging modality) was less than 200 μm. The simulation also showed that the metabolic rate, blood perfusion, and hemoglobin concentration were dominant factors in tissue oxygenation. The impact of the measurement error of functional imaging to the pO2 precision and accuracy was simulated. A Gaussian error function with FWHM equal to 20 % of blood perfusion or fractional vascular volume measurement contributed to average 7 % statistical error in pO2. Conclusion The simulation results indicate that the fusion of multiple parametric maps through the biophysically derived mathematical models can monitor the intra-tumor spatial variations of hypoxia in tumors with existing imaging methods, and the potential to further investigate different forms of hypoxia, such as chronic and acute hypoxia, in response to cancer therapies

Validating Hemoglobin Saturation and Dissolved Oxygen in Tumors using the OxyLab Probe and Photoacoustic Imaging

The goal of this experiment is to validate the relationship between hemoglobin saturation (SaO2) and partial pressure of dissolved oxygen (pO2) in breast tumors in mice using photoacoustic computed tomographic (PCT) imaging and OxyLite probe, respectively. In its simplest form, the relationship is described by the dissociation curve, or Hill’s equation, for hemoglobin, and is modeled as a sigmoidal curve that is a function of two parameters – the Hill coefficient, n, and the net association constant of HbO2, K (or pO2 at 50% SaO2). First, a calibration study to validate Hill’s equation in blood was performed by creating a closed circuit phantom to test the SaO2 (co-oximeter) and pO2 (Oxylite probe) relationship (K=23.2mmHg and n=2.26). Next, non-invasive localized measurements of SaO2 in MDA-MD-231 and MCF7 breast tumors using PCT spectroscopic methods were compared to pO2 levels, where pO2 levels were measured in 1mm increments across the central axis of the tumor. The fitted results for MCF7 and MDA-MD-231 were K=17.2mmHg and 20.7mmHg, and n=1.76and 1.63, respectively. The results are consistent with sigmoidal form of Hill’s equation. The lower value of K is indicative of the acidic microenvironment associated with tumors. Ongoing work to correct for photon transport and image artifacts are anticipated to enhance the quality of the results. In conclusion, the results from this study demonstrate photoacoustic can be used to measure tumor oxygenation, and its potential use in investigating the effectiveness of anti-angiogenesis therapy