Computational modeling of PET tracer distribution in solid tumors integrating microvasculature

A Comparative Analysis of Alpha and Beta Therapy in Prostate Cancer Using a 3D Image-Based Spatiotemporal Model

PURPOSE

In treating prostate cancer, distinguishing alpha and beta therapies is vital for efficient radiopharmaceutical delivery. Our study introduces a 3D image-based spatiotemporal computational model that utilizes MRI-derived images to evaluate the efficacy of 225Ac-PSMA and 177Lu-PSMA therapies. We examine the impact of tumor size, diffusion, interstitial fluid pressure (IFP), and interstitial fluid velocity (IFV) on the absorbed doses.

METHODS

An MRI-based geometric model of the tumor and its surrounding environment is initially developed. Subsequently, COMSOL Multiphysics software is utilized to solve convection-diffusion-reaction equations and conduct numerical analyses of blood pressure distribution. This computational methodology provides valuable insights into interstitial fluid patterns and the spatiotemporal distribution of extracellular and intracellular concentrations of 225Ac-PSMA and 177Lu-PSMA. In addition, our study investigates the impacts of increasing tumor size on absorbed doses and mechanisms involved in radiopharmaceutical transport and delivery.

RESULTS

Larger tumors have diminished absorbed doses, highlighting the need for customized treatments according to tumor size. Diffusion significantly influences the transport and delivery of radiopharmaceuticals. Additionally, alpha therapy was observed to consistently yield higher absorbed doses within the tumor than beta therapy.

CONCLUSIONS

This study reveals the complex interplay between radiopharmaceutical properties, the tumor microenvironment, and treatment outcomes. It highlights the potential of 225Ac-PSMA in prostate cancer treatment, advocating for personalized treatment strategies tailored to the specific characteristics of each patient and their tumor.

Mathematical modeling of18F-Fluoromisonidazole (18F-FMISO) radiopharmaceutical transport in vascularized solid tumors

18F-Fluoromisonidazole (18F-FMISO) is a highly promising positron emission tomography radiopharmaceutical for identifying hypoxic regions in solid tumors. This research employs spatiotemporal multi-scale mathematical modeling to explore how different levels of angiogenesis influence the transport of radiopharmaceuticals within tumors. In this study, two tumor geometries with heterogeneous and uniform distributions of capillary networks were employed to incorporate varying degrees of microvascular density. The synthetic image of the heterogeneous and vascularized tumor was generated by simulating the angiogenesis process. The proposed multi-scale spatiotemporal model accounts for intricate physiological and biochemical factors within the tumor microenvironment, such as the transvascular transport of the radiopharmaceutical agent, its movement into the interstitial space by diffusion and convection mechanisms, and ultimately its uptake by tumor cells. Results showed that both quantitative and semi-quantitative metrics of18F-FMISO uptake differ spatially and temporally at different stages during tumor growth. The presence of a high microvascular density in uniformly vascularized tumor increases cellular uptake, as it allows for more efficient release and rapid distribution of radiopharmaceutical molecules. This results in enhanced uptake compared to the heterogeneous vascularized tumor. In both heterogeneous and uniform distribution of microvessels in tumors, the diffusion transport mechanism has a more pronounced than convection. The findings of this study shed light on the transport phenomena behind18F-FMISO radiopharmaceutical distribution and its delivery in the tumor microenvironment, aiding oncologists in their routine decision-making processes.

Radiopharmaceutical transport in solid tumors via a 3-dimensional image-based spatiotemporal model

Lutetium-177 prostate-specific membrane antigen (177Lu-PSMA)-targeted radiopharmaceutical therapy is a clinically approved treatment for patients with metastatic castration-resistant prostate cancer (mCRPC). Even though common practice reluctantly follows "one size fits all" approach, medical community believes there is significant room for deeper understanding and personalization of radiopharmaceutical therapies. To pursue this aim, we present a 3-dimensional spatiotemporal radiopharmaceutical delivery model based on clinical imaging data to simulate pharmacokinetic of 177Lu-PSMA within the prostate tumors. The model includes interstitial flow, radiopharmaceutical transport in tissues, receptor cycles, association/dissociation with ligands, synthesis of PSMA receptors, receptor recycling, internalization of radiopharmaceuticals, and degradation of receptors and drugs. The model was studied for a range of values for injection amount (100-1000 nmol), receptor density (10-500 nmol•l-1), and recycling rate of receptors (10-4 to 10-1 min-1). Furthermore, injection type, different convection-diffusion-reaction mechanisms, characteristic time scales, and length scales are discussed. The study found that increasing receptor density, ligand amount, and labeled ligands improved radiopharmaceutical uptake in the tumor. A high receptor recycling rate (0.1 min-1) increased radiopharmaceutical concentration by promoting repeated binding to tumor cell receptors. Continuous infusion results in higher radiopharmaceutical concentrations within tumors compared to bolus administration. These insights are crucial for advancing targeted therapy for prostate cancer by understanding the mechanism of radiopharmaceutical distribution in tumors. Furthermore, measures of characteristic length and advection time scale were computed. The presented spatiotemporal tumor transport model can analyze different physiological parameters affecting 177Lu-PSMA delivery.

Prospective Study to Evaluate the Role of Dual Point Contrast-enhanced Magnetic Resonance Imaging in Differentiation of Brain Tumoral from Nontumoral Tissue: A Magnetic Resonance/PET Study

Background and Purpose

Follow-up imaging of gliomas is crucial to look for residual or recurrence and to differentiate them from nontumoral tissue. Positron emission tomography (PET)-magnetic resonance imaging (MRI) is the problem-solving tool in such cases. We investigated the role of dual point contrast (DPC)-enhanced MRI to discriminate tumoral from the nontumoral tissue compared to PET-MRI taken as the gold standard.

Materials and Methods

The institutional ethics committee approved the study, and consent was obtained from all the patients included in the study. We prospectively did immediate and 75-min delayed contrast MRI in glioma cases who came for follow-up as a part of PET-MRI study in our institute. Subtracted images were obtained using immediate and 75-min delayed contrast images. Color-coded subtracted images were compared with PET-MRI images. 75-min delayed contrast MRI and diffusion-weighted imaging (DWI) images with Gray Scale inversion were compared with PET attenuation-corrected images.

Results

We included 23 PET MRI cases done with different radiotracers in our study. Overall, we found PET-DPC correlation in (20/20 ~ 100%) cases of enhancing tumors. In two cases (DOPA and fluorodeoxyglucose), since they were nonenhancing low-grade gliomas and the other one was melanoma with intrinsic T1 hyperintensity and the DPC technique could not be used. DWI-PET correlated in 17/19 (~89.4%) cases, and perfusion-weighted imaging (PWI)-PET dynamic susceptibility contrast (DSC)/ASL correlated in 14/18 (~77.7%) cases after cases with hemorrhage were excluded.

Conclusion

DPC MRI showed a good correlation with PET MRI in discriminating tumoral from the nontumoral tissue. DPC MRI can act as a potential alternative to PET MRI in peripheral hospitals where PET is not available. However, the DPC technique is limited in low-grade nonenhancing gliomas.

Spatiotemporal multi-scale modeling of radiopharmaceutical distributions in vascularized solid tumors

We present comprehensive mathematical modeling of radiopharmaceutical spatiotemporal distributions within vascularized solid tumors. The novelty of the presented model is at mathematical level. From the mathematical viewpoint, we provide a general modeling framework for the process of radiopharmaceutical distribution in the tumor microenvironment to enable an analysis of the effect of various tumor-related parameters on the distribution of different radiopharmaceuticals. We argue that partial differential equations (PDEs), beyond conventional methods, including ODE-based kinetic compartment modeling, can be used to evaluate radiopharmaceutical distribution in both time and space. In addition, we consider the spatially-variable dynamic structure of tumor microvascular networks to simulate blood flow distribution. To examine the robustness of the model, the effects of microvessel density (MVD) and tumor size, as two important factors in tumor prognosis, on the radiopharmaceutical distribution within the tumor are investigated over time (in the present work, we focus on the radiopharmaceutical [¹⁸F]FDG, yet the framework is broadly applicable to radiopharmaceuticals). Results demonstrate that the maximum total uptake of [¹⁸F]FDG at all time frames occurs in the tumor area due to the high capillary permeability and lack of a functional lymphatic system. As the MVD of networks increases, the mean total uptake in the tumor is also enhanced, where the rate of diffusion from vessel to tissue has the highest contribution and the rate of convection transport has the lowest contribution. The results of this study can be used to better investigate various phenomena and bridge a gap among cancer biology, mathematical oncology, medical physics, and radiology.

A spatiotemporal multi-scale computational model for FDG PET imaging at different stages of tumor growth and angiogenesis

A deeper understanding of the tumor microenvironment (TME) and its role in metabolic activity at different stages of vascularized tumors can provide useful insights into cancer progression and better support clinical assessments. In this study, a robust and comprehensive multi-scale computational model for spatiotemporal transport of F-18 fluorodeoxyglucose (FDG) is developed to incorporate important aspects of the TME, spanning subcellular-, cellular-, and tissue-level scales. Our mathematical model includes biophysiological details, such as radiopharmaceutical transport within interstitial space via convection and diffusion mechanisms, radiopharmaceutical exchange between intracellular and extracellular matrices by glucose transporters, cellular uptake of radiopharmaceutical, as well as its intracellular phosphorylation by the enzyme. Further, to examine the effects of tumor size by varying microvascular densities (MVDs) on FDG dynamics, four different capillary networks are generated by angiogenesis modeling. Results demonstrate that as tumor grows, its MVD increases, and hence, the spatiotemporal distribution of total FDG uptake by tumor tissue changes towards a more homogenous distribution. In addition, spatiotemporal distributions in tumor with lower MVD have relatively smaller magnitudes, due to the lower diffusion rate of FDG as well as lower local intravenous FDG release. Since mean standardized uptake value (SUV_mean) differs at various stages of microvascular networks with different tumor sizes, it may be meaningful to normalize the measured values by tumor size and the MVD prior to routine clinical reporting. Overall, the present framework has the potential for more accurate investigation of biological phenomena within TME towards personalized medicine.

Synthetic 18F-FDG PET Image Generation Using a Combination of Biomathematical Modeling and Machine Learning

No previous works have attempted to combine generative adversarial network (GAN) architectures and the biomathematical modeling of positron emission tomography (PET) radiotracer uptake in tumors to generate extra training samples. Here, we developed a novel computational model to produce synthetic 18F-fluorodeoxyglucose (18F-FDG) PET images of solid tumors in different stages of progression and angiogenesis. First, a comprehensive biomathematical model is employed for creating tumor-induced angiogenesis, intravascular and extravascular fluid flow, as well as modeling of the transport phenomena and reaction processes of 18F-FDG in a tumor microenvironment. Then, a deep convolutional GAN (DCGAN) model is employed for producing synthetic PET images using 170 input images of 18F-FDG uptake in each of 10 different tumor microvascular networks. The interstitial fluid parameters and spatiotemporal distribution of 18F-FDG uptake in tumor and healthy tissues have been compared against previously published numerical and experimental studies, indicating the accuracy of the model. The structural similarity index measure (SSIM) and peak signal-to-noise ratio (PSNR) of the generated PET sample and the experimental one are 0.72 and 28.53, respectively. Our results demonstrate that a combination of biomathematical modeling and GAN-based augmentation models provides a robust framework for the non-invasive and accurate generation of synthetic PET images of solid tumors in different stages.

Drug delivery through nanoparticles in solid tumors: a mechanistic understanding

Aim: In this study, the main goal was to apply a multi-scale computational model in evaluating nano-sized drug-delivery systems, following extracellular drug release, into solid tumors in order to predict treatment efficacy. Methods: The impact of several parameters related to tumor (size, shape, vessel-wall pore size, and necrotic core size) and therapeutic agents (size of nanoparticles, binding affinity of drug, drug release rate from nanoparticles) are examined in detail. Results: This study illustrates that achieving a higher treatment efficacy requires smaller nanoparticles (NPs) or a low binding affinity and drug release rate. Long-term analysis finds that a slow release rate in extracellular space does not always improve treatment efficacy compared with a rapid release rate; NP size as well as binding affinity of drug are also highly influential. Conclusions: The presented methodology can be used as a step forward towards optimization of patient-specific nanomedicine plans.