Spatiotemporal distribution modeling of PET tracer uptake in solid tumors

Abstract

The proposed framework of spatiotemporal modeling for PET tracers can be utilized to comprehensively assess the impact of various parameters on the spatiotemporal distribution of PET tracers.

Image-based spatio-temporal model of drug delivery in a heterogeneous vasculature of a solid tumor — Computational approach

“…Soltani andChen (2011, 2013) improved the mathematical model and applied it to investigate two new parameters of spherical tumors: critical radius of the tumor and critical radius of the necrotic zone. Also, to study the shape and size effects of tumors on drug delivery, they applied the model to different geometries (Soltani, 2012;Soltani and Chen, 2012;Soltani et al, 2014). El-Kareh and Secomb (2005) and Eikenberry ( 2009) used a mathematical model tool to determine the drug concentration respectively in the extracellular and intracellular spaces of solid tumors.…”

“…El-Kareh and Secomb (2005) and Eikenberry ( 2009) used a mathematical model tool to determine the drug concentration respectively in the extracellular and intracellular spaces of solid tumors. There exist many new efforts in mathematical modeling and simulation of drug delivery to solid tumors, in the literature (Pishko et al, 2011;Sefidgar et al, 2014a, 2014b, Asgari et al, 2018Soltani et al, 2017;Chou et al, 2017;Zhan and Xu, 2013;Zhan et al, 2014Zhan et al, , 2017Stylianopoulos et al, 2015;Mpekris et al, 2017;Steuperaert et al, 2017;Shamsi et al, 2018) to study the effect of different factors and parameters including IFP, IFV, capillary network, and concentration.…”

“…Recently, Stephanou et al (2005), J. Wu et al (2008), Welter and Rieger (2013), M. Wu et al (2014), Sefidgar et al (2015), and Soltani et al (2017) simulated the drug delivery to solid tumors in the presence of heterogeneous microvasculature but their mathematical approach is not absolutely accurate and real. These models are helpful for investigating the interaction of various physiological phenomena within the tumor during drug transport; however, they cannot accurately predict the tumor behavior in a specific patient, as the tumor microenvironment changes widely from one case to another.…”

“…Then, they pass through the wall of the tumor vessel and after that, they travel the remaining distance from the vessel wall to the cancer cells. Free molecules of doxorubicin in tumor interstitial space can bind to receptors of the cell surface, unbind or get internalized (Soltani et al, 2017;Stylianopoulos et al, 2015). Fig.…”

Numerical modeling of high-intensity focused ultrasound-mediated intraperitoneal delivery of thermosensitive liposomal doxorubicin for cancer chemotherapy

“…Previous studies have detailed the derivation of these equations (Baxter & Jain, 1991; Stylianopoulos & Jain, 2013; Soltani et al., 2014; Sefidgar et al., 2015; Kashkooli et al., 2019). The general mass transfer model is based on compartment models, which are widely used to describe the drug transfer (Soltani et al., 2017). In compartment models, it is assumed that the concentration in each compartment is distributed independently while in the CDR equations, spatial variations of the concentration are also considered by taking convection and diffusion mechanisms into account.…”