Are Metastases from Metastases Clinical Relevant? Computer Modelling of Cancer Spread in a Case of Hepatocellular Carcinoma

Background: Metastasis formation remains an enigmatic process and one of the main questions recently asked is whether metastases are able to generate further metastases. Different models have been proposed to answer this question; however, their clinical significance remains unclear. Therefore a computer model was developed that permits comparison of the different models quantitatively with clinical data and that additionally predicts the outcome of treatment interventions. Methods: The computer model is based on discrete events simulation approach. On the basis of a case from an untreated patient with hepatocellular carcinoma and its multiple metastases in the liver, it was evaluated whether metastases are able to metastasise and in particular if late disseminated tumour cells are still capable to form metastases. Additionally, the resection of the primary tumour was simulated. The simulation results were compared with clinical data. Results: The simulation results reveal that the number of metastases varies significantly between scenarios where metastases metastasise and scenarios where they do not. In contrast, the total tumour mass is nearly unaffected by the two different modes of metastasis formation. Furthermore, the results provide evidence that metastasis formation is an early event and that late disseminated tumour cells are still capable of forming metastases. Simulations also allow estimating how the resection of the primary tumour delays the patient’s death. Conclusion: The simulation results indicate that for this particular case of a hepatocellular carcinoma late metastases, i.e.

The influence of P-glycoprotein expression and its inhibitors on the distribution of doxorubicin in breast tumors

Abstract Background Anti-cancer drugs access solid tumors via blood vessels, and must penetrate tumor tissue to reach all cancer cells. Previous studies have demonstrated steep gradients of decreasing doxorubicin fluorescence with increasing distance from blood vessels, such that many tumor cells are not exposed to drug. Studies using multilayered cell cultures show that increased P-glycoprotein (PgP) is associated with better penetration of doxorubicin, while PgP inhibitors decrease drug penetration in tumor tissue. Here we evaluate the effect of PgP expression on doxorubicin distribution in vivo. Methods Mice bearing tumor sublines with either high or low expression of PgP were treated with doxorubicin, with or without pre-treatment with the PgP inhibitors verapamil or PSC 833. The distribution of doxorubicin in relation to tumor blood vessels was quantified using immunofluorescence. Results Our results indicate greater uptake of doxorubicin by cells near blood vessels in wild type as compared to PgP-overexpressing tumors, and pre-treatment with verapamil or PSC 833 increased uptake in PgP-overexpressing tumors. However, there were steeper gradients of decreasing doxorubicin fluorescence in wild-type tumors compared to PgP overexpressing tumors, and treatment of PgP overexpressing tumors with PgP inhibitors led to steeper gradients and greater heterogeneity in the distribution of doxorubicin. Conclusion PgP inhibitors increase uptake of doxorubicin in cells close to blood vessels, have little effect on drug uptake into cells at intermediate distances, and might have a paradoxical effect to decrease doxorubicin uptake into distal cells. This effect probably contributes to the limited success of PgP inhibitors in clinical trials

A tumor cord model for Doxorubicin delivery and dose optimization in solid tumors

<p>Abstract</p> <p>Background</p> <p>Doxorubicin is a common anticancer agent used in the treatment of a number of neoplasms, with the lifetime dose limited due to the potential for cardiotoxocity. This has motivated efforts to develop optimal dosage regimes that maximize anti-tumor activity while minimizing cardiac toxicity, which is correlated with peak plasma concentration. Doxorubicin is characterized by poor penetration from tumoral vessels into the tumor mass, due to the highly irregular tumor vasculature. I model the delivery of a soluble drug from the vasculature to a solid tumor using a tumor cord model and examine the penetration of doxorubicin under different dosage regimes and tumor microenvironments.</p> <p>Methods</p> <p>A coupled ODE-PDE model is employed where drug is transported from the vasculature into a tumor cord domain according to the principle of solute transport. Within the tumor cord, extracellular drug diffuses and saturable pharmacokinetics govern uptake and efflux by cancer cells. Cancer cell death is also determined as a function of peak intracellular drug concentration.</p> <p>Results</p> <p>The model predicts that transport to the tumor cord from the vasculature is dominated by diffusive transport of free drug during the initial plasma drug distribution phase. I characterize the effect of all parameters describing the tumor microenvironment on drug delivery, and large intercapillary distance is predicted to be a major barrier to drug delivery. Comparing continuous drug infusion with bolus injection shows that the optimum infusion time depends upon the drug dose, with bolus injection best for low-dose therapy but short infusions better for high doses. Simulations of multiple treatments suggest that additional treatments have similar efficacy in terms of cell mortality, but drug penetration is limited. Moreover, fractionating a single large dose into several smaller doses slightly improves anti-tumor efficacy.</p> <p>Conclusion</p> <p>Drug infusion time has a significant effect on the spatial profile of cell mortality within tumor cord systems. Therefore, extending infusion times (up to 2 hours) and fractionating large doses are two strategies that may preserve or increase anti-tumor activity and reduce cardiotoxicity by decreasing peak plasma concentration. However, even under optimal conditions, doxorubicin may have limited delivery into advanced solid tumors.</p

A Computational Model for Predicting Nanoparticle Accumulation in Tumor Vasculature

Vascular targeting of malignant tissues with systemically injected nanoparticles (NPs) holds promise in molecular imaging and anti-angiogenic therapies. Here, a computational model is presented to predict the development of tumor neovasculature over time and the specific, vascular accumulation of blood-borne NPs. A multidimensional tumor-growth model is integrated with a mesoscale formulation for the NP adhesion to blood vessel walls. The fraction of injected NPs depositing within the diseased vasculature and their spatial distribution is computed as a function of tumor stage, from 0 to day 24 post-tumor inception. As the malignant mass grows in size, average blood flow and shear rates increase within the tumor neovasculature, reaching values comparable with those measured in healthy, pre-existing vessels already at 10 days. The NP vascular affinity, interpreted as the likelihood for a blood-borne NP to firmly adhere to the vessel walls, is a fundamental parameter in this analysis and depends on NP size and ligand density, and vascular receptor expression. For high vascular affinities, NPs tend to accumulate mostly at the inlet tumor vessels leaving the inner and outer vasculature depleted of NPs. For low vascular affinities, NPs distribute quite uniformly intra-tumorally but exhibit low accumulation doses. It is shown that an optimal vascular affinity can be identified providing the proper balance between accumulation dose and uniform spatial distribution of the NPs. This balance depends on the stage of tumor development (vascularity and endothelial receptor expression) and the NP properties (size, ligand density and ligand-receptor molecular affinity). Also, it is demonstrated that for insufficiently developed vascular networks, NPs are transported preferentially through the healthy, pre-existing vessels, thus bypassing the tumor mass. The computational tool described here can effectively select an optimal NP formulation presenting high accumulation doses and uniform spatial intra-tumor distributions as a function of the development stage of the malignancy

Mathematical oncology:how are the mathematical and physical sciences contributing to the war on breast cancer?

Mathematical modeling has recently been added as a tool in the fight against cancer. The field of mathematical oncology has received great attention and increased enormously, but over-optimistic estimations about its ability have created unrealistic expectations. We present a critical appraisal of the current state of mathematical models of cancer. Although the field is still expanding and useful clinical applications may occur in the future, managing over-expectation requires the proposal of alternative directions for mathematical modeling. Here, we propose two main avenues for this modeling: 1) the identification of the elementary biophysical laws of cancer development, and 2) the development of a multiscale mathematical theory as the framework for models predictive of tumor growth. Finally, we suggest how these new directions could contribute to addressing the current challenges of understanding breast cancer growth and metastasis