Mathematical modeling of the metastatic process

Mathematical modeling in cancer has been growing in popularity and impact since its inception in 1932. The first theoretical mathematical modeling in cancer research was focused on understanding tumor growth laws and has grown to include the competition between healthy and normal tissue, carcinogenesis, therapy and metastasis. It is the latter topic, metastasis, on which we will focus this short review, specifically discussing various computational and mathematical models of different portions of the metastatic process, including: the emergence of the metastatic phenotype, the timing and size distribution of metastases, the factors that influence the dormancy of micrometastases and patterns of spread from a given primary tumor.Comment: 24 pages, 6 figures, Revie

Normalization of tumour blood vessels improves the delivery of nanomedicines in a size-dependent manner

The blood vessels of cancerous tumours are leaky and poorly organized. This can increase the interstitial fluid pressure inside tumours and reduce blood supply to them, which impairs drug delivery. Anti-angiogenic therapies—which ‘normalize’ the abnormal blood vessels in tumours by making them less leaky—have been shown to improve the delivery and effectiveness of chemotherapeutics with low molecular weights, but it remains unclear whether normalizing tumour vessels can improve the delivery of nanomedicines. Here, we show that repairing the abnormal vessels in mammary tumours, by blocking vascular endothelial growth factor receptor-2, improves the delivery of smaller nanoparticles (diameter, 12 nm) while hindering the delivery of larger nanoparticles (diameter, 125 nm). Using a mathematical model, we show that reducing the sizes of pores in the walls of vessels through normalization decreases the interstitial fluid pressure in tumours, thus allowing small nanoparticles to enter them more rapidly. However, increased steric and hydrodynamic hindrances, also associated with smaller pores, make it more difficult for large nanoparticles to enter tumours. Our results further suggest that smaller (~12 nm) nanomedicines are ideal for cancer therapy due to their superior tumour penetration.ImClone Systems IncorporatedNational Institutes of Health (U.S.) (P01-CA080124)National Institutes of Health (U.S.) (R01-CA126642)National Institutes of Health (U.S.) (R01-CA115767)National Institutes of Health (U.S.) (R01-CA096915)National Institutes of Health (U.S.) (R01-CA085140)National Institutes of Health (U.S.) (R01-CA098706)National Institutes of Health (U.S.) (T32-CA073479)United States. Dept. of Defense (Breast Cancer Research Innovator Award W81XWH-10-1-0016

High Acute Myeloid Leukemia derived VEGFA levels are associated with a specific vascular morphology in the leukemic bone marrow

Acute Myeloid Leukemia (AML) bone marrow biopsies at diagnosis display enhanced angiogenesis and increased VEGFA expression. In a xenograft mouse model it was described that availability of free VEGFA versus bound VEGFA is related to different vascular morphology. In this study we investigate the relationship between vascular morphology within AML bone marrow biopsies and AML derived VEGFA levels. Vessel count and surface area (Chalkley count) were calculated in AML bone marrow biopsies at diagnosis (n = 32), at remission (n = 8) and Normal Bone Marrow (n = 32) using immunohistochemical staining for FVIII, CD31, CTIV, SMA and VEGFA. VEGFA protein levels were measured. High vessel count was associated with an immature vessel status. Combining vessel count and Chalkley count different vessel morphology patterns were quantified within AML bone marrow biopsies. Three different subgroups could be distinguished. The subgroup (37.5% of the samples) exhibiting a high vessel count and vessels with predominantly large lumen (normal Chalkley count) was associated with high secreted VEGFA protein levels. Different vasculature patterns are seen in AML bone marrow biopsies, defined by combining number and size of vessel. These quantified morphology patterns, combined with VEGFA levels, might be of value in the success of VEGF/VEGFR-signaling interference approaches

Computer-assisted and fractal-based morphometric assessment of microvascularity in histological specimens of gliomas

Fractal analysis is widely applied to investigate the vascular system in physiological as well as pathological states. We propose and examine a computer-aided and fractal-based image analysis technique to quantify the microvascularity in histological specimens of WHO grade II and III gliomas. A computer-aided and fractal-based analysis was used to describe the microvessels and to quantify their geometrical complexity in histological specimens collected from 17 patients. The statistical analysis showed that the fractal-based indexes are the most discriminant parameters to describe the microvessels. The computer-aided quantitative analysis also showed that grade III gliomas are generally more vascularized than grade II gliomas. The fractal parameters are reliable quantitative indicators of the neoplastic microvasculature, making them potential surrogate biomarkers. The qualitative evaluation currently performed by the neuropathologist can be combined with the computer-assisted quantitative analysis of the microvascularity to improve the diagnosis and optimize the treatment of patients with brain cancer

Multimodality Imaging of Abnormal Vascular Perfusion and Morphology in Preclinical 9L Gliosarcoma Model

This study demonstrates that a dynamic susceptibility contrast-magnetic resonance imaging (DSC-MRI) perfusion parameter may indicate vascular abnormality in a brain tumor model and reflects an effect of dexamethasone treatment. In addition, X-ray computed tomography (CT) measurements of vascular tortuosity and tissue markers of vascular morphology were performed to investigate the underpinnings of tumor response to dexamethasone.One cohort of Fisher 344 rats (N = 13), inoculated intracerebrally with 9L gliosarcoma cells, was treated with dexamethasone (i.p. 3 mg/kg/day) for five consecutive days, and another cohort (N = 11) was treated with equal volume of saline. Longitudinal DSC-MRI studies were performed at the first (baseline), third and fifth day of treatments. Relative cerebral blood volume (rCBV) was significantly reduced on the third day of dexamethasone treatment (0.65 ± .13) as compared to the fifth day during treatment (1.26 ±.19, p < 0.05). In saline treated rats, relative CBV gradually increased during treatment (0.89 ±.13, 1.00 ± .21, 1.13 ± .23) with no significant difference on the third day of treatment (p>0.05). In separate serial studies, microfocal X-ray CT of ex vivo brain specimens (N = 9) and immunohistochemistry for endothelial cell marker anti-CD31 (N = 8) were performed. Vascular morphology of ex vivo rat brains from micro-CT analysis showed hypervascular characteristics in tumors, and both vessel density (41.32 ± 2.34 branches/mm(3), p<0.001) and vessel tortuosity (p<0.05) were significantly reduced in tumors of rats treated with dexamethasone compared to saline (74.29 ± 3.51 branches/mm(3)). The vascular architecture of rat brain tissue was examined with anti-CD31 antibody, and dexamethasone treated tumor regions showed reduced vessel area (16.45 ± 1.36 µm(2)) as compared to saline treated tumor regions (30.83 ± 4.31 µm(2), p<0.001) and non-tumor regions (22.80 ± 1.11 µm(2), p<0.01).Increased vascular density and tortuosity are culprit to abnormal perfusion, which is transiently reduced during dexamethasone treatment

Self-organization of developing embryo using scale-invariant approach

<p>Abstract</p> <p>Background</p> <p>Self-organization is a fundamental feature of living organisms at all hierarchical levels from molecule to organ. It has also been documented in developing embryos.</p> <p>Methods</p> <p>In this study, a scale-invariant power law (SIPL) method has been used to study self-organization in developing embryos. The SIPL coefficient was calculated using a centro-axial skew symmetrical matrix (CSSM) generated by entering the components of the Cartesian coordinates; for each component, one CSSM was generated. A basic square matrix (BSM) was constructed and the determinant was calculated in order to estimate the SIPL coefficient. This was applied to developing <it>C. elegans </it>during early stages of embryogenesis. The power law property of the method was evaluated using the straight line and Koch curve and the results were consistent with fractal dimensions (fd). Diffusion-limited aggregation (DLA) was used to validate the SIPL method.</p> <p>Results and conclusion</p> <p>The fractal dimensions of both the straight line and Koch curve showed consistency with the SIPL coefficients, which indicated the power law behavior of the SIPL method. The results showed that the ABp sublineage had a higher SIPL coefficient than EMS, indicating that ABp is more organized than EMS. The fd determined using DLA was higher in ABp than in EMS and its value was consistent with type 1 cluster formation, while that in EMS was consistent with type 2.</p

A Systems Approach for Tumor Pharmacokinetics

Recent advances in genome inspired target discovery, small molecule screens, development of biological and nanotechnology have led to the introduction of a myriad of new differently sized agents into the clinic. The differences in small and large molecule delivery are becoming increasingly important in combination therapies as well as the use of drugs that modify the physiology of tumors such as anti-angiogenic treatment. The complexity of targeting has led to the development of mathematical models to facilitate understanding, but unfortunately, these studies are often only applicable to a particular molecule, making pharmacokinetic comparisons difficult. Here we develop and describe a framework for categorizing primary pharmacokinetics of drugs in tumors. For modeling purposes, we define drugs not by their mechanism of action but rather their rate-limiting step of delivery. Our simulations account for variations in perfusion, vascularization, interstitial transport, and non-linear local binding and metabolism. Based on a comparison of the fundamental rates determining uptake, drugs were classified into four categories depending on whether uptake is limited by blood flow, extravasation, interstitial diffusion, or local binding and metabolism. Simulations comparing small molecule versus macromolecular drugs show a sharp difference in distribution, which has implications for multi-drug therapies. The tissue-level distribution differs widely in tumors for small molecules versus macromolecular biologic drugs, and this should be considered in the design of agents and treatments. An example using antibodies in mouse xenografts illustrates the different in vivo behavior. This type of transport analysis can be used to aid in model development, experimental data analysis, and imaging and therapeutic agent design.National Institutes of Health (U.S.) (grant T32 CA079443

A Dialogue between the Hypoxia-Inducible Factor and the Tumor Microenvironment

The hypoxia-inducible factor is the key protein responsible for the cellular adaptation to low oxygen tension. This transcription factor becomes activated as a result of a drop in the partial pressure of oxygen, to hypoxic levels below 5% oxygen, and targets a panel of genes involved in maintenance of oxygen homeostasis. Hypoxia is a common characteristic of the microenvironment of solid tumors and, through activation of the hypoxia-inducible factor, is at the center of the growth dynamics of tumor cells. Not only does the microenvironment impact on the hypoxia-inducible factor but this factor impacts on microenvironmental features, such as pH, nutrient availability, metabolism and the extracellular matrix. In this review we discuss the influence the tumor environment has on the hypoxia-inducible factor and outline the role of this factor as a modulator of the microenvironment and as a powerful actor in tumor remodeling. From a fundamental research point of view the hypoxia-inducible factor is at the center of a signaling pathway that must be deciphered to fully understand the dynamics of the tumor microenvironment. From a translational and pharmacological research point of view the hypoxia-inducible factor and its induced downstream gene products may provide information on patient prognosis and offer promising targets that open perspectives for novel “anti-microenvironment” directed therapies

Consensus guidelines for the use and interpretation of angiogenesis assays

The formation of new blood vessels, or angiogenesis, is a complex process that plays important roles in growth and development, tissue and organ regeneration, as well as numerous pathological conditions. Angiogenesis undergoes multiple discrete steps that can be individually evaluated and quantified by a large number of bioassays. These independent assessments hold advantages but also have limitations. This article describes in vivo, ex vivo, and in vitro bioassays that are available for the evaluation of angiogenesis and highlights critical aspects that are relevant for their execution and proper interpretation. As such, this collaborative work is the first edition of consensus guidelines on angiogenesis bioassays to serve for current and future reference