Oxygen supply plays a central role in cancer cell proliferation. While vascular density increases at the early stages of carcinogenesis, mechanical solid stresses developed during growth compress tumor blood vessels and, thus, drastically reduce the supply of oxygen, but also the delivery of drugs at inner tumor regions. Among other effects, hypoxia and reduced drug delivery compromise the efficacy of radiation and chemo/nano therapy, respectively. In the present study, we developed a mathematical model of tumor growth to investigate the interconnections among tumor oxygenation that supports cancer cell proliferation, the heterogeneous accumulation of mechanical stresses owing to tumor growth, the non-uniform compression of intratumoral blood vessels due to the mechanical stresses, and the insufficient delivery of oxygen and therapeutic agents because of vessel compression. We found that the high vascular density and increased cancer cell proliferation often observed in the periphery compared to the interior of a tumor can be attributed to heterogeneous solid stress accumulation. Highly vascularized peripheral regions are also associated with greater oxygenation compared with the compressed, less vascularized inner regions. We also modeled the delivery of drugs of two distinct sizes, namely chemotherapy and nanomedicine. Model predictions suggest that drug delivery is affected negatively by vessel compression independently of the size of the therapeutic agent. Finally, we demonstrated the applicability of our model to actual geometries, employing a breast tumor model derived from MR images.

Biomechanical forces are central in tumor progression and response to treatment. This becomes more important in brain cancers where tumors are surrounded by tissues with different mechanical properties. Existing mathematical models ignore direct mechanical interactions of the tumor with the normal brain. Here, we developed a clinically relevant model, which predicts tumor growth accounting directly for mechanical interactions. A three-dimensional model of the gray and white matter and the cerebrospinal fluid was constructed from magnetic resonance images of a normal brain. Subsequently, a biphasic tissue growth theory for an initial tumor seed was employed, incorporating the effects of radiotherapy. Additionally, three different sets of brain tissue properties taken from the literature were used to investigate their effect on tumor growth. Results show the evolution of solid stress and interstitial fluid pressure within the tumor and the normal brain. Heterogeneous distribution of the solid stress exerted on the tumor resulted in a 35% spatial variation in cancer cell proliferation. Interestingly, the model predicted that distant from the tumor, normal tissues still undergo significant deformations while it was found that intratumoral fluid pressure is elevated. Our predictions relate to clinical symptoms of brain cancers and present useful tools for therapy planning.

Previous studies to simulate brain tumor progression, often investigate either temporal changes in cancer cell density or the overall tissue-level growth of the tumor mass. Here, we developed a computational model to bridge these two approaches. The model incorporates the tumor biomechanical response at the tissue level and accounts for cellular events by modeling cancer cell proliferation, infiltration to surrounding tissues, and invasion to distant locations. Moreover, acquisition of high resolution human data from anatomical magnetic resonance imaging, diffusion tensor imaging and perfusion imaging was employed within the simulations towards a realistic and patient specific model. The model predicted the intratumoral mechanical stresses to range from 20 to 34 kPa, which caused an up to 4.5 mm displacement to the adjacent healthy tissue. Furthermore, the model predicted plausible cancer cell invasion patterns within the brain along the white matter fiber tracts. Finally, by varying the tumor vascular density and its invasive outer ring thickness, our model showed the potential of these parameters for guiding the timing (83–90 days) of cancer cell distant invasion as well as the number (0–2 sites) and location (temportal and/or parietal lobe) of the invasion sites.

The morphometry of the large conducting airways is presumed to have a strong effect on the regional deposition of inhaled aerosol particles. Nevertheless, sex-based differences have not been fully quantified and are still largely ignored in designing inhalation therapies. To this end, we retrospectively analyzed high-resolution computer-tomography scans for 185 individuals (90 women, 95 men) in the age range of 12−89 years to determine airway luminal areas, airway lengths and bifurcation angles. Only subjects free of chronic airway disease were considered. In men, luminal areas of the upper conducting airways were on the average ~ 30-50% larger when compared to those in women, with the largest differences found in the trachea (289.72±54.25mm2 vs. 193.50±42.37mm2 for men/women respectively). The ratio of the largest luminal area in men to the smallest luminal area in women (in any given segment) ranged between 4.5 and 8.6, the largest differences being found in the lobar bronchi. Sex-based differences were minor in the case of bifurcation angles (e.g. average main bifurcation angle: 93.04±9.58o vs. 91.03±9.81o for men/women respectively), but large inter-subject variability was found irrespective of sex (e.g. range of main bifurcation angle: 65.04−122.01o vs. 69.46−113.94o for men/women respectively). Bronchial segments were shorter by ~ 5-20% in women relative to men, the largest differences being located in the upper lobes. False discovery rate (FDR) analysis revealed statistically significant associations among morphometric measures of the right lung in women (but not in men) suggesting two phenotypes among women that we attribute to the smaller female thoracic volume.

BackgroundThe complex cardiac fiber structural organization and spatial arrangement of cardiomyocytes in laminar sheetlets contributes greatly to cardiac functional and contractile ejection patterns. This study presents the first comprehensive, ultra-high resolution, fully quantitative statistical tensor map of the fixed murine heart at isotropic resolution of 43 μm using diffusion tensor (DT) cardiovascular magnetic resonance (CMR).MethodsImaging was completed in approximately 12 hours using a six-directional encoding scheme, in five ex vivo healthy C57BL/6 mouse hearts. The tensor map constructed from this data provides an average description of the murine fiber architecture visualized with fiber tractography, and its population variability, using the latest advances in image tensor analysis and statistics.ResultsResults show that non-normalized cardiac tensor maps are associated with mean fractional anisotropy of 0.25 ± 0.07 and mean diffusivity of 8.9 ± 1.6 × 10−4 mm2/s. Moreover, average mid-ventricular helical angle distributions ranged between –41 ± 3° and +52 ± 5° and were highly correlated with transmural depth, in agreement with prior published results in humans and canines. Calculated variabilities of local myocyte orientations were 2.0° and 1.4°. Laminar sheet orientation variability was found to be less stable at 2.6°. Despite such variations, the murine heart seems to be highly structured, particularly when compared to canines and humans.ConclusionsThis tensor map has the potential to yield an accurate mean representation and identification of common or unique features of the cardiac myocyte architecture, to establish a baseline standard reference of DTI indices, and to improve detection of biomarkers, especially in pathological states or post-transgenetic modifications.