Michael Welter

Interstitial Fluid Flow and Drug Delivery in Vascularized Tumors: A Computational Model

Interstitial fluid is a solution that bathes and surrounds the human cells and provides them with nutrients and a way of waste removal. It is generally believed that elevated tumor interstitial fluid pressure (IFP) is partly responsible for the poor penetration and distribution of therapeutic agents in solid tumors, but the complex interplay of extravasation, permeabilities, vascular heterogeneities and diffusive and convective drug transport remains poorly understood. Here we consider–with the help of a theoretical model–the tumor IFP, interstitial fluid flow (IFF) and its impact upon drug delivery within tumor depending on biophysical determinants such as vessel network morphology, permeabilities and diffusive vs. convective transport. We developed a vascular tumor growth model, including vessel co-option, regression, and angiogenesis, that we extend here by the interstitium (represented by a porous medium obeying Darcys law) and sources (vessels) and sinks (lymphatics) for IFF. With it we compute the spatial variation of the IFP and IFF and determine its correlation with the vascular network morphology and physiological parameters like vessel wall permeability, tissue conductivity, distribution of lymphatics etc. We find that an increased vascular wall conductivity together with a reduction of lymph function leads to increased tumor IFP, but also that the latter does not necessarily imply a decreased extravasation rate: Generally the IF flow rate is positively correlated with the various conductivities in the system. The IFF field is then used to determine the drug distribution after an injection via a convection diffusion reaction equation for intra- and extracellular concentrations with parameters guided by experimental data for the drug Doxorubicin. We observe that the interplay of convective and diffusive drug transport can lead to quite unexpected effects in the presence of a heterogeneous, compartmentalized vasculature. Finally we discuss various strategies to increase drug exposure time of tumor cells.

Physical determinants of vascular network remodeling during tumor growth

Abstract.The process in which a growing tumor transforms a hierarchically organized arterio-venous blood vessel network into a tumor specific vasculature is analyzed with a theoretical model. The physical determinants of this remodeling involve the morphological and hydrodynamic properties of the initial network, generation of new vessels (sprouting angiogenesis), vessel dilation (circumferential growth), vessel regression, tumor cell proliferation and death, and the interdependence of these processes via spatio-temporal changes of blood flow parameters, oxygen/nutrient supply and growth factor concentration fields. The emerging tumor vasculature is non-hierarchical, compartmentalized into well-characterized zones, displays a complex geometry with necrotic zones and “hot spots” of increased vascular density and blood flow of varying size, and transports drug injections efficiently. Implications for current theoretical views on tumor-induced angiogenesis are discussed.

Integrative models of vascular remodeling during tumor growth

Malignant solid tumors recruit the blood vessel network of the host tissue for nutrient supply, continuous growth, and gain of metastatic potential. Angiogenesis (the formation of new blood vessels), vessel cooption (the integration of existing blood vessels into the tumor vasculature), and vessel regression remodel the healthy vascular network into a tumor‐specific vasculature that is in many respects different from the hierarchically organized arterio‐venous blood vessel network of the host tissues. Integrative models based on detailed experimental data and physical laws implement in silico the complex interplay of molecular pathways, cell proliferation, migration, and death, tissue microenvironment, mechanical and hydrodynamic forces, and the fine structure of the host tissue vasculature. With the help of computer simulations high‐precision information about blood flow patterns, interstitial fluid flow, drug distribution, oxygen and nutrient distribution can be obtained and a plethora of therapeutic protocols can be tested before clinical trials. In this review, we give an overview over the current status of integrative models describing tumor growth, vascular remodeling, blood and interstitial fluid flow, drug delivery, and concomitant transformations of the microenvironment. WIREs Syst Biol Med 2015, 7:113–129. doi: 10.1002/wsbm.1295

Computational Model for Tumor Oxygenation Applied to Clinical Data on Breast Tumor Hemoglobin Concentrations Suggests Vascular Dilatation and Compression.

We present a computational model for trans-vascular oxygen transport in synthetic tumor and host tissue blood vessel networks, aiming at qualitatively explaining published data of optical mammography, which were obtained from 87 breast cancer patients. The data generally show average hemoglobin concentration to be higher in tumors versus host tissue whereas average oxy-to total hemoglobin concentration (vascular segment RBC-volume-weighted blood oxygenation) can be above or below normal. Starting from a synthetic arterio-venous initial network the tumor vasculature was generated by processes involving cooption, angiogenesis, and vessel regression. Calculations of spatially resolved blood flow, hematocrit, oxy- and total hemoglobin concentrations, blood and tissue oxygenation were carried out for ninety tumor and associated normal vessel networks starting from various assumed geometries of feeding arteries and draining veins. Spatial heterogeneity in the extra-vascular partial oxygen pressure distribution can be related to various tumor compartments characterized by varying capillary densities and blood flow characteristics. The reported higher average hemoglobin concentration of tumors is explained by growth and dilatation of tumor blood vessels. Even assuming sixfold metabolic rate of oxygen consumption in tumorous versus host tissue, the predicted oxygen hemoglobin concentrations are above normal. Such tumors are likely associated with high tumor blood flow caused by high-caliber blood vessels crossing the tumor volume and hence oxygen supply exceeding oxygen demand. Tumor oxy- to total hemoglobin concentration below normal could only be achieved by reducing tumor vessel radii during growth by a randomly selected factor, simulating compression caused by intra-tumoral solid stress due to proliferation of cells and extracellular matrix. Since compression of blood vessels will impede chemotherapy we conclude that tumors with oxy- to total hemoglobin concentration below normal are less likely to respond to chemotherapy. Such behavior was recently reported for neo-adjuvant chemotherapy of locally advanced breast tumors.

Computer Simulations of the Tumor Vasculature: Applications to Interstitial Fluid Flow, Drug Delivery, and Oxygen Supply

Tumor vasculature, the blood vessel network supplying a growing tumor with nutrients such as oxygen or glucose, is in many respects different from the hierarchically organized arterio-venous blood vessel network in normal tissues. Angiogenesis (the formation of new blood vessels), vessel cooption (the integration of existing blood vessels into the tumor vasculature), and vessel regression remodel the healthy vascular network into a tumor-specific vasculature. Integrative models, based on detailed experimental data and physical laws, implement, in silico, the complex interplay of molecular pathways, cell proliferation, migration, and death, tissue microenvironment, mechanical and hydrodynamic forces, and the fine structure of the host tissue vasculature. With the help of computer simulations high-precision information about blood flow patterns, interstitial fluid flow, drug distribution, oxygen and nutrient distribution can be obtained and a plethora of therapeutic protocols can be tested before clinical trials. This chapter provides an overview over the current status of computer simulations of vascular remodeling during tumor growth including interstitial fluid flow, drug delivery, and oxygen supply within the tumor. The model predictions are compared with experimental and clinical data and a number of longstanding physiological paradigms about tumor vasculature and intratumoral solute transport are critically scrutinized.

Adaption of artificial microvascular networks

Abstract Blood vessel networks of living organisms continuously adapt their structure under the influence of hemodynamic and metabolic stimuli. For a fixed vessel arrangement, blood flow characteristics still depend crucially on the morphology of each vessel. Vessel diameters adapt dynamically according to internal and external stimuli: endothelial wall shear stress, intravascular pressure, flow-dependent metabolic stimuli, and electrical stimuli conducted from distal to proximal segments along vascular walls. Pries et al. formulated a theoretical model involving these four local stimuli to simulate long-term changes of vessel diameters during structural adaption of microvascular networks. Here we apply this vessel adaptation algorithm to synthetic arteriovenous blood vessel networks generated by our simulation framework “Tumor-code”. We fixed the free model parameters by an optimization method combined with the requirement of homogeneous flow in the capillary bed. We find that the local blood volume, surface to volume ratio and branching ratio differs from networks with radii fulfilling Murray’s law exactly to networks with radii obtained by the adaptation algorithm although their relation is close to Murray’s law. In addition, we find that the application of the vessel adaptation algorithm to synthetic tumor vascularture does not lead to a stable radii distributions due to emerging short cuts between arteries and veins.We explored the application of the adaption algorithm introduced by Secomb et. al. to artificial blood vessel networks and find that the resulting networks to not obey Murray’s law. The reported analysis and visual examples document the contrast of the 2 types of networks. We conjecture that an interrupt of a established signaling cascade could be a hallmark of solid vascular tumors.

Tumorcode: A framework to simulate vascularized tumors

During the past years our group published several articles using computer simulations to address the complex interaction of tumors and the vasculature as underlying transport network. Advances in imaging and lab techniques pushed in vitro research of tumor spheroids forward and animal models as well as clinical studies provided more insights to single processes taking part in tumor growth, however, an overall picture is still missing. Computer simulations are a non-invasive option to cumulate current knowledge and form a quasi in vivo system. In our software, several known models were assembled into a multi-scale approach which allows to study length scales relevant for clinical applications. We release our code to the public domain, together with a detailed description of the implementation and several examples, with the hope of usage and futher development by the community. A justification for the included algorithms and the biological models was obtained in previous publications, here we summarize the technical aspects following the workflow of a typical simulation procedure.

Blood Vessel Network Remodeling During Tumor Growth

With the help of a theoretical model the process in which a growing tumor transforms a hierarchically organized arterio-venous blood vessel network into a tumor specific vasculature is analyzed. The determinants of this remodeling process involve the morphological and hydrodynamic properties of the initial network, generation of new vessels (sprouting angiogenesis), vessel dilation (circumferential growth), blood flow correlated vessel regression, tumor cell proliferation and death, and the interdependence of these processes via spatio-temporal changes of blood flow parameters, oxygen/nutrient supply and growth factor concentration fields. The emerging tumor vasculature is nonhierarchical, compartmentalized into well characterized zones, displays a complex geometry with necrotic zones and “hot spots” of increased vascular density and blood flow of varying size, and transports drug injections efficiently. Implications for current theoretical views on tumor-induced angiogenesis are discussed.