A 3D Hybrid Model for Tissue Growth: The Interplay between Cell Population and Mass Transport Dynamics

To provide theoretical guidance for the design and in vitro cultivation of bioartificial tissues, we have developed a multiscale computational model that can describe the complex interplay between cell population and mass transport dynamics that governs the growth of tissues in three-dimensional scaffolds. The model has three components: a transient partial differential equation for the simultaneous diffusion and consumption of a limiting nutrient; a cellular automaton describing cell migration, proliferation, and collision; and equations that quantify how the varying nutrient concentration modulates cell division and migration. The hybrid discrete-continuous model was parallelized and solved on a distributed-memory multicomputer to study how transport limitations affect tissue regeneration rates under conditions encountered in typical bioreactors. Simulation results show that the severity of transport limitations can be estimated by the magnitude of two dimensionless groups: the Thiele modulus and the Biot number. Key parameters including the initial seeding mode, cell migration speed, and the hydrodynamic conditions in the bioreactor are shown to affect not only the overall rate, but also the pattern of tissue growth. This study lays the groundwork for more comprehensive models that can handle mixed cell cultures, multiple nutrients and growth factors, and other cellular processes, such as cell death.     

Fluorescence lifetime-based pH mapping of tumors in vivo using genetically encoded sensor SypHerRed

Changes in intracellular pH (pHi) reflect metabolic states of cancer cells during tumor growth and dissemination. Therefore, monitoring of pHi is essential for understanding the metabolic mechanisms that support cancer progression. Genetically encoded fluorescent pH sensors have become irreplaceable tools for real-time tracking pH in particular subcellular compartments of living cells. However, ratiometric readout of most of the pH probes is poorly suitable to measure pH in thick samples ex vivo or tissues in vivo including solid tumors. Fluorescence lifetime imaging (FLIM) is a promising alternative to the conventional fluorescent microscopy. Here, we present a quantitative approach to map pHi in cancer cells and tumors in vivo, relying on fluorescence lifetime of a genetically encoded pH sensor SypHerRed. We demonstrate the utility of SypHerRed in visualizing pHi in cancer cell culture and in mouse tumor xenografts using fluorescence lifetime imaging microscopy and macroscopy. For the first time to our knowledge, the absolute pHi value is obtained for tumors in vivo by an optical technique. In addition, we demonstrate the possibility of simultaneous detection of pHi and endogenous fluorescence of metabolic cofactor NADH, which provides a complementary insight into metabolic aspects of cancer. Fluorescence lifetime-based readout and red-shifted spectra make pH sensor SypHerRed a promising instrument for multiparameter in vivo imaging applications.     

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 Darcy''s 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.     

A Continuum Mechanics Model of Enzyme-Based Tissue Degradation in Cancer Therapies

We propose a mathematical model to describe enzyme-based tissue degradation in cancer therapies. The proposed model combines the poroelastic theory of mixtures with the transport of enzymes or drugs in the extracellular space. The effect of the matrix-degrading enzymes on the tissue composition and its mechanical response are accounted for. Numerical simulations in 1D, 2D and axisymmetric (3D) configurations show how an injection of matrix-degrading enzymes alters the porosity of a biological tissue. We eventually exhibit numerically the main consequences of a matrix-degrading enzyme pretreatment in the framework of chemotherapy: the removal of the diffusive hindrance to the penetration of therapeutic molecules in tumors and the reduction of interstitial fluid pressure which improves transcapillary transport. Both effects are consistent with previous biological observations.     

Effect of tumor shape,size, and tissue transport properties on drug delivery to solid tumors

Background

The computational methods provide condition for investigation related to the process of drug delivery, such as convection and diffusion of drug in extracellular matrices, drug extravasation from microvessels or to lymphatic vessels. The information of this process clarifies the mechanisms of drug delivery from the injection site to absorption by a solid tumor. In this study, an advanced numerical method is used to solve fluid flow and solute transport equations simultaneously to investigate the effect of tumor shape and size on drug delivery to solid tumor.

Methods

The advanced mathematical model used in our previous work is further developed by adding solute transport equation to the governing equations. After applying appropriate boundary and initial conditions on tumor and surrounding tissue geometry, the element-based finite volume method is used for solving governing equations of drug delivery in solid tumor. Also, the effects of size and shape of tumor and some of tissue transport parameters such as effective pressure and hydraulic conductivity on interstitial fluid flow and drug delivery are investigated.

Results

Sensitivity analysis shows that drug delivery in prolate shape is significantly better than other tumor shapes. Considering size effect, increasing tumor size decreases drug concentration in interstitial fluid. This study shows that dependency of drug concentration in interstitial fluid to osmotic and intravascular pressure is negligible.

Conclusions

This study shows that among diffusion and convection mechanisms of drug transport, diffusion is dominant in most different tumor shapes and sizes. In tumors in which the convection has considerable effect, the drug concentration is larger than that of other tumors at the same time post injection.

     

Diffusion and convection in collagen gels: implications for transport in the tumor interstitium

Diffusion coefficients of tracer molecules in collagen type I gels prepared from 0-4.5% w/v solutions were measured by fluorescence recovery after photobleaching. When adjusted to account for in vivo tortuosity, diffusion coefficients in gels matched previous measurements in four human tumor xenografts with equivalent collagen concentrations. In contrast, hyaluronan solutions hindered diffusion to a lesser extent when prepared at concentrations equivalent to those reported in these tumors. Collagen permeability, determined from flow through gels under hydrostatic pressure, was compared with predictions obtained from application of the Brinkman effective medium model to diffusion data. Permeability predictions matched experimental results at low concentrations, but underestimated measured values at high concentrations. Permeability measurements in gels did not match previous measurements in tumors. Visualization of gels by transmission electron microscopy and light microscopy revealed networks of long collagen fibers at lower concentrations along with shorter fibers at high concentrations. Negligible assembly was detected in collagen solutions pregelation. However, diffusion was similarly hindered in pre and postgelation samples. Comparison of diffusion and convection data in these gels and tumors suggests that collagen may obstruct diffusion more than convection in tumors. These findings have significant implications for drug delivery in tumors and for tissue engineering applications.     

A multiscale modeling study of particle size effects on the tissue penetration efficacy of drug-delivery nanoparticles

Background

Particle size is a key parameter for drug-delivery nanoparticle design. It is believed that the size of a nanoparticle may have important effects on its ability to overcome the transport barriers in biological tissues. Nonetheless, such effects remain poorly understood. Using a multiscale model, this work investigates particle size effects on the tissue distribution and penetration efficacy of drug-delivery nanoparticles.

Results

We have developed a multiscale spatiotemporal model of nanoparticle transport in biological tissues. The model implements a time-adaptive Brownian Dynamics algorithm that links microscale particle-cell interactions and adhesion dynamics to tissue-scale particle dispersion and penetration. The model accounts for the advection, diffusion, and cellular uptakes of particles. Using the model, we have analyzed how particle size affects the intra-tissue dispersion and penetration of drug delivery nanoparticles. We focused on two published experimental works that investigated particle size effects in in vitro and in vivo tissue conditions. By analyzing experimental data reported in these two studies, we show that particle size effects may appear pronounced in an in vitro cell-free tissue system, such as collagen matrix. In an in vivo tissue system, the effects of particle size could be relatively modest. We provide a detailed analysis on how particle-cell interactions may determine distribution and penetration of nanoparticles in a biological tissue.

Conclusion

Our work suggests that the size of a nanoparticle may play a less significant role in its ability to overcome the intra-tissue transport barriers. We show that experiments involving cell-free tissue systems may yield misleading observations of particle size effects due to the absence of advective transport and particle-cell interactions.

     

A Mathematical Model of the Enhanced Permeability and Retention Effect for Liposome Transport in Solid Tumors

The discovery of the enhanced permeability and retention (EPR) effect has resulted in the development of nanomedicines, including liposome-based formulations of drugs, as cancer therapies. The use of liposomes has resulted in substantial increases in accumulation of drugs in solid tumors; yet, significant improvements in therapeutic efficacy have yet to be achieved. Imaging of the tumor accumulation of liposomes has revealed that this poor or variable performance is in part due to heterogeneous inter-subject and intra-tumoral liposome accumulation, which occurs as a result of an abnormal transport microenvironment. A mathematical model that relates liposome accumulation to the underlying transport properties in solid tumors could provide insight into inter and intra-tumoral variations in the EPR effect. In this paper, we present a theoretical framework to describe liposome transport in solid tumors. The mathematical model is based on biophysical transport equations that describe pressure driven fluid flow across blood vessels and through the tumor interstitium. The model was validated by direct comparison with computed tomography measurements of tumor accumulation of liposomes in three preclinical tumor models. The mathematical model was fit to liposome accumulation curves producing predictions of transport parameters that reflect the tumor microenvironment. Notably, all fits had a high coefficient of determination and predictions of interstitial fluid pressure agreed with previously published independent measurements made in the same tumor type. Furthermore, it was demonstrated that the model attributed inter-subject heterogeneity in liposome accumulation to variations in peak interstitial fluid pressure. These findings highlight the relationship between transvascular and interstitial flow dynamics and variations in the EPR effect. In conclusion, we have presented a theoretical framework that predicts inter-subject and intra-tumoral variations in the EPR effect based on fundamental properties of the tumor microenvironment and forms the basis for transport modeling of liposome drug delivery.     

Modeling of neutral solute transport in a dynamically loaded porous permeable gel: implications for articular cartilage biosynthesis and tissue engineering

A primary mechanism of solute transport in articular cartilage is believed to occur through passive diffusion across the articular surface, but cyclical loading has been shown experimentally to enhance the transport of large solutes. The objective of this study is to examine the effect of dynamic loading within a theoretical context, and to investigate the circumstances under which convective transport induced by dynamic loading might supplement diffusive transport. The theory of incompressible mixtures was used to model the tissue (gel) as a mixture of a gel solid matrix (extracellular matrix/scaffold), and two fluid phases (interstitial fluid solvent and neutral solute), to solve the problem of solute transport through the lateral surface of a cylindrical sample loaded dynamically in unconfined compression with frictionless impermeable platens in a bathing solution containing an excess of solute. The resulting equations are governed by nondimensional parameters, the most significant of which are the ratio of the diffusive velocity of the interstitial fluid in the gel to the solute diffusivity in the gel (Rg), the ratio of actual to ideal solute diffusive velocities inside the gel (Rd), the ratio of loading frequency to the characteristic frequency of the gel (f), and the compressive strain amplitude (epsilon 0). Results show that when Rg > 1, Rd < 1, and f > 1, dynamic loading can significantly enhance solute transport into the gel, and that this effect is enhanced as epsilon 0 increases. Based on representative material properties of cartilage and agarose gels, and diffusivities of various solutes in these gels, it is found that the ranges Rg > 1, Rd < 1, correspond to large solutes, whereas f > 1 is in the range of physiological loading frequencies. These theoretical predictions are thus in agreement with the limited experimental data available in the literature. The results of this study apply to any porous hydrated tissue or material, and it is therefore plausible to hypothesize that dynamic loading may serve to enhance solute transport in a variety of physiological processes.     

In vivo mimicking model for solid tumor towards hydromechanics of tissue deformation and creation of necrosis

The present work addresses transvascular and interstitial fluid transport inside a solid tumor surrounded by normal tissue (close to an in vivo mimicking setup). In general, biological tissues behave like a soft porous material and show mechanical behavior towards the fluid motion through the interstitial space. In general, forces like viscous drag that are associated with the fluid flow may compress the tissue material. On the macroscopic level, we try to model the motion of fluids and macromolecules through the interstitial space of solid tumor and the normal tissue layer. The transvascular fluid transport is assumed to be governed by modified Starling’s law. The poroelastohydrodynamics (interstitial hydrodynamics and the deformation of tissue material) inside the tumor and normal tissue regions is modeled using linearized biphasic mixture theory. Correspondingly, the velocity distribution of fluid is coupled to the displacement field of the solid phase (mainly cellular phase and extracellular matrix) in both the normal and tumor tissue regions. The corresponding velocity field is used within the transport reaction equation for fluids and macromolecules through interstitial space to get the overall solute (e.g., nutrients, drug, and other macromolecules) distribution. This study justifies that the presence of the normal tissue layer plays a significant role in delaying/assisting necrosis inside the tumor tissue. It is observed that the exchange process of fluids and macromolecules across the interface of the tumor and normal tissue affects the effectiveness factor corresponding to the tumor tissue.     

An Intermittent Model for Intracellular Motions of Gold Nanostars by k-Space Scattering Image Correlation

Anisotropic metallic nanoparticles have been devised as powerful potential tools for in vivo imaging, photothermal therapy, and drug delivery thanks to plasmon-enhanced absorption and scattering cross sections, ease in synthesis and functionalization, and controlled cytotoxicity. The rational design of all these applications requires the characterization of the nanoparticles intracellular trafficking pathways. In this work, we exploit live-cell time-lapse confocal reflectance microscopy and image correlation in both direct and reciprocal space to investigate the intracellular transport of branched gold nanostars (GNSs). Different transport mechanisms, spanning from pure Brownian diffusion to (sub-)ballistic superdiffusion, are revealed by temporal and spatio-temporal image correlation spectroscopy on the tens-of-seconds timescale. According to these findings, combined with numerical simulations and with a Bayesian (hidden Markov model-based) analysis of single particle tracking data, we ascribe the superdiffusive, subballistic behavior characterizing the GNSs dynamics to a two-state switching between Brownian diffusion in the cytoplasm and molecular motor-mediated active transport. For the investigation of intermittent-type transport phenomena, we derive an analytical theoretical framework for Fourier-space image correlation spectroscopy (kICS). At first, we evaluate the influence of all the dynamic and kinetic parameters (the diffusion coefficient, the drift velocity, and the transition rates between the diffusive and the active transport regimes) on simulated kICS correlation functions. Then we outline a protocol for data analysis and employ it to derive whole-cell maps for each parameter underlying the GNSs intracellular dynamics. Capable of identifying even simpler transport phenomena, whether purely diffusive or ballistic, our intermittent kICS approach allows an exhaustive investigation of the dynamics of GNSs and biological macromolecules.     

Numerical Modeling of Interstitial Fluid Flow Coupled with Blood Flow through a Remodeled Solid Tumor Microvascular Network

Modeling of interstitial fluid flow involves processes such as fluid diffusion, convective transport in extracellular matrix, and extravasation from blood vessels. To date, majority of microvascular flow modeling has been done at different levels and scales mostly on simple tumor shapes with their capillaries. However, with our proposed numerical model, more complex and realistic tumor shapes and capillary networks can be studied. Both blood flow through a capillary network, which is induced by a solid tumor, and fluid flow in tumor’s surrounding tissue are formulated. First, governing equations of angiogenesis are implemented to specify the different domains for the network and interstitium. Then, governing equations for flow modeling are introduced for different domains. The conservation laws for mass and momentum (including continuity equation, Darcy’s law for tissue, and simplified Navier–Stokes equation for blood flow through capillaries) are used for simulating interstitial and intravascular flows and Starling’s law is used for closing this system of equations and coupling the intravascular and extravascular flows. This is the first study of flow modeling in solid tumors to naturalistically couple intravascular and extravascular flow through a network. This network is generated by sprouting angiogenesis and consisting of one parent vessel connected to the network while taking into account the non-continuous behavior of blood, adaptability of capillary diameter to hemodynamics and metabolic stimuli, non-Newtonian blood flow, and phase separation of blood flow in capillary bifurcation. The incorporation of the outlined components beyond the previous models provides a more realistic prediction of interstitial fluid flow pattern in solid tumors and surrounding tissues. Results predict higher interstitial pressure, almost two times, for realistic model compared to the simplified model.     

Targeting nucleolin to obstruct vasculature feeding with an intelligent DNA nanorobot

A prototype of DNA nanorobot with the ability to transport molecular payloads was designed to target cancer cells in tissue culture. Moreover, a further step was taken to succeed in the first in vivo application of the DNA nanorobot for cancer therapy. The robot was constructed using aptamer and DNA origami to fold a 90‐nm tubular device to carry the blood coagulation protease thrombin inside, shielded from circulating platelets and plasma fibrinogen. The recognition and binding of the aptamer to its tumour‐specific target molecule triggered the robot unfolding to expose thrombin to the blood, which in turn activated coagulation at the local tumour site, resulting in tumour necrosis and inhibition of tumour growth. Since all solid‐tumour feeding vessels are virtually the same, this strategy could be effective against many types of malignant diseases.     

Aberrant regulation of choline metabolism by mitochondrial electron transport system inhibition in neuroblastoma cells

Anomalous choline metabolic patterns have been consistently observed in vivo using Magnetic Resonance Spectroscopy (MRS) analysis of patients with neurodegenerative diseases and tissues from cancer patient. It remains unclear; however, what signaling events may have triggered these choline metabolic aberrancies. This study investigates how changes in choline and phospholipid metabolism are regulated by distinct changes in the mitochondrial electron transport system (ETS). We used specific inhibitors to down regulate the function of individual protein complexes in the ETS of SH-SY5Y neuroblastoma cells. Interestingly, we found that dramatic elevation in the levels of phosphatidylcholine metabolites could be induced by the inhibition of individual ETS complexes, similar to in vivo observations. Such interferences produced divergent metabolic patterns, which were distinguishable via principal component analysis of the cellular metabolomes. Functional impairments in ETS components have been reported in several central nervous system (CNS) diseases, including Alzheimer’s disease (AD) and Parkinson’s disease (PD); however, it remains largely unknown how the suppression of individual ETS complex function could lead to specific dysfunction in different cell types, resulting in distinct disease phenotypes. Our results suggest that the inhibition of each of the five ETS complexes might differentially regulate phospholipase activities within choline metabolic pathways in neuronal cells, which could contribute to the overall understanding of mitochondrial diseases. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Significance of the zebrafish model in the discovery of bioactive molecules from nature

Natural products have immense therapeutic potential not only due to their structural variation and complexity but also due to their range of biological activities. Research based on natural products has led to the discovery of molecules with biomedical and pharmaceutical applications in different therapeutic areas like cancer, inflammation responses, diabetes, and infectious diseases. There are still several challenges to be overcome in natural product drug discovery research programs and the challenge of high throughput screening of natural substances is one of them. Bioactivity screening is an integral part of the drug discovery process and several in vitro and in vivo biological models are now available for this purpose. Among other well-reported biological models, the zebrafish (Danio rerio) is emerging as an important in vivo model for preclinical studies of synthetic molecules in different therapeutic areas. Zebrafish embryos have a short reproductive cycle, show ease of maintenance at high densities in the laboratory and administration of drugs is a straightforward procedure. The embryos are optically transparent, allowing for the visualization of drug effects on internal organs during the embryogenesis process. In this review, we illustrate the importance of using zebrafish as an important biological model in the discovery of bioactive drugs from natural sources.     

Drug delivery to brain tumors

We develop a macroscopic model for delivering drug to brain tumors. The model accounts for bulk convective and diffusive transport across the blood-brain barrier and through the interstitial space. Through mathematical analysis and simulations, we assess the effects of changing parameters (within physiological bounds) on drug delivery. We find that there is an optimal treatment for convective drug delivery to the center of the tumor. We interpret this phenomenon in terms of traffic flow. The implications of our analyses on existing chemotherapeutic protocols are discussed.     

Effect of tumor shape and size on drug delivery to solid tumors

ABSTRACT: Tumor shape and size effect on drug delivery to solid tumors are studied, based on the application of the governing equations for fluid flow, i.e., the conservation laws for mass and momentum, to physiological systems containing solid tumors. The discretized form of the governing equations, with appropriate boundary conditions, is developed for predefined tumor geometries. The governing equations are solved using a numerical method, the element-based finite volume method. Interstitial fluid pressure and velocity are used to show the details of drug delivery in a solid tumor, under an assumption that drug particles flow with the interstitial fluid. Drug delivery problems have been most extensively researched in spherical tumors, which have been the simplest to examine with the analytical methods. With our numerical method, however, more complex shapes of the tumor can be studied. The numerical model of fluid flow in solid tumors previously introduced by our group is further developed to incorporate and investigate non-spherical tumors such as prolate and oblate ones. Also the effects of the surface area per unit volume of the tissue, vascular and interstitial hydraulic conductivity on drug delivery are investigated.     

Inorganic carbon concentrating mechanisms in free-living and symbiotic dinoflagellates and chromerids

Photosynthetic dinoflagellates are ecologically and biogeochemically important in marine and freshwater environments. However, surprisingly little is known of how this group acquires inorganic carbon or how these diverse processes evolved. Consequently, how CO₂ availability ultimately influences the success of dinoflagellates over space and time remains poorly resolved compared to other microalgal groups. Here we review the evidence. Photosynthetic core dinoflagellates have a Form II RuBisCO (replaced by Form IB or Form ID in derived dinoflagellates). The in vitro kinetics of the Form II RuBisCO from dinoflagellates are largely unknown, but dinoflagellates with Form II (and other) RuBisCOs have inorganic carbon concentrating mechanisms (CCMs), as indicated by in vivo internal inorganic C accumulation and affinity for external inorganic C. However, the location of the membrane(s) at which the essential active transport component(s) of the CCM occur(s) is (are) unresolved; isolation and characterization of functionally competent chloroplasts would help in this respect. Endosymbiotic Symbiodiniaceae (in Foraminifera, Acantharia, Radiolaria, Ciliata, Porifera, Acoela, Cnidaria, and Mollusca) obtain inorganic C by transport from seawater through host tissue. In corals this transport apparently provides an inorganic C concentration around the photobiont that obviates the need for photobiont CCM. This is not the case for tridacnid bivalves, medusae, or, possibly, Foraminifera. Overcoming these long-standing knowledge gaps relies on technical advances (e.g., the in vitro kinetics of Form II RuBisCO) that can functionally track the fate of inorganic C forms.