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arXiv2015

Image-based Modelling of Organogenesis

One of the major challenges in biology concerns the integration of data across length and time scales into a consistent framework: how do macroscopic properties and functionalities arise from the molecular regulatory networks - and how can they change as a result of mutations? Morphogenesis provides an excellent model system to study how simple molecular networks robustly control complex processes on the macroscopic scale in spite of molecular noise, and how important functional variants can emerge from small genetic changes. Recent advancements in 3D imaging technologies, computer algorithms, and computer power now allow us to develop and analyse increasingly realistic models of biological control. Here we present our pipeline for image-based modeling that includes the segmentation of images, the determination of displacement fields, and the solution of systems of partial differential equations (PDEs) on the growing, embryonic domains. The development of suitable mathematical models, the data-based inference of parameter sets, and the evaluation of competing models are still challenging, and current approaches are discussed.

cs.CE↗

arXiv2015

Spatial measures of genetic heterogeneity during carcinogenesis

In this work we explore the temporal dynamics of spatial heterogeneity during the process of tumorigenesis from healthy tissue. We utilize a spatial stochastic process model of mutation accumulation and clonal expansion in a structured tissue to describe this process. Under a two-step tumorigenesis model, we first derive estimates of a non-spatial measure of diversity: Simpson's Index, which is the probability that two individuals sampled at random from the population are identical, in the premalignant population. We next analyze two new measures of spatial population heterogeneity. In particular we study the typical length scale of genetic heterogeneity during the carcinogenesis process and estimate the extent of a surrounding premalignant clone given a clinical observation of a premalignant point biopsy. This evolutionary framework contributes to a growing literature focused on developing a better understanding of the spatial population dynamics of cancer initiation and progression. Although initially motivated by understanding questions in cancer, these results can be applied more generally to help understand the dynamics of heterogeneity and diversity in a variety of spatially structured, evolving populations.

q-bio.PE↗

arXiv2015

Imaging Renal Urea Handling in Rats at Millimeter Resolution using Hyperpolarized Magnetic Resonance Relaxometry

\textit{In vivo} spin spin relaxation time ($T_2$) heterogeneity of hyperpolarized \textsuperscript{13}C urea in the rat kidney was investigated. Selective quenching of the vascular hyperpolarized \textsuperscript{13}C signal with a macromolecular relaxation agent revealed that a long-$T_2$ component of the \textsuperscript{13}C urea signal originated from the renal extravascular space, thus allowing the vascular and renal filtrate contrast agent pools of the \textsuperscript{13}C urea to be distinguished via multi-exponential analysis. The $T_2$ response to induced diuresis and antidiuresis was performed with two imaging agents: hyperpolarized \textsuperscript{13}C urea and a control agent hyperpolarized bis-1,1-(hydroxymethyl)-1-\textsuperscript{13}C-cyclopropane-$^2\textrm{H}_8$. Large $T_2$ increases in the inner-medullar and papilla were observed with the former agent and not the latter during antidiuresis suggesting that $T_2$ relaxometry may be used to monitor the inner-medullary urea transporter (UT)-A1 and UT-A3 mediated urea concentrating process. Two high resolution imaging techniques - multiple echo time averaging and ultra-long echo time sub-2 mm$^3$ resolution 3D imaging - were developed to exploit the particularly long relaxation times observed.

physics.med-ph↗

arXiv2015

A short review on techniques for processes and process simulation of scaffold-free tissue engineering

The invention of three-dimensional printers has led to major innovations in tissue engineering. They have enabled the printing of complex geometries such as those that occur in natural tissues, that were not possible with traditional manufacturing techniques. Tissue engineering in particular deals with printing bio-compatible material that may be infused with live cells. Thus additional complexity is incurred because the live cells can migrate and proliferate and thus change the printed geometry. One of the important issues is the prediction of geometry and possibly mechanical properties of the steady state tissue. In this short review, we will provide an overview of different tissue engineering processes that are currently available. Furthermore, we will review two important techniques, namely, Cellular Potts Model (CPM), and Cellular Particle Dynamics (CPD) that have been used to predict the steady state of printed tissue.

q-bio.QM↗

arXiv2015

On the growth and dissemination laws in a mathematical model of metastatic growth

Metastasis represents one of the main clinical challenge in cancer treatment since it is associated with the majority of deaths. Recent technological advances allow quantification of the dynamics of the process by means of noninvasive techniques such as longitudinal tracking of bioluminescent cells. The metastatic process was simplified here into two essential components -- dissemination and colonization -- which were mathematically formalized in terms of simple quantitative laws. The resulting mathematical model was confronted to in vivo experimental data of spontaneous metastasis after primary tumor resection. We discuss how much information can be inferred from confrontation of theories to the data with emphasis on identifiability issues. It is shown that two mutually exclusive assumptions for the secondary growth law (namely same or different from the primary tumor growth law) could fit equally well the data. Similarly, the fractal dimension coefficient in the dissemination law could not be uniquely determined from data on total metastatic burden only. Together, these results delimitate the range of information that can be recovered from fitting data of metastatic growth to already simplified mathematical models.

q-bio.TO↗

arXiv2015

Emergence of proto-organisms from bistable stochastic differentiation and adhesion

The rise of multicellularity in the early evolution of life represents a major challenge for evolutionary biology. Guidance for finding answers has emerged from disparate fields, from phylogenetics to modelling and synthetic biology, but little is known about the potential origins of multicellular aggregates before genetic programs took full control of developmental processes. Such aggregates should involve spatial organisation of differentiated cells and the modification of flows and concentrations of metabolites within well defined boundaries. Here we show that, in an environment where limited nutrients and toxic metabolites are introduced, a population of cells capable of stochastic differentiation and differential adhesion can develop into multicellular aggregates with a complex internal structure. The morphospace of possible patterns is shown to be very rich, including proto-organisms that display a high degree of organisational complexity, far beyond simple heterogeneous populations of cells. Our findings reveal that there is a potentially enormous richness of organismal complexity between simple mixed cooperators and embodied living organisms.

q-bio.PE↗

arXiv2015

A stochastic model for tumor heterogeneity

Phenotype variations define heterogeneity of biological and molecular systems, which play a crucial role in several mechanisms. Heterogeneity has been demonstrated in tumor cells. Here, samples from blood of patients affected from colon tumor were analyzed and fished with a microfluidic assay based on galactose active moieties, and incubated, for culturing, in SCID mice. Following the experimental investigation, a model based on Markov theory was implemented and discussed to explain the equilibrium existing between phenotypes of subpopulations of cells sorted using the microfluidic assay. The model in combination with the experimental results had many implications for tumor heterogeneity. It displayed interconversion of phenotypes, as observed after experiments. The interconversion generates of metastatic cells and implies that targeting the CTCs will be not an efficient method to prevent tumor recurrence. Most importantly, understanding the transitions between cell phenotypes in cell population can boost the understanding of tumor generation and growth.

physics.bio-ph↗

arXiv2015

A kinetic model of tumor growth and its radiation response with an application to Gamma Knife stereotactic radiosurgery

We developed a mathematical model to simulate the growth of tumor volume and its response to a single fraction of high dose irradiation. We made several key assumptions of the model. Tumor volume is composed of proliferating (or dividing) cancer cells and non-dividing (or dead) cells. Tumor growth rate (or tumor volume doubling time, Td) is proportional to the ratio of the volumes of tumor vasculature and the tumor. The vascular volume grows slower than the tumor by introducing the vascular growth retardation factor, theta. Upon irradiation the proliferating cells gradually die over a fixed time period after irradiation. Dead cells are cleared away with cell clearance time, Tcl. The model was applied to simulate pre-treatment growth and post-treatment radiation response of rat rhabdomyosarcoma tumor and metastatic brain tumors of five patients who were treated by Gamma Knife stereotactic radiosurgery (GKSRS). By selecting appropriate model parameters, we showed the temporal variation of the tumors for both the rat experiment and the clinical GKSRS cases could be easily replicated by the simple model. Additionally, the application of our model to the GKSRS cases showed that the alpha-value, which is an indicator of radiation sensitivity in the LQ model, and the retardation factor theta could be predictors of the post-treatment volume change. Since there is a large statistical uncertainty of this result due to the small sample size, a future clinical study with a larger number of patients is needed to confirm this finding.

physics.med-ph↗

arXiv2015

Modeling the Multiple Myeloma Vicious Cycle: Signaling Across the Bone Marrow Microenvironment

Multiple myeloma is a plasma cell cancer that leads to a dysregulated bone remodeling process. We present a partial differential equation model describing the dynamics of bone remodeling with the presence of myeloma tumor cells. The model explicitly takes into account the roles of osteoclasts, osteoblasts, precursor cells, stromal cells, osteocytes, and tumor cells. Previous models based on ordinary differential equations make the simplifying assumption that the bone and tumor cells are adjacent to each other. However, in actuality, these cell populations are separated by the bone marrow. Our model takes this separation into account by including the diffusion of chemical factors across the marrow, which can be viewed as communication between the tumor and bone. Additionally, this model incorporates the growth of the tumor and the diminishing bone mass by utilizing a ``moving boundary.'' We present numerical simulations that qualitatively validate our model's description of the cell population dynamics.

q-bio.CB↗

arXiv2016

Well-posedness of a Cahn--Hilliard system modelling tumour growth with chemotaxis and active transport

We consider a diffuse interface model for tumour growth consisting of a Cahn--Hilliard equation with source terms coupled to a reaction-diffusion equation. The coupled system of partial differential equations models a tumour growing in the presence of a nutrient species and surrounded by healthy tissue. The model also takes into account transport mechanisms such as chemotaxis and active transport. We establish well-posedness results for the tumour model and a variant with a quasi-static nutrient. It will turn out that the presence of the source terms in the Cahn--Hilliard equation leads to new difficulties when one aims to derive a priori estimates. However, we are able to prove continuous dependence on initial and boundary data for the chemical potential and for the order parameter in strong norms.

math.AP↗

arXiv2015

Vulnerability of geriatric patients to biomaterial associated infections: in vitro study of biofilm formation by Pseudomonas aeruginosa on orthopedic implants

Fibronectin, a glycoprotein secreted by connective tissue cells is found in the human plasma as well as in the ECM. It is known to have an adhesive property and plays a role in cell-to-cell and cell-to-substratum adhesions. In rheumatoid arthritis (RA) and osteoarthritis (OA), fibronectin is locally synthesized by the synovial cells, and the synovial fluid level of fibronectin is found to be double that in plasma. The concentration of fibronectin in the synovial fluid under such conditions is found escalate to 2-3 times higher than in the corresponding plasma. The present article demonstrates that the protein has a strong tendency to get adsorbed on biomaterials after an implant surgery in preference to lighter proteins like albumin, which in turn enhances the growth of robust biofilms. The present article demonstrates that, heightened risk of dangerous implant infections due to the formation of such biofilms coupled with the degrading immunity levels of the geriatric patients have the potential to transform an implant surgery to a 'life threatening' event.

q-bio.TO↗

arXiv2015

An asymptotic model for the deformation of a transversely isotropic, transversely homogeneous biphasic cartilage layer

In the present paper, an asymptotic model is constructed for the short-time deformation of an articular cartilage layer modeled as transversely isotropic, transversely homogeneous (TITH) biphasic material. It is assumed that the layer thickness is relatively small compared with the characteristic size of the normal surface load applied to the upper surface of the cartilage layer, while the bottom surface is assumed to be firmly attached to a rigid impermeable substrate. In view of applications to articular contact problems it is assumed that the interstitial fluid is not allowed to escape through the articular surface.

q-bio.TO↗

arXiv2015

An improved model of an actively contracting lymphatic vessel composed of several lymphangions: pumping characteristics

Using essentially our 2011 numerical model of a multi-lymphangion segment of a collecting lymphatic vessel, but augmented by inclusion of a refractory period and definition of a mid lymphangion pressure, we explore the effect of several parameters on the form of pump function curves. Pump function is sensitively dependent on the shape of the passive constitutive relation between lymphangion diameter and transmural pressure. Maximum flow-rate increases with the diameter scale applied to the constitutive relation and decreases with the pressure scale. Both maximum flow-rate and maximum pressure difference which can be overcome increase as the excess of lymphangion chain inlet pressure over external pressure is reduced, until inlet pressure is low enough that lymphangion collapse intervenes. The results are discussed in comparison with findings from biological experiments.

physics.flu-dyn↗

arXiv2015

Designer dynamics through chaotic traps: Controlling complex behavior in driven nonlinear systems

Control schemes for dynamical systems typically involve stabilizing unstable periodic orbits. In this paper we introduce a new paradigm of control that involves `trapping' the dynamics arbitrarily close to any desired trajectory. This is achieved by a state-dependent dynamical selection of the input signal applied to the driven nonlinear system. An emergent property of the trapping process is that the signal changes in a chaotic sequence: a manifestation of chaos-induced order. The simplicity of the control scheme makes it easily implementable in experimental systems.

nlin.CD↗

arXiv2015

A Poroelastic Mixture Model of Mechanobiological Processes in Tissue Engineering. Part I: Mathematical Formulation

An adequate control of cell response in tissue engineering applications is of utmost importance to obtain products suitable to clinical practice. This paper is the first part of a series of two connected publications in which we study via mathematical tools the cultivation in bioreactors of articular chondrocytes. The proposed model combines poroelastic theory of mixtures and cellular population models into a framework including stress state and oxygen tension as main determinants of engineered culture evolution. The special mechanosensitivity of articular chondrocytes to the surrounding environment is accounted for in the model through the novel concept of "force isotropy" acting on the cell which is assumed as the promoting factor of the production of new cells or extracellular matrix.

q-bio.TO↗

arXiv2017

The impact of cellular characteristics on the evolution of shape homeostasis

The importance of individual cells in a developing multicellular organism is well known but precisely how the individual cellular characteristics of those cells collectively drive the emergence of robust, homeostatic structures is less well understood. For example cell communication via a diffusible factor allows for information to travel across large distances within the population, and cell polarisation makes it possible to form structures with a particular orientation, but how do these processes interact to produce a more robust and regulated structure? In this study we investigate the ability of cells with different cellular characteristics to grow and maintain homeostatic structures. We do this in the context of an individual-based model where cell behaviour is driven by an intra-cellular network that determines the cell phenotype. More precisely, we investigated evolution with 96 different permutations of our model, where cell motility, cell death, long-range growth factor (LGF), short-range growth factor (SGF) and cell polarisation were either present or absent. The results show that LGF has the largest positive impact on the fitness of the evolved solutions. SGF and polarisation also contribute, but all other capabilities essentially increase the search space, effectively making it more difficult to achieve a solution. By perturbing the evolved solutions, we found that they are highly robust to both mutations and wounding. In addition, we observed that by evolving solutions in more unstable environments they produce structures that were more robust and adaptive. In conclusion, our results suggest that robust collective behaviour is most likely to evolve when cells are endowed with long range communication, cell polarisation, and selection pressure from an unstable environment.

q-bio.TO↗

arXiv2015

A Poroelastic Mixture Model of Mechanobiological Processes in Tissue Engineering. Part II: Numerical Simulations

In Part I of this article we have developed a novel mechanobiological model of a Tissue Engineering process that accounts for the mechanisms through which an isotropic or anisotropic adherence condition regulates the active functions of the cells in the construct. The model expresses mass balance and force equilibrium balance for a multi-phase mixture in a 3D computational domain and in time dependent conditions. In the present Part II, we study the mechanobiological model in a simplified 1D geometrical setting with the purpose of highlighting the ability of the formulation to represent the influence of force isotropy and nutrient availability on the growth of the tissue construct. In particular, an example of isotropy estimator is proposed and coded within a fixed-point solution map that is used at each discrete time level for system linearization and subsequent finite element approximation of the linearized equations. Extensively conducted simulations show that: 1) the spatial and temporal evolution of the cellular populations are in good agrement with the local growth/production conditions predicted by the mechanobiological stress-dependent model; and 2) the isotropy indicator and all model variables are strongly influenced by both maximum cell specific growth rate and mechanical boundary conditions enforced at the interface between the biomass construct and the interstitial fluid.

math.NA↗

arXiv2018

Optimal occlusion uniformly partitions red blood cells fluxes within a microvascular network

In animals, gas exchange between blood and tissues occurs in narrow vessels, whose diameter is comparable to that of a red blood cell. Red blood cells must deform to squeeze through these narrow vessels, transiently blocking or occluding the vessels they pass through. Although the dynamics of vessel occlusion have been studied extensively, it remains an open question why microvessels need to be so narrow. We study occlusive dynamics within a model microvascular network: the embryonic zebrafish trunk. We show that pressure feedbacks created when red blood cells enter the finest vessels of the trunk act together to uniformly partition red blood cells through the microvasculature. Using mathematical models as well as direct observation, we show that these occlusive feedbacks are tuned throughout the trunk network to prevent the vessels closest to the heart from short-circuiting the network. Thus occlusion is linked with another open question of microvascular function: how are red blood cells delivered at the same rate to each micro-vessel? Our analysis shows that tuning of occlusive feedbacks increase the total dissipation within the network by a factor of 11, showing that uniformity of flows rather than minimization of transport costs may be prioritized by the microvascular network.

q-bio.TO↗