Computational Growth Model Research Articles

Age- and gender-related changes in pediatric thoracic vertebral morphology

Background contextAlthough it is well known that the growth of thoracic spine changes significantly with age, gender, and vertebral level in the skeletally normal pediatric population, there have been very few studies attempting to comprehensively quantify such variations. Biomechanical and computational models of the growing thoracic spine have provided insight into safety and efficacy of surgical and noninvasive treatments for spinal deformity. However, many of these models only consider growth of the vertebral body and pedicles and assume a consistent growth rate for these structures across thoracic levels. PurposeTo enhance the understanding of age-, gender-, and level-related growth dynamics of the pediatric thoracic spine by comprehensively quantifying the thoracic vertebral morphology for subjects between 1 and 19 years. Study designA retrospective computed tomography (CT) image analysis study. MethodsRetrospectively obtained chest CT scans from 100 skeletally normal pediatric subjects (45 males and 55 females between the ages 1 and 19 years) were digitally reconstructed using medical imaging software. Surface point clouds of thoracic vertebrae were extracted and 26 vertebral geometry parameters were measured using 25 semiautomatically identified surface landmarks and anatomical slices from each thoracic vertebra (T1–T12). Data were assessed for normality, symmetry, and age-, gender-, and level-related differences in geometric measures and growth. Linear regression was performed to estimate of the rates of variation with age for each measurement. ResultsAsymmetries (bilateral, superior-inferior, and anteroposterior) were observed in vertebral body heights, end plate widths and depths, and interfacet widths. Within genders, significant interlevel differences were observed for all geometric measures, and significant differences in the rates of growth were found across thoracic levels for most parameters. Significant differences were observed between genders for pedicle, spinous process, and facet measurements. Growth rates of the pedicles and vertebral bodies were also found to vary significantly between genders. ConclusionsThe rates of growth for most thoracic vertebral structures varied between genders and across vertebral levels. These growth rates followed trends similar to those of their associated vertebral dimensions and this indicates that, across levels and between genders, larger vertebral structures grow at faster rates, whereas smaller structures grow at a slower rate. Such level- and gender-specific information could be used to inform clinical decisions about spinal deformity treatment and adapted for use in biomechanical and computational modeling of thoracic growth and growth modulation.

A hybrid ten-species phase-field model of tumor growth

The development of predictive computational models of tumor initiation, growth, and decline is faced with many formidable challenges. Phenomenological models which attempt to capture the complex interactions of multiple tissue and cellular species must cope with moving interfaces of heterogeneous media and the sprouting vascular structures due to angiogenesis and their evolution. They must be able to deliver predictions consistent with events that take place at cellular scales, and they must faithfully depict biological mechanisms and events that are known to be associated with various forms of cancer. In the present work, a ten-species vascular model for the tumor growth is presented which falls within the framework of phase-field (or diffuse-interface) models suggested by continuum mixture theory. This framework provides for the simultaneous treatment of interactions of multiple evolving species, such as tumor cells, necrotic cell cores, nutrients, and other cellular and tissue types that exist and interact in living tissue. We develop a hybrid model that couples the tumor growth with sprouting through angiogenesis. The model is able to represent the branching of new vessels through coupling a discrete model for which the angiogenesis is started upon pre-defined conditions on the nutrient deprivation in the continuum model. Such conditions are represented by hypoxic cells that release tumor growth factors that ultimately trigger vascular growth. We discuss the numerical approximation of the model using mixed finite elements. The results of numerical experiments are also presented and discussed.

Biomechanics and mechanobiology in functional tissue engineering

The field of tissue engineering continues to expand and mature, and several products are now in clinical use, with numerous other preclinical and clinical studies underway. However, specific challenges still remain in the repair or regeneration of tissues that serve a predominantly biomechanical function. Furthermore, it is now clear that mechanobiological interactions between cells and scaffolds can critically influence cell behavior, even in tissues and organs that do not serve an overt biomechanical role. Over the past decade, the field of “functional tissue engineering” has grown as a subfield of tissue engineering to address the challenges and questions on the role of biomechanics and mechanobiology in tissue engineering. Originally posed as a set of principles and guidelines for engineering of load-bearing tissues, functional tissue engineering has grown to encompass several related areas that have proven to have important implications for tissue repair and regeneration. These topics include measurement and modeling of the in vivo biomechanical environment; quantitative analysis of the mechanical properties of native tissues, scaffolds, and repair tissues; development of rationale criteria for the design and assessment of engineered tissues; investigation of the effects biomechanical factors on native and repair tissues, in vivo and in vitro; and development and application of computational models of tissue growth and remodeling. Here we further expand this paradigm and provide examples of the numerous advances in the field over the past decade. Consideration of these principles in the design process will hopefully improve the safety, efficacy, and overall success of engineered tissue replacements.

Computational modeling of chemical reactions and interstitial growth and remodeling involving charged solutes and solid-bound molecules.

Mechanobiological processes are rooted in mechanics and chemistry, and such processes may be modeled in a framework that couples their governing equations starting from fundamental principles. In many biological applications, the reactants and products of chemical reactions may be electrically charged, and these charge effects may produce driving forces and constraints that significantly influence outcomes. In this study, a novel formulation and computational implementation are presented for modeling chemical reactions in biological tissues that involve charged solutes and solid-bound molecules within a deformable porous hydrated solid matrix, coupling mechanics with chemistry while accounting for electric charges. The deposition or removal of solid-bound molecules contributes to the growth and remodeling of the solid matrix; in particular, volumetric growth may be driven by Donnan osmotic swelling, resulting from charged molecular species fixed to the solid matrix. This formulation incorporates the state of strain as a state variable in the production rate of chemical reactions, explicitly tying chemistry with mechanics for the purpose of modeling mechanobiology. To achieve these objectives, this treatment identifies the specific theoretical and computational challenges faced in modeling complex systems of interacting neutral and charged constituents while accommodating any number of simultaneous reactions where reactants and products may be modeled explicitly or implicitly. Several finite element verification problems are shown to agree with closed-form analytical solutions. An illustrative tissue engineering analysis demonstrates tissue growth and swelling resulting from the deposition of chondroitin sulfate, a charged solid-bound molecular species. This implementation is released in the open-source program FEBio ( www.febio.org ). The availability of this framework may be particularly beneficial to optimizing tissue engineering culture systems by examining the influence of nutrient availability on the evolution of inhomogeneous tissue composition and mechanical properties, the evolution of construct dimensions with growth, the influence of solute and solid matrix electric charge on the transport of cytokines, the influence of binding kinetics on transport, the influence of loading on binding kinetics, and the differential growth response to dynamically loaded versus free-swelling culture conditions.

Analysis and modeling of Nannochloropsis growth in lab, greenhouse, and raceway experiments

Efficient production of algal biofuels could reduce dependence on foreign oil by providing a domestic renewable energy source. Moreover, algae-based biofuels are attractive for their large oil yield potential despite decreased land use and natural resource (e.g., water and nutrients) requirements compared to terrestrial energy crops. Important factors controlling algal lipid productivity include temperature, nutrient availability, salinity, pH, and the light-to-biomass conversion rate. Computational approaches allow for inexpensive predictions of algae growth kinetics for various bioreactor sizes and geometries without the need for multiple, expensive measurement systems. Parametric studies of algal species include serial experiments that use off-line monitoring of growth and lipid levels. Such approaches are time consuming and usually incomplete, and studies on the effect of the interaction between various parameters on algal growth are currently lacking. However, these are the necessary precursors for computational models, which currently lack the data necessary to accurately simulate and predict algae growth. In this work, we conduct a lab-scale parametric study of the marine alga Nannochloropsis salina and apply the findings to our physics-based computational algae growth model. We then compare results from the model with experiments conducted in a greenhouse tank and an outdoor, open-channel raceway pond. Results show that the computational model effectively predicts algae growth in systems across varying scale and identifies the causes for reductions in algal productivities. Applying the model facilitates optimization of pond designs and improvements in strain selection.

Extracellular Matrix Density Regulates the Rate of Neovessel Growth and Branching in Sprouting Angiogenesis

Angiogenesis is regulated by the local microenvironment, including the mechanical interactions between neovessel sprouts and the extracellular matrix (ECM). However, the mechanisms controlling the relationship of mechanical and biophysical properties of the ECM to neovessel growth during sprouting angiogenesis are just beginning to be understood. In this research, we characterized the relationship between matrix density and microvascular topology in an in vitro 3D organ culture model of sprouting angiogenesis. We used these results to design and calibrate a computational growth model to demonstrate how changes in individual neovessel behavior produce the changes in vascular topology that were observed experimentally. Vascularized gels with higher collagen densities produced neovasculatures with shorter vessel lengths, less branch points, and reduced network interconnectivity. The computational model was able to predict these experimental results by scaling the rates of neovessel growth and branching according to local matrix density. As a final demonstration of utility of the modeling framework, we used our growth model to predict several scenarios of practical interest that could not be investigated experimentally using the organ culture model. Increasing the density of the ECM significantly reduced angiogenesis and network formation within a 3D organ culture model of angiogenesis. Increasing the density of the matrix increases the stiffness of the ECM, changing how neovessels are able to deform and remodel their surroundings. The computational framework outlined in this study was capable of predicting this observed experimental behavior by adjusting neovessel growth rate and branching probability according to local ECM density, demonstrating that altering the stiffness of the ECM via increasing matrix density affects neovessel behavior, thereby regulated vascular topology during angiogenesis.

A storage-based model of heterocyst commitment and patterning in cyanobacteria

When deprived of fixed nitrogen (fN), certain filamentous cyanobacteria differentiate nitrogen-fixing heterocysts. There is a large and dynamic fraction of stored fN in cyanobacterial cells, but its role in directing heterocyst commitment has not been identified. We present an integrated computational model of fN transport, cellular growth, and heterocyst commitment for filamentous cyanobacteria. By including fN storage proportional to cell length, but without any explicit cell-cycle effect, we are able to recover a broad and late range of heterocyst commitment times and we observe a strong indirect cell-cycle effect. We propose that fN storage is an important component of heterocyst commitment and patterning in filamentous cyanobacteria. The model allows us to explore both initial and steady-state heterocyst patterns. The developmental model is hierarchical after initial commitment: our only source of stochasticity is observed growth rate variability. Explicit lateral inhibition allows us to examine ΔpatS, ΔhetN, and ΔpatN phenotypes. We find that ΔpatS leads to adjacent heterocysts of the same generation, while ΔhetN leads to adjacent heterocysts only of different generations. With a shortened inhibition range, heterocyst spacing distributions are similar to those in experimental ΔpatN systems. Step-down to non-zero external fN concentrations is also investigated.

Computational modeling of hypertensive growth in the human carotid artery.

Arterial hypertension is a chronic medical condition associated with an elevated blood pressure. Chronic arterial hypertension initiates a series of events, which are known to collectively initiate arterial wall thickening. However, the correlation between macrostructural mechanical loading, microstructural cellular changes, and macrostructural adaptation remains unclear. Here, we present a microstructurally motivated computational model for chronic arterial hypertension through smooth muscle cell growth. To model growth, we adopt a classical concept based on the multiplicative decomposition of the deformation gradient into an elastic part and a growth part. Motivated by clinical observations, we assume that the driving force for growth is the stretch sensed by the smooth muscle cells. We embed our model into a finite element framework, where growth is stored locally as an internal variable. First, to demonstrate the features of our model, we investigate the effects of hypertensive growth in a real human carotid artery. Our results agree nicely with experimental data reported in the literature both qualitatively and quantitatively.

Nanoscale texture development of C-S-H gel: A computational model for nucleation and growth

The development of C-S-H (Calcium-Silicate-Hydrate) gels during cement hydration is often investigated by nucleation and growth models which fit reasonably well with the calorimetric measurements but predict hydration degrees which grossly exceed the experimental values. Here, a computational model is presented which explicitly considers the intrinsic nanoparticulate nature of C-S-H gel. Based on a nucleation and growth algorithm the model reproduces the experimental calorimetric and hydration degree measurements without invoking to any diffusion mechanism. The model also suggests that the peak in the calorimetric curves can be ascribed to the percolation point of the hydrates themselves within the interstitial pore volume.

Synthesis rates and binding kinetics of matrix products in engineered cartilage constructs using chondrocyte-seeded agarose gels

Large-sized cartilage constructs suffer from inhomogeneous extracellular matrix deposition due to insufficient nutrient availability. Computational models of nutrient consumption and tissue growth can be utilized as an efficient alternative to experimental trials to optimize the culture of large constructs; models require system-specific growth and consumption parameters. To inform models of the [bovine chondrocyte]−[agarose gel] system, total synthesis rate (matrix accumulation rate+matrix release rate) and matrix retention fractions of glycosaminoglycans (GAG), collagen, and cartilage oligomeric matrix protein (COMP) were measured either in the presence (continuous or transient) or absence of TGF-β3 supplementation. TGF-β3's influences on pyridinoline content and mechanical properties were also measured. Reversible binding kinetic parameters were characterized using computational models. Based on our recent nutrient supplementation work, we measured glucose consumption and critical glucose concentration for tissue growth to computationally simulate the culture of a human patella-sized tissue construct, reproducing the experiment of Hung et al. (2003). Transient TGF-β3 produced the highest GAG synthesis rate, highest GAG retention ratio, and the highest binding affinity; collagen synthesis was elevated in TGF-β3 supplementation groups over control, with the highest binding affinity observed in the transient supplementation group; both COMP synthesis and retention were lower than those for GAG and collagen. These results informed the modeling of GAG deposition within a large patella construct; this computational example was similar to the previous experimental results without further adjustments to modeling parameters. These results suggest that these nutrient consumption and matrix synthesis models are an attractive alternative for optimizing the culture of large-sized constructs.

On the mechanics of growing thin biological membranes

Despite their seemingly delicate appearance, thin biological membranes fulfill various crucial roles in the human body and can sustain substantial mechanical loads. Unlike engineering structures, biological membranes are able to grow and adapt to changes in their mechanical environment. Finite element modeling of biological growth holds the potential to better understand the interplay of membrane form and function and to reliably predict the effects of disease or medical intervention. However, standard continuum elements typically fail to represent thin biological membranes efficiently, accurately, and robustly. Moreover, continuum models are typically cumbersome to generate from surface-based medical imaging data. Here we propose a computational model for finite membrane growth using a classical midsurface representation compatible with standard shell elements. By assuming elastic incompressibility and membrane-only growth, the model a priori satisfies the zero-normal stress condition. To demonstrate its modular nature, we implement the membrane growth model into the general-purpose non-linear finite element package Abaqus/Standard using the concept of user subroutines. To probe efficiently and robustness, we simulate selected benchmark examples of growing biological membranes under different loading conditions. To demonstrate the clinical potential, we simulate the functional adaptation of a heart valve leaflet in ischemic cardiomyopathy. We believe that our novel approach will be widely applicable to simulate the adaptive chronic growth of thin biological structures including skin membranes, mucous membranes, fetal membranes, tympanic membranes, corneoscleral membranes, and heart valve membranes. Ultimately, our model can be used to identify diseased states, predict disease evolution, and guide the design of interventional or pharmaceutic therapies to arrest or revert disease progression.

Micromechanisms and a computational model of growth of low-temperature creep cracks in materials

We analyze and synthesize the results of investigations available from the literature on the micromechanisms of growth of creep cracks and, on the basis of this analysis, show that these cracks grow mainly by the initiation, increase, and coalescence of pores. This enables us to formulate a computational model for the evaluation of the period of subcritical growth of low-temperature creep cracks in structural materials. As a result, we obtain a kinetic equation of growth of these cracks in the form of dependence of the crack growth rate on the stress intensity factor. Together with the initial and the final conditions, this equation forms a computational model for the evaluation of the period of subcritical growth of lowtemperature creep cracks.

SELECTION AND ASSESSMENT OF PHENOMENOLOGICAL MODELS OF TUMOR GROWTH

We address general approaches to the rational selection and validation of mathematical and computational models of tumor growth using methods of Bayesian inference. The model classes are derived from a general diffuse-interface, continuum mixture theory and focus on mass conservation of mixtures with up to four species. Synthetic data are generated using higher-order base models. We discuss general approaches to model calibration, validation, plausibility, and selection based on Bayesian-based methods, information theory, and maximum information entropy. We also address computational issues and provide numerical experiments based on Markov chain Monte Carlo algorithms and high performance computing implementations.

Abstract P5-05-05: Computational modeling of breast cancer growth and spread: the role of matrix degrading enzymes

Abstract Background: A “hallmark” of cancer growth and metastatic spread is the process of local invasion of the surrounding tissue. Cancer cells achieve this by the secretion of enzymes involved in proteolysis (tissue degradation) including matrix metalloproteinases (MMPs). These over-expressed proteolytic enzymes then proceed to degrade the host tissue allowing the cancer cells to disseminate throughout the microenvironment by active migration and interaction with components of the extracellular matrix such as collagen. The implications of MMP-2 activation by MMP-14 and the tissue inhibitor of metalloproteinases-2 (TIMP2) can be considered alongside the suitability of the matrix to be invaded. The suitability of the matrix incorporates pore size, since in some highly dense collagen structures such as breast tissue, the cancer cells are unable to physically fit through a porous region and rely on membrane-bound MMPs to forge a path through which degradation by other MMPs and movement of cancer cells can occur. Method: We have developed a multi-scale mathematical model of breast cancer cell invasion of host tissue by combining both micro- (cell) and macro- (tissue) scale dynamics. The model considers cancer cells and two matrix-degrading enzymes from the MMP family of differing mechanistic actions, namely MMP-2 and the membrane bound MMP-14 (also called MT1-MMP), and their interaction with, and effect on, the extracellular matrix (ECM) in a 2-D spatial domain. For the macro-scale we use a system of reaction-diffusion-taxis partial differential equations to capture the qualitative dynamics of the migratory response of the cancer cells. The micro-scale operates over a smaller spatial and temporal scale, and as such allows us to explicitly examine the stochastic role which is inherent within the region of enzyme operation. Computational simulations of the equations predict the spatio-temporal evolution of the cancer cell density, the concentration levels of the various enzymes and the density of the extracellular matrix. Results: The model exhibits a rich range of dynamic and heterogeneous spatio-temporal solutions, which qualitatively match experimental and clinically observed results for aggressive breast carcinoma invasion and can be used to determine the speed of invasion through a variety of structured mediums such as the highly dense collagen constitution of some peritumoral stroma. Using the “worst case” scenario, an estimate for the maximum region of invasion over time from the initial data can be obtained suggesting the likely extent of breast cancer cell invasion into the surrounding tissue. Conclusion: This modeling is most relevant to and informs the biological processes occurring in early stage breast cancer, in which local invasion is a crucial aspect of tumor behavior. Citation Information: Cancer Res 2012;72(24 Suppl):Abstract nr P5-05-05.

Abstract P5-05-02: The role of cellular heterogeneity on the therapeutic response of breast cancer: Clinical insights from a hybrid multiscale computational model

Abstract Background: The therapeutic control of cancer progression critically depends on the responses of the individual cells that constitute the entire tumor mass. A key reason for poor therapeutic responses is the emergence of drug resistance due to intracellular and extracellular cellular heterogeneity that seriously impair the efficacy of chemotherapy and radiation therapy. Method: We have developed a hybrid multiscale computational model of breast cancer growth and treatment that incorporates individual cell-cycle dynamics and the effects of a changing microenvironment through the oxygen dynamics to consider optimum treatment protocols for breast cancer. In this model, the internal cell-cycle dynamics determine the growth strategy of the cancer cells, making the model more biologically relevant. This also helps classify the cancer cells according to their cell-cycle state and to analyse the effect of various cell-cycle-dependent chemotherapeutic drugs. The incorporation of oxygen dynamics within this hybrid model allows study of the effects of the microenvironment in cell-cycle regulation and drug resistance due to a hypoxia-induced quiescence (G0/G1 arrest) of the cancer cells. Furthermore, the effects of radiation therapy are included in the model using a modified linear quadratic model for the radiation damage, incorporating the effects of hypoxia and cell-cycle in determining the cell based radiosensitivity. The model is then used to study various combinations of multiple doses of cell-cycle-dependent chemotherapies and radiation therapy given that radiation may work better by the partial synchronisation of cells in a radiosensitive phase of the cell-cycle. Results: Using this computational model, we have shown that the cytotoxic effect of combination therapy is very much dependent on the timing of drug delivery, the time delay between the doses of chemotherapeutic drug and cell-cycle heterogeneity. The effectiveness of the drugs is also dependent on the spatial distribution of the tumor cell mass as this greatly influences the surrounding tumor microenvironment and drug distribution. After each dose of the chemotherapeutic drug, the changing spatial dynamics of the tumor cells redistributes the tissue oxygen and subsequently delivered drug doses within the tumor. Moreover, the cell-cycle phase-based chemotherapy also helps in favor of radiation therapy through the partial synchronisation of cells in the most radiosensitive phase of the cell-cycle. Conclusions: The incorporation of the spatial distribution of the breast cancer cells along with the internal and external cellular heterogeneity is critical to optimising scheduling strategies for chemotherapy and combined chemotherapy and radiation therapy. Overall, the computational simulation results highlight the potential usefulness of the model in developing patient-specific optimal treatment strategies. Citation Information: Cancer Res 2012;72(24 Suppl):Abstract nr P5-05-02.

Mechanical discoordination increases continuously after the onset of left bundle branch block despite constant electrical dyssynchrony in a computational model of cardiac electromechanics and growth

To test whether a functional growth law leads to asymmetric hypertrophy and associated changes in global and regional cardiac function when integrated with a computational model of left bundle branch block (LBBB). In recent studies, we proposed that cardiac myocytes grow longer when a threshold of maximum fibre strain is exceeded and grow thicker when the smallest maximum principal strain in the cellular cross-sectional plane exceeds a threshold. A non-linear cardiovascular model of the beating canine ventricles was combined with the cellular growth law. After inducing LBBB, the ventricles were allowed to adapt in shape over time in response to mechanical stimuli. When subjected to electrical dyssynchrony, the combined model of ventricular electromechanics, haemodynamics, and growth led to asymmetric hypertrophy with a faster increase of wall mass in the left ventricular (LV) free wall (FW) than the septum, increased LV end-diastolic and end-systolic volumes, and decreased LV ejection fraction. Systolic LV pressure decreased during the acute phase of LBBB and increased at later stages. The relative changes of these parameters were similar to those obtained experimentally. Most of the dilation was due to radial and axial fibre growth, and hence altered shape of the LVFW. Our previously proposed growth law reproduced measured dyssynchronously induced asymmetric hypertrophy and the associated functional changes, when combined with a computational model of the LBBB heart. The onset of LBBB leads to a step increase in LV mechanical discoordination that continues to increase as the heart remodels despite the constant electrical dyssynchrony.

Computational modeling of adherent cell growth in a hollow-fiber membrane bioreactor for large-scale 3-D bone tissue engineering

The use of hollow-fiber membrane bioreactors (HFMBs) has been proposed for three-dimensional bone tissue growth at the clinical scale. However, to achieve an efficient HFMB design, the relationship between cell growth and environmental conditions must be determined. Therefore, in this work, a dynamic double-porous media model was developed to determine nutrient-dependent cell growth for bone tissue formation in a HFMB. The whole hollow-fiber scaffold within the bioreactor was treated as a porous domain in this model. The domain consisted of two interpenetrating porous regions, including a porous lumen region available for fluid flow and a porous extracapillary space filled with a collagen gel that contained adherent cells for promoting long-term growth into tissue-like mass. The governing equations were solved numerically and the model was validated using previously published experimental results. The contributions of several bioreactor design and process parameters to the performance of the bioreactor were studied. The results demonstrated that the process and design parameters of the HFMB significantly affect nutrient transport and thus cell behavior over a long period of culture. The approach presented here can be applied to any cell type and used to develop tissue engineering hollow-fiber scaffolds.

What can imaging tell us about physiology? Lung growth and regional mechanical strain

The interplay of mechanical forces transduces diverse physico-biochemical processes to influence lung morphogenesis, growth, maturation, remodeling and repair. Because tissue stress is difficult to measure in vivo, mechano-sensitive responses are commonly inferred from global changes in lung volume, shape, or compliance and correlated with structural changes in tissue blocks sampled from postmortem-fixed lungs. Recent advances in noninvasive volumetric imaging technology, nonrigid image registration, and deformation analysis provide valuable tools for the quantitative analysis of in vivo regional anatomy and air and tissue-blood distributions and when combined with transpulmonary pressure measurements, allow characterization of regional mechanical function, e.g., displacement, strain, shear, within and among intact lobes, as well as between the lung and the components of its container-rib cage, diaphragm, and mediastinum-thereby yielding new insights into the inter-related metrics of mechanical stress-strain and growth/remodeling. Here, we review the state-of-the-art imaging applications for mapping asymmetric heterogeneous physical interactions within the thorax and how these interactions permit as well as constrain lung growth, remodeling, and compensation during development and following pneumonectomy to illustrate how advanced imaging could facilitate the understanding of physiology and pathophysiology. Functional imaging promises to facilitate the formulation of realistic computational models of lung growth that integrate mechano-sensitive events over multiple spatial and temporal scales to accurately describe in vivo physiology and pathophysiology. Improved computational models in turn could enhance our ability to predict regional as well as global responses to experimental and therapeutic interventions.

Optimization of vascular-targeting drugs in a computational model of tumor growth

A biophysical tool is introduced that seeks to provide a theoretical basis for helping drug design teams assess the most promising drug targets and design optimal treatment strategies. The tool is grounded in a previously validated computational model of the feedback that occurs between a growing tumor and the evolving vasculature. In this paper, the model is particularly used to explore the therapeutic effectiveness of two drugs that target the tumor vasculature: angiogenesis inhibitors (AIs) and vascular disrupting agents (VDAs). Using sensitivity analyses, the impact of VDA dosing parameters is explored, as is the effects of administering a VDA with an AI. Further, a stochastic optimization scheme is utilized to identify an optimal dosing schedule for treatment with an AI and a chemotherapeutic. The treatment regimen identified can successfully halt simulated tumor growth, even after the cessation of therapy.

Anisotropic density growth of bone—A computational micro-sphere approach

Bones are able to adapt their local density when exposed to mechanical loading. Such growth processes result in densification of the bone in regions of high loading levels and in resorption of the material in regions of low loading levels. This evolution and optimisation process generates heterogeneous distributions of bone density accompanied by pronounced anisotropic mechanical properties. While several constitutive models reported in the literature assume the growth process to be purely isotropic, only few studies focus on the modelling and simulation of anisotropic functional adaptation we can observe in vivo. Some of these few computational models for anisotropic growth characterise the evolution of anisotropy by analogy to anisotropic continuum damage mechanics while others include anisotropic growth but assume isotropic elastic properties.The objective of this work is to generalise a well-established framework of energy-driven isotropic functional adaptation to anisotropic microstructural growth and density evolution. We adopt the so-called micro-sphere concept, which proves to be extremely versatile and flexible to extend sophisticated one-dimensional constitutive relations to the three-dimensional case. In this work we apply this framework to the modelling and simulation of anisotropic functional adaptation by means of a directional density distribution, which evolves in time and in response to the mechanical loading condition. Several numerical studies highlight the characteristics and properties of the anisotropic growth model we establish. The formulation is embedded into an iterative finite element algorithm to solve complex boundary value problems. In particular, we consider the finite-element-simulation of a subject-specific proximal tibia bone and a comparison to experimental measurements. The proposed model is able to appropriately represent the heterogeneous bone density distribution. As an advantage over several other computational growth models proposed in the literature, a pronounced local anisotropy evolution is identified and illustrated by means of orientation-distribution-type density plots.