Cholesterol Regulation in Age-Related Macular Degeneration: A Framework for Mathematical Modelling of Drusen Biogenesis.

In age-related macular degeneration (AMD), there is, in common with many other age-related diseases, the need to distinguish between changes in the ageing eye that lead to disease and those changes that are considered part of a healthy, ageing eye. Various studies investigating the multitude of mechanisms involved in the aetiology of AMD exist within the field of ophthalmology and related medical fields, yet many aspects of it remain poorly understood and only a limited number of therapies are available. A recent study relates drusen's topographically cellular characteristics to the neural retina's metabolic needs and associated cholesterol involvement within the retina. In particular, there is a need to fully understand the maintenance of cholesterol homeostasis in the retina to prevent normal ageing processes from being perturbed towards maculopathy. Here, we present an extensive review of the clinical and physiological features of the ageing retina, as well as mechanisms implicated in pathology, synthesised from a vast body of the published literature. We use this novel synthesis to construct a comprehensive process schematic, encompassing all key species and physiological processes such as nutrients, waste and lipoprotein management. We are therefore able to express these processes in a mathematical language via a comprehensive modelling framework, comprising a set of twenty-three equations spanning three distinct biological compartments. This very general modelling framework may now be adapted to more focused studies on individual mechanisms, processes or components underlying of the many facets of AMD. As an example of such a focused application, we conclude this article with a one-compartment, four-species model of the retinal pigment epithelium, which considers the parametric conditions under which either cholesterol homeostasis or unregulated accumulation of cholesterol may obtain in the ageing eye.

Space-Limited Mitosis in the Glazier-Graner-Hogeweg Model.

The Glazier-Graner-Hogeweg (GGH) model is a cellular automata framework for representing the time evolution of cellular systems, appealing because unlike many other individual-cell-based models it dynamically simulates changes in cell shape and size. Proliferation has seen some implementation into this modelling framework, but without consensus in the literature as to how this behaviour is best represented. Additionally, the majority of published GGH model implementations which feature proliferation do so in order to simulate a certain biological situation where mitosis is important, but without analysis of how these proliferation routines operate on a fundamental level. Here, a method of proliferation for the GGH model which uses separate cell phenotypes to differentiate cells which have entered or just left the mitotic phase of the cell cycle is presented and demonstrated to correctly predict logistic growth on a macroscopic scale (in accordance with experimental evidence). Comparisons between model simulations and the generalised logistic growth model provide an interpretation of the latter's 'shape parameter', and the proliferation routine used here is shown to offer the modeller somewhat predictable control over the proliferation rate, important for ensuring temporal consistency between different cellular behaviours in the model. All results are found to be insensitive to the inclusion of active cell motility. The implications of these simulated proliferation assays towards problems in cell biology are also discussed.

Melanoma Cell Colony Expansion Parameters Revealed by Approximate Bayesian Computation.

In vitro studies and mathematical models are now being widely used to study the underlying mechanisms driving the expansion of cell colonies. This can improve our understanding of cancer formation and progression. Although much progress has been made in terms of developing and analysing mathematical models, far less progress has been made in terms of understanding how to estimate model parameters using experimental in vitro image-based data. To address this issue, a new approximate Bayesian computation (ABC) algorithm is proposed to estimate key parameters governing the expansion of melanoma cell (MM127) colonies, including cell diffusivity, D, cell proliferation rate, λ, and cell-to-cell adhesion, q, in two experimental scenarios, namely with and without a chemical treatment to suppress cell proliferation. Even when little prior biological knowledge about the parameters is assumed, all parameters are precisely inferred with a small posterior coefficient of variation, approximately 2-12%. The ABC analyses reveal that the posterior distributions of D and q depend on the experimental elapsed time, whereas the posterior distribution of λ does not. The posterior mean values of D and q are in the ranges 226-268 µm2h-1, 311-351 µm2h-1 and 0.23-0.39, 0.32-0.61 for the experimental periods of 0-24 h and 24-48 h, respectively. Furthermore, we found that the posterior distribution of q also depends on the initial cell density, whereas the posterior distributions of D and λ do not. The ABC approach also enables information from the two experiments to be combined, resulting in greater precision for all estimates of D and λ.

Gravity-induced coronal plane joint moments in adolescent idiopathic scoliosis.

BACKGROUND: Adolescent Idiopathic Scoliosis is the most common type of spinal deformity, and whilst the isk of progression appears to be biomechanically mediated (larger deformities are more likely to progress), the detailed biomechanical mechanisms driving progression are not well understood. Gravitational forces in the upright position are the primary sustained loads experienced by the spine. In scoliosis they are asymmetrical, generating moments about the spinal joints which may promote asymmetrical growth and deformity progression. Using 3D imaging modalities to estimate segmental torso masses allows the gravitational loading on the scoliotic spine to be determined. The resulting distribution of joint moments aids understanding of the mechanics of scoliosis progression. METHODS: Existing low-dose CT scans were used to estimate torso segment masses and joint moments for 20 female scoliosis patients. Intervertebral joint moments at each vertebral level were found by summing the moments of each of the torso segment masses above the required joint. RESULTS: The patients' mean age was 15.3 years (SD 2.3; range 11.9-22.3 years); mean thoracic major Cobb angle 52(°) (SD 5.9(°); range 42-63(°)) and mean weight 57.5 kg (SD 11.5 kg; range 41-84.7 kg). Joint moments of up to 7 Nm were estimated at the apical level. No significant correlation was found between the patients' major Cobb angles and apical joint moments. CONCLUSIONS: Patients with larger Cobb angles do not necessarily have higher joint moments, and curve shape is an important determinant of joint moment distribution. These findings may help to explain the variations in progression between individual patients. This study suggests that substantial corrective forces are required of either internal instrumentation or orthoses to effectively counter the gravity-induced moments acting to deform the spinal joints of idiopathic scoliosis patients.

Biomaterial science meets computational biology.

There is a pressing need for a predictive tool capable of revealing a holistic understanding of fundamental elements in the normal and pathological cell physiology of organoids in order to decipher the mechanoresponse of cells. Therefore, the integration of a systems bioengineering approach into a validated mathematical model is necessary to develop a new simulation tool. This tool can only be innovative by combining biomaterials science with computational biology. Systems-level and multi-scale experimental data are incorporated into a single framework, thus representing both single cells and collective cell behaviour. Such a computational platform needs to be validated in order to discover key mechano-biological factors associated with cell-cell and cell-niche interactions.

Towards a quantitative theory of epidermal calcium profile formation in unwounded skin.

We propose and mathematically examine a theory of calcium profile formation in unwounded mammalian epidermis based on: changes in keratinocyte proliferation, fluid and calcium exchange with the extracellular fluid during these cells' passage through the epidermal sublayers, and the barrier functions of both the stratum corneum and tight junctions localised in the stratum granulosum. Using this theory, we develop a mathematical model that predicts epidermal sublayer transit times, partitioning of the epidermal calcium gradient between intracellular and extracellular domains, and the permeability of the tight junction barrier to calcium ions. Comparison of our model's predictions of epidermal transit times with experimental data indicates that keratinocytes lose at least 87% of their volume during their disintegration to become corneocytes. Intracellular calcium is suggested as the main contributor to the epidermal calcium gradient, with its distribution actively regulated by a phenotypic switch in calcium exchange between keratinocytes and extracellular fluid present at the boundary between the stratum spinosum and the stratum granulosum. Formation of the extracellular calcium distribution, which rises in concentration through the stratum granulosum towards the skin surface, is attributed to a tight junction barrier in this sublayer possessing permeability to calcium ions that is less than 15 nm s-1 in human epidermis and less than 37 nm s-1 in murine epidermis. Future experimental work may refine the presented theory and reduce the mathematical uncertainty present in the model predictions.

Segmental torso masses in adolescent idiopathic scoliosis.

BACKGROUND: Adolescent idiopathic scoliosis is the most common type of spinal deformity whose aetiology remains unclear. Studies suggest that gravitational forces in the standing position play an important role in scoliosis progression, therefore anthropometric data is required to develop biomechanical models of the deformity. Few studies have analysed the trunk by vertebral level and none have performed investigations of the scoliotic trunk. The aim of this study was to determine the centroid, thickness, volume and estimated mass, for sections of the scoliotic trunk. METHODS: Existing low-dose CT scans were used to estimate vertebral level-by-level torso masses for 20 female adolescent idiopathic scoliosis patients. ImageJ processing software was used to analyse the CT images and enable estimation of the segmental torso mass corresponding to each vertebral level. FINDINGS: The patients' mean age was 15.0 (SD 2.7) years with mean major Cobb angle of 52 (SD 5.9)° and mean patient weight of 58.2 (SD 11.6) kg. The magnitude of torso segment mass corresponding to each vertebral level increased by 150% from 0.6kg at T1 to 1.5kg at L5. Similarly, segmental thickness from T1-L5 increased inferiorly from a mean 18.5 (SD 2.2) mm at T1 to 32.8 (SD 3.4) mm at L5. The mean total trunk mass, as a percentage of total body mass, was 27.8 (SD 0.5) % which was close to values reported in previous literature. INTERPRETATION: This study provides new anthropometric reference data on segmental (vertebral level-by-level) torso mass in adolescent idiopathic scoliosis patients, useful for biomechanical models of scoliosis progression and treatment.

A multiscale road map of cancer spheroids--incorporating experimental and mathematical modelling to understand cancer progression.

Computational models represent a highly suitable framework, not only for testing biological hypotheses and generating new ones but also for optimising experimental strategies. As one surveys the literature devoted to cancer modelling, it is obvious that immense progress has been made in applying simulation techniques to the study of cancer biology, although the full impact has yet to be realised. For example, there are excellent models to describe cancer incidence rates or factors for early disease detection, but these predictions are unable to explain the functional and molecular changes that are associated with tumour progression. In addition, it is crucial that interactions between mechanical effects, and intracellular and intercellular signalling are incorporated in order to understand cancer growth, its interaction with the extracellular microenvironment and invasion of secondary sites. There is a compelling need to tailor new, physiologically relevant in silico models that are specialised for particular types of cancer, such as ovarian cancer owing to its unique route of metastasis, which are capable of investigating anti-cancer therapies, and generating both qualitative and quantitative predictions. This Commentary will focus on how computational simulation approaches can advance our understanding of ovarian cancer progression and treatment, in particular, with the help of multicellular cancer spheroids, and thus, can inform biological hypothesis and experimental design.

Computational model of the lumbar spine musculature: implications of spinal surgery.

BACKGROUND: The development of a comprehensive and detailed model of the musculature of the lumbar region is required if biomechanical models are to accurately predict the forces and moments experienced by the lumbar spine. METHODS: A new anatomical model representing the nine major muscles of the lumbar spine and the thoracolumbar fascia is presented. These nine muscles are modeled as numerous fascicles, each with its own force producing potential based on size and line of action. The simulated spine is fully deformable, allowing rotation in any direction, while respecting the physical constraints imposed by the skeletal structure. Maximal moments were predicted by implementing the model using a pseudo force distribution algorithm. Three types of surgery that affect the spinal musculature were simulated: posterior spinal surgery, anterior surgery, and total hip replacement. FINDINGS: Predicted moments matched published data from maximum isometric exertions in male volunteers. The biomechanical changes for the three different types of surgery demonstrated several common features: decreased spinal compression and production of asymmetric moments during symmetric tasks. INTERPRETATION: This type of analysis provides new opportunities to explore the effect of different patterns of muscle activity including muscle injury on the biomechanics of the spine.