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Trinity College Dublin

Multi-scale, Multi-science, and Multi-outcome: Challenges in Computational Mechanobiology

Multi-scale, Multi-science, and Multi-outcome: Challenges in Computational Mechanobiology

Alex Lennon and Patrick Prendergast, Trinity Centre for Bioengineering, School of Engineering, Trinity College, Dublin

Medical device design, particularly in orthopaedics, has benefited greatly from the interaction between mechanical engineering and the life sciences. However, computer simulation of mechanical performance, so engrained in more traditional fields of mechanical engineering, such as the automotive and aerospace industries, has struggled to achieve similar penetration in medical device design. While considerable advances have been made in computing the immediate post-operative behaviour of a device on a patient-specific basis, the long-term performance of a device is often inferred from the response at this single time point [1]. Mechanobiology specifically aims to address this issue by studying the role of mechanical forces in morphological adaptation of living tissue over time. (e.g. in deformational moulding of newborn infant skulls; Fig.1). Incorporation of mechanobiology in computer simulation of medical device performance faces significant challenges but offers the potential to reduce the burden of clinical trials.

Plagiocephaly FigureFig. 1: Newborn infant skulls are prone to deformational moulding if persistently placed in a single position for long durations. This can result in deformity of the skull (e.g. plagiocephaly or brachiocephaly). These processes are related to the low stiffness of the immature bone and the soft tissue which hosts the ossification fronts between the bone plates (sutures). Computational analaysis of an oblique contact condition between either a mattress or specially designed foam pillow demonstrates how both sutures and parietal bone are highly strained under normal conditions but that both these load concentrations can be reduced by use of a more compliant support surface.

Multiscale mechanobiology Fig. 2: Multiscale mechanobiology — investigations at different scales can be used to motivate or interact with simulations at other scales. In this schematic, tensegrity network models are motivated from macro-molecular structures within the cytoskeleton. The whole cell models in turn can be used to motivate agent-based cell population models, implemented in cell lattices for computational efficiency, which further motivate macroscopic mechanobiology rules suitable for implementation in organ level finite element simulations

Inner Space: from intra-cellular structure to organ level response

Understanding the role of mechanical forces in biological processes requires adoption of approaches from numerous disciplines that span a staggering range of spatio-temporal scales [2]. For example, many mechanobiology processes impact an organism at a gross anatomical scale while the cells orchestrating such effects act at a scale of microns over periods of days and may require months or even years before the organism is affected. Cells themselves are ultimately governed by the interaction of molecules ranging from sub nanometre to several hundred nanometres that fold, bind, or chemically react in timespans ranging from femtoseconds to milliseconds. Thus, a multi-scale and multi-disciplinary approach is required to investigate these diverse structures and processes (Fig. 2).

At the level of individual cells, accurate modelling of the cytoskeleton is in itself a significant challenge. One approach to modelling these structure is to use an aggregate representation of the network based on the principle of tensional integrity (tensegrity) to represent the basic structural characteristics of a cell's cytoskeleton [3]. Using hybrid finite element models consisting of continuum elements and tensegrity inspired networks, we have investigated several aspects of single cell mechanics, including (i) how different types of biophysical stimulation of a cell, e.g. stretching vs fluid flow, affect parts of the cell known to be involved in mechanotransduction and (ii) whether ageing of a cell may affect mechanosensitiviy by altering geometric and material properties of the cytoskeleton and membrane.

Tissue level behaviour is characterised by coordinated activity within a population of cells and is well suited to agent-based modelling, in which cells can be represented as point-based agents that behave according to a set of rules. A particularly efficient computational implementation can be achieved by restricting movement to sites within a regular lattice. These lattices can be interfaced with lower resolution finite element models to approximate biophysical stimuli, such as extracellular matrix strain or interstitial fluid flow, to influence cell behaviour through a set of mechanobiological rules. This multi-scale approach has been used in applications such as bone formation in tissue engineering scaffolds [4] and experimental bone chambers used to investigate in vivo skeletal tissue differentiation [5].

Bone Adaptation Model Fig. 3: Mechanobiology rule for bone adaptation and its application to a conceptual model of a joint replacement prosthesis. On the left is a summary of the rule in graphical form. Bone resorbs when mechanical strain drops below a lower threshold while bone formation occurs at strains above an upper threshold; equilibrium is assumed between these mechanosensitivity thresholds with no net change in bone density. Finally, if strain becomes so high that micro-cracking occurs, bone is again resorbed. Dashed lines indicate how these mechanosensitivity thresholds may vary within a population. On the right are predictions for two different implants (high stiffness and low stiffness) within an “average” patient. Quite different bone adaptation patterns are evident for the two implants.

Migration Plots Fig. 4: Virtual clinical trial. Comparison of deterministic (left) and Monte Carlo simulation (right) for the conceptual joint replacement prostheses example from Fig. 3.

Cells range in size from circa 1 μm to 200 μm in diameter [6]; typical cells included in our mechanobiology simulations range in size from 10 – 50 um. This means that modelling tissue adaptation using the agent-based lattice approach described above can realistically only simulate small regions of tissue; e.g. a 10x10x10 mm3 with a 10 μm spacing would require 1x109 lattice points. However, finite element modelling is well established in organ level biomechanical analysis. By extrapolating mechanobiology rules used in agent-based models, it is possible to create analogous rules that can be implemented within finite element algorithms to build simulations of tissue adaptation at organ level, e.g. remodelling of bone around a hip replacement prosthesis [7].

Convergence of MeansFig. 5: Response surface modelling of hip replacement prosthesis performance in response to variation in surgical placement. (a-c) Schematic illustration of variation in implant positions studied. (d) Plot of convergence behaviour of mean of response variable for two different activities (walking in red and stair-climbing in blue).

Predicting the unpredictable? Simulating performance in a population

The pharmaceutical and medical device industries have long recognised the influence of variability and typically undertake costly and time consuming clinical trials to test their products likely performance when released into a real population. Variability arises from many sources but can be broadly characterised as patient-specific (e.g. size, shape, ethnicity), environmental (e.g. activity, food sources), device-specific (e.g. shape, material properties, biocompatibility), and surgical (e.g. achieved vs. desired positioning, damage to surrounding tissues). If computer simulation is ever to reduce the cost burden of clinical trials it will need to tackle the problem of variable performance of medical devices when they are introduced into a population.

Monte Carlo simulations, i.e. multiple simulation trials with different values of input parameters for each trial, has recently been employed within TCBE to investigate the potential impact of variability of mechanosensitivity on bone adaptation around joint replacements within a population (Figs. 3 and 4). Predictions from a virtual clinical trial show that variability in mechanosensitivity can cause dramatic variation in device performance, so much so that differences predicted by “average” case simulations, which are currently the main tool used during design of many devices, are obliterated when considering a population sample (Fig. 4). However, these simulations can place a considerable burden on computing resources, e.g. between 12 hours and 2 weeks for a single trial. Response Surface Methods (RSM) generate analytical approximations, analogous to polynomial regression analysis, of a full featured failure simulation from small training sets of such simulations. These analytical approximations, which execute in fractions of a second, can be used as the computational kernel of Monte Carlo simulations, enabling thousands of trials to be simulated in a matter of seconds , thereby dramatically accelerating analysis of probable device performance (Fig. 5).

Conclusion

By taking on the challenges of multiple processes occurring at different length scales, subject to stochastic variation, computational mechanobiology is attempting to bridge the gap to functional simulation of tissue response to medical treatment and device implantation.

Acknowledgements:

This research has been supported by Science Foundation Ireland (Principle Investigator Award and two Research Frontiers Programme awards).

References

  1. Prendergast P. J., Lally C., and Lennon A. B., 2009, “Finite element modelling of medical devices,” Medical Engineering and Physics, 31(4), pp. 419 - 419.
  2. Bao G., Kamm R., Thomas W., Hwang W., Fletcher D., Grodzinsky A., Zhu C., and Mofrad M., 2010, “Molecular Biomechanics: The Molecular Basis of How Forces Regulate Cellular Function,” Cellular and Molecular Bioengineering, 3(2), pp. 91-105.
  3. Ingber D. E., 1997, “Tensegrity: the architectural basis of cellular mechanotransduction,” Annu. Rev. Physiol, 59, pp. 575-599.
  4. Byrne D. P., Lacroix D., Planell J. A., Kelly D. J., and Prendergast P. J., 2007, “Simulation of tissue differentiation in a scaffold as a function of porosity, Young's modulus and dissolution rate: application of mechanobiological models in tissue engineering,” Biomaterials, 28, pp. 5544-54.
  5. Khayyeri H., Checa S., Tägil M., and Prendergast P. J., 2009, “Corroboration of mechanobiological simulations of tissue differentiation in an in vivo bone chamber using a lattice-modeling approach,” J. Orthop. Res, 27(12), pp. 1659-1666.
  6. Alberts B., Bray D., Hopkin K., Johnson A., Lewis J., Raff M., Roberts K., and Walter P., 2010, Essential cell biology, Garland Science.
  7. Lennon A. B., and Prendergast P., 2009, “The Cement-Bone Interface: Is It Susceptible To Damage Adaptive Remodeling?,” 4th European Conference of the International Federation for Medical and Biological Engineering, Springer Berlin Heidelberg, pp. 1990-1993.

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