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    ABSTRACT: Biological systems are typically modelled by nonlinear differential equations. In an effort to produce high fidelity representations of the underlying phenomena, these models are usually of high dimension and involve multiple temporal and spatial scales. However, this complexity and associated stiffness makes numerical simulation difficult and mathematical analysis impossible. In order to understand the functionality of these systems, these models are usually approximated by lower dimensional descriptions. These can be analysed and simulated more easily, and the reduced description also simplifies the parameter space of the model. This model reduction inevitably introduces error: the accuracy of the conclusions one makes about the system, based on reduced models, depends heavily on the error introduced in the reduction process. In this paper we propose a method to calculate the error associated with a model reduction algorithm, using ideas from dynamical systems. We first define an error system, whose output is the error between observables of the original and reduced systems. We then use convex optimisation techniques in order to find approximations to the error as a function of the initial conditions. In particular, we use the Sum of Squares decomposition of polynomials in order to compute an upper bound on the worst-case error between the original and reduced systems. We give biological examples to illustrate the theory, which leads us to a discussion about how these techniques can be used to model-reduce large, structured models typical of systems biology.
    Journal of Theoretical Biology 04/2012; 304:172-82. DOI:10.1016/j.jtbi.2012.04.002
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    ABSTRACT: Tendons are composed of cells, blood vessels and extracellular matrix, intricately wo-ven together to form a vital musculoskeletal connective tissue. They act as a mechanical buffer for transmitting forces generated in muscles to bones, thus enabling movement. There is a growing need for functional imaging of tendon, for example to provide non-invasive biochemical and biomechanical insight into injured, diseased or repairing ten-don. This study focuses on ex vivo imaging using a novel combination of state of the art imaging technology, specifically ultra-high field magnetic resonance imaging (MRI) and near infrared-multiphoton laser scanning microscopy (NIR-MPLSM). We show that both imaging modalities are able to distinguish between normal and damaged tendon. MR imaging revealed macroscopic changes and evidence of tissue disruption; high sig-nal intensity corresponding to surrounding sheaths and some intra-tendinous regions. NIR-MPLSM demonstrated that local interactions between collagen and other matrix components are altered in enzyme-digested tendon. We propose a novel method for quantifying tendon disruption based on tendon crimp waveform parameterisation. Our findings suggest that MRI and NIR-MPLSM are useful technologies for extracting func-tional information from tendon. We provide insight into how biomechanical properties are related to biochemical parameters, and thus consider the future of in vivo functional MR imaging of tendon.
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    ABSTRACT: This paper presents a Particle Filter (PF) framework that stochastically detects and labels vessel bifurca-tions. The PF has previously been utilised in the segmentation of vascular structures, however has not demonstrated a consistent ability to detect and track bifurcations without the aid of user intervention. By incorporating a number of techniques into a specially designed vascular PF, including Markov Chain Monte Carlo (MCMC) rejuvenation and a spatially adaptive likelihood, we show that the simultaneous extraction of vessel centrelines, bifurcations and a hierarchical vascular representation is possible. This algorithm is shown to perform well on both synthetic and clinical data.
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    ABSTRACT: Cardiac computational models of electrical conduction, mechanical activation, hemodynamics and metabolism require detailed information about the structural arrangement of functionally heterogeneous cardiac cell types. However, current state-of-the-art models lack anatomically accurate cell type localization, which limits their utility. Histological sections combine unique resolution with discrimination of tissues and anatomical structures, but they suffer from alignment and deformation problems. On the other hand, MRI datasets preserve the correct geometry, but provide less micro structural detail. This paper presents a method for aligning MRI and histological datasets to obtain a highly detailed, geometrically correct anatomical description of the heart. An iterative process is used to correct the various 2D and 3D, rigid and non-rigid transforms, introduced in the histology preparation and acquisition. Validation is performed by calculating distances between anatomical landmarks in both datasets, and by quantifying tissue overlap. Results illustrate the suitability of the proposed algorithm to produce detailed, accurate cardiac models.
    Proceedings of the 2007 IEEE International Symposium on Biomedical Imaging: From Nano to Macro, Washington, DC, USA, April 12-16, 2007; 04/2007
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    ABSTRACT: Tendons are composed of cells, blood vessels and extracellular matrix, intricately woven together to form a vital musculoskeletal connective tissue. There is a growing need for functional imaging of tendon, for example to provide non-invasive biochemical and biomechanical insight into injured, diseased or repairing tendon. This study describes the possibility of developing an magnetic resonance imaging (MRI) tool for tissue quality assessment. Near infrared-multiphoton laser scanning microscopy (NIR-MPLSM) was used to validate ultra-high field MRI-based distinctions between normal and damaged tendon. Using a novel interpretation framework based on intrinsic tissue geometry, tissue damage at the matrix level was quantified according to local and global geometric parameters. The tendon characteristic crimp waveform and matrix geometric regularity were disrupted by enzyme-digestion, potentially compromising the tissue mechanical properties. These findings suggest that different imaging modalities can reveal complementary and corresponding information about tendon structures at functionally relevant scales. The proposed framework provides a robust and quantifiable physiological description of tendon, which can be exploited for clinical tendon tissue classification, and related to in vivo MR imaging.
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