Reduced formulation of a steady fluid-structure interaction problem with parametric coupling

We propose a two-fold approach to model reduction of fluid-structure interaction. The state equations for the fluid are solved with reduced basis methods. These are model reduction methods for parametric partial differential equations using well-chosen snapshot solutions in order to build a set of global basis functions. The other reduction is in terms of the geometric complexity of the moving fluid-structure interface. We use free-form deformations to parameterize the perturbation of the flow channel at rest configuration. As a computational example we consider a steady fluid-structure interaction problem: an incmpressible Stokes flow in a channel that has a flexible wall.Comment: 10 pages, 3 figure

Model reduction and level set methods for shape optimization problems

In this work two topics related to mathematical shape optimization are considered. Topological optimization methods need not know the correct topology (number of connected components and possible holes) of the optimal shape beforehand. Shape optimization can be performed by a topological gradient descent algorithm. Computational applications of topological optimization and level set based shape optimization involve the optimal damping of vibrating structures and an inverse problem of reconstructing a shape based on noisy interferogram measurements. For parametric shape optimization with partial differential constraints the model reduction approach of reduced basis methods is considered. In the reduced basis method a basis of snapshot solutions is used to construct a problem-dependent approximation space that has much smaller dimension than the underlying finite element approximations. The state constraints for optimization are then replaced with their reduced basis approximation, leading to efficient shape optimization methods. Computational examples involve the optimal engineering design of airfoils in potential and thermal flow

Shape-guided Conditional Latent Diffusion Models for Synthesising Brain Vasculature

The Circle of Willis (CoW) is the part of cerebral vasculature responsible for delivering blood to the brain. Understanding the diverse anatomical variations and configurations of the CoW is paramount to advance research on cerebrovascular diseases and refine clinical interventions. However, comprehensive investigation of less prevalent CoW variations remains challenging because of the dominance of a few commonly occurring configurations. We propose a novel generative approach utilising a conditional latent diffusion model with shape and anatomical guidance to generate realistic 3D CoW segmentations, including different phenotypical variations. Our conditional latent diffusion model incorporates shape guidance to better preserve vessel continuity and demonstrates superior performance when compared to alternative generative models, including conditional variants of 3D GAN and 3D VAE. We observed that our model generated CoW variants that are more realistic and demonstrate higher visual fidelity than competing approaches with an FID score 53\% better than the best-performing GAN-based model

Learned Local Attention Maps for Synthesising Vessel Segmentations

Magnetic resonance angiography (MRA) is an imaging modality for visualising blood vessels. It is useful for several diagnostic applications and for assessing the risk of adverse events such as haemorrhagic stroke (resulting from the rupture of aneurysms in blood vessels). However, MRAs are not acquired routinely, hence, an approach to synthesise blood vessel segmentations from more routinely acquired MR contrasts such as T1 and T2, would be useful. We present an encoder-decoder model for synthesising segmentations of the main cerebral arteries in the circle of Willis (CoW) from only T2 MRI. We propose a two-phase multi-objective learning approach, which captures both global and local features. It uses learned local attention maps generated by dilating the segmentation labels, which forces the network to only extract information from the T2 MRI relevant to synthesising the CoW. Our synthetic vessel segmentations generated from only T2 MRI achieved a mean Dice score of $0.79 \pm 0.03$ in testing, compared to state-of-the-art segmentation networks such as transformer U-Net ($0.71 \pm 0.04$) and nnU-net($0.68 \pm 0.05$), while using only a fraction of the parameters. The main qualitative difference between our synthetic vessel segmentations and the comparative models was in the sharper resolution of the CoW vessel segments, especially in the posterior circulation

Geometrical multiscale model of an idealized left ventricle with fluid-structure interaction effects coupled to a one-dimensional viscoelastic arterial network

A geometrical multiscale model for blood flow through an ideal left ventricle and the main arteries is presented. The blood flow in the three-dimensional idealized left ventricle is solved through a monolithic fluid-structure interaction solver. To account for the interaction between the heart and the circulatory system the heart flow is coupled through an ideal valve with a network of viscoelastic one-dimensional models representing the arterial network. The geometrical multiscale approach used in this work is based on the exchange of averaged/integrated quantities between the fluid problems. The peripheral circulation is modelled by zero-dimensional windkessel terminals. We demonstrate that the geometrical multiscale model is (i) highly modular in that component models can be easily replaced with higher-fidelity ones whenever the user has a specific interest in modelling a particular part of the system, (ii) passive in that it reaches a stable limit cycle of flow rate and pressure in a few heartbeat cycles when driven by a periodic force acting on the epicardium, and (iii) capable of operating at physiological regimes

Carboxylesterase Activities and Protein Expression in Rabbit and Pig Ocular Tissues

Hydrolytic reactions constitute an important pathway of drug metabolism and a significant route of prodrug activation. Many ophthalmic drugs and prodrugs contain ester groups that greatly enhance their permeation across several hydrophobic barriers in the eye before the drugs are either metabolized or released, respectively, via hydrolysis. Thus, the development of ophthalmic drug therapy requires the thorough profiling of substrate specificities, activities, and expression levels of ocular esterases. However, such information is scant in the literature, especially for preclinical species often used in ophthalmology such as rabbits and pigs. Therefore, our aim was to generate systematic information on the activity and expression of carboxylesterases (CESs) and arylacetamide deacetylase (AADAC) in seven ocular tissue homogenates from these two species. The hydrolytic activities were measured using a generic esterase substrate (4-nitrophenyl acetate) and, in the absence of validated substrates for rabbit and pig enzymes, with selective substrates established for human CES1, CES2, and AADAC (D-luciferin methyl ester, fluorescein diacetate, procaine, and phenacetin). Kinetics and inhibition studies were conducted using these substrates and, again due to a lack of validated rabbit and pig CES inhibitors, with known inhibitors for the human enzymes. Protein expression levels were measured using quantitative targeted proteomics. Rabbit ocular tissues showed significant variability in the expression of CES1 (higher in cornea, lower in conjunctiva) and CES2 (higher in conjunctiva, lower in cornea) and a poor correlation of CES expression with hydrolytic activities. In contrast, pig tissues appear to express only CES1, and CES3 and AADAC seem to be either low or absent, respectively, in both species. The current study revealed remarkable species and tissue differences in ocular hydrolytic enzymes that can be taken into account in the design of esterase-dependent prodrugs and drug conjugates, the evaluation of ocular effects of systemic drugs, and in translational and toxicity studies.Peer reviewe

Parametric free-form shape design with PDE models and reduced basis method

We present a coupling of the reduced basis methods and free-form deformations for shape optimization and design of systems modelled by elliptic PDEs. The free-form deformations give a parameterization of the shape that is independent of the mesh, the initial geometry, and the underlying PDE model. The resulting parametric PDEs are solved by reduced basis methods. An important role in our implementation is played by the recently proposed empirical interpolation method, which allows approximating the non-affinely parameterized deformations with affinely parameterized ones. These ingredients together give rise to an efficient online computational procedure for a repeated evaluation design environment like the one for shape optimization. The proposed approach is demonstrated on an airfoil inverse design problem. © 2010 Elsevier B.V