WarpPINN: Cine-MR image registration with physics-informed neural networks

Heart failure is typically diagnosed with a global function assessment, such as ejection fraction. However, these metrics have low discriminate power, failing to distinguish different types of this disease. Quantifying local deformations in the form of cardiac strain can provide helpful information, but it remains a challenge. In this work, we introduce WarpPINN, a physics-informed neural network to perform image registration to obtain local metrics of the heart deformation. We apply this method to cine magnetic resonance images to estimate the motion during the cardiac cycle. We inform our neural network of near-incompressibility of cardiac tissue by penalizing the jacobian of the deformation field. The loss function has two components: an intensity-based similarity term between the reference and the warped template images, and a regularizer that represents the hyperelastic behavior of the tissue. The architecture of the neural network allows us to easily compute the strain via automatic differentiation to assess cardiac activity. We use Fourier feature mappings to overcome the spectral bias of neural networks, allowing us to capture discontinuities in the strain field. We test our algorithm on a synthetic example and on a cine-MRI benchmark of 15 healthy volunteers. We outperform current methodologies both landmark tracking and strain estimation. We expect that WarpPINN will enable more precise diagnostics of heart failure based on local deformation information. Source code is available at https://github.com/fsahli/WarpPINN.Comment: 18 pages, 10 figure

Multiscale modelling of perfusion and mechanics in poroelastic biological tissues

The Theory of Poroelasticity is embraced to model the effective mechanical behaviour of a porous elastic structure with fluid percolating in the pores. Key examples of the linear theory include hard hierarchical tissues, such as the bones, the interstitial matrix in healthy and tumorous biological tissues, the human eye, artificial constructs and biomaterials, as well as rocks and soil. Nonlinear poroelasticity has been applied to modelling tumour growth and in imaging to locate tumours in an incompressible medium, to the lungs and to consider the perfused myocardium. Poroelasticity has also been applied to studying the artery walls. The current modelling approaches assume simplistic microstructures for the materials which are in general unrealistic for the desired applications. This thesis will extend the current literature by proposing exciting, novel computationally feasible macroscale models that account for realistic microstructures and can help capture the true behaviour of materials. To fulfil this modelling goal we use the asymptotic homogenization technique. To provide a complete overview of the area we begin with a re-derivation of stan- dard Biot’s poroelasticity via the asymptotic homogenization technique. In the following chapters we build upon this to create appropriate models for complex, realistic biological scenarios. We begin our development by deriving the quasi-static governing equations for the macroscale behaviour of a linear elastic porous composite comprising a matrix interacting with inclusions and/or fibres, and an incompressible Newtonian fluid flowing in the pores. This is a novel model that can account for interactions between a variety of phases at the porescale which is much more realistic of biological tissues than the previously assumed matrix homogeneity. We then further extend this theory to assume that both the matrix and fibres/inclusions are hyperelastic, thus providing one of the first few works to use asymptotic homogenization in the context of nonlinear elasticity and making the theory more applicable to the heart and arteries. We continue the development by considering an approach over three microstructural scales. We derive the balance equations for a double poroelastic material which comprises a matrix with embedded subphases. Both the matrix and subphases can be described by Biot’s anisotropic, heterogeneous, compressible poroelasticity. This gives us a macroscale model that can account for the difference in a full set of poroelastic parameters and encodes structural details on three scales. We complete our analysis by investigating our novel poroelastic composite model nu- merically. We perform a study to investigate the role that the microstructure of a poroe- lastic material has on the resulting elastic parameters. We are considering how important an effect that multiple elastic and fluid phases at the same scale have on the estimation of the material’s elastic parameters when compared with a standard poroelastic approach. This work justifies the work of this thesis. That is, the introduction of novel models with detailed microstructures should be used instead of the previously known Biot’s poroelas- ticity for materials with non-homogeneous microstructures. The final part of this thesis applies the novel poroelastic composite model to investigate how physiologically observed microstructural changes induced by myocardial infarction impact the elastic parameters of the heart

Feature based estimation of myocardial motion from tagged MR images

In the past few years we witnessed an increase in mortality due to cancer relative to mortality due to cardiovascular diseases. In 2008, the Netherlands Statistics Agency reports that 33.900 people died of cancer against 33.100 deaths due to cardiovascular diseases, making cancer the number one cause of death in the Netherlands [33]. Even if the rate of people affected by heart diseases is continually rising, they "simply don’t die of it", according to the research director Prof. Mat Daemen of research institute CARIM of the University of Maastricht [50]. The reason for this is the early diagnosis, and the treatment of people with identified risk factors for diseases like ischemic heart disease, hypertrophic cardiomyopathy, thoracic aortic disease, pericardial (sac around the heart) disease, cardiac tumors, pulmonary artery disease, valvular disease, and congenital heart disease before and after surgical repair. Cardiac imaging plays a crucial role in the early diagnosis, since it allows the accurate investigation of a large amount of imaging data in a small amount of time. Moreover, cardiac imaging reduces costs of inpatient care, as has been shown in recent studies [77]. With this in mind, in this work we have provided several tools with the aim to help the investigation of the cardiac motion. In chapters 2 and 3 we have explored a novel variational optic flow methodology based on multi-scale feature points to extract cardiac motion from tagged MR images. Compared to constant brightness methods, this new approach exhibits several advantages. Although the intensity of critical points is also influenced by fading, critical points do retain their characteristic even in the presence of intensity changes, such as in MR imaging. In an experiment in section 5.4 we have applied this optic flow approach directly on tagged MR images. A visual inspection confirmed that the extracted motion fields realistically depicted the cardiac wall motion. The method exploits also the advantages from the multiscale framework. Because sparse velocity formulas 2.9, 3.7, 6.21, and 7.5 provide a number of equations equal to the number of unknowns, the method does not suffer from the aperture problem in retrieving velocities associated to the critical points. In chapters 2 and 3 we have moreover introduced a smoothness component of the optic flow equation described by means of covariant derivatives. This is a novelty in the optic flow literature. Many variational optic flow methods present a smoothness component that penalizes for changes from global assumptions such as isotropic or anisotropic smoothness. In the smoothness term proposed deviations from a predefined motion model are penalized. Moreover, the proposed optic flow equation has been decomposed in rotation-free and divergence-free components. This decomposition allows independent tuning of the two components during the vector field reconstruction. The experiments and the Table of errors provided in 3.8 showed that the combination of the smoothness term, influenced by a predefined motion model, and the Helmholtz decomposition in the optic flow equation reduces the average angular error substantially (20%-25%) with respect to a similar technique that employs only standard derivatives in the smoothness term. In section 5.3 we extracted the motion field of a phantom of which we know the ground truth of and compared the performance of this optic flow method with the performance of other optic flow methods well known in the literature, such as the Horn and Schunck [76] approach, the Lucas and Kanade [111] technique and the tuple image multi-scale optic flow constraint equation of Van Assen et al. [163]. Tests showed that the proposed optic flow methodology provides the smallest average angular error (AAE = 3.84 degrees) and L2 norm = 0.1. In this work we employed the Helmholtz decomposition also to study the cardiac behavior, since the vector field decomposition allows to investigate cardiac contraction and cardiac rotation independently. In chapter 4 we carried out an analysis of cardiac motion of ten volunteers and one patient where we estimated the kinetic energy for the different components. This decomposition is useful since it allows to visualize and quantify the contributions of each single vector field component to the heart beat. Local measurements of the kinetic energy have also been used to detect areas of the cardiac walls with little movement. Experiments on a patient and a comparison between a late enhancement cardiac image and an illustration of the cardiac kinetic energy on a bull’s eye plot illustrated that a correspondence between an infarcted area and an area with very small kinetic energy exists. With the aim to extend in the future the proposed optic flow equation to a 3D approach, in chapter 6 we investigated the 3D winding number approach as a tool to locate critical points in volume images. We simplified the mathematics involved with respect to a previous work [150] and we provided several examples and applications such as cardiac motion estimation from 3-dimensional tagged images, follicle and neuronal cell counting. Finally in chapter 7 we continued our investigation on volume tagged MR images, by retrieving the cardiac motion field using a 3-dimensional and simple version of the proposed optic flow equation based on standard derivatives. We showed that the retrieved motion fields display the contracting and rotating behavior of the cardiac muscle. We moreover extracted the through-plane component, which provides a realistic illustration of the vector field and is missed by 2-dimensional approaches

Real-time measurement corrected prediction of soft tissue response for medical simulations

Medical simulators, such as in palpation and disease diagnosis, require an efficient model of the biological soft tissue deformation. Hence, a computationally fast and accurate algorithm is required to support and enhance user interactions in near real-time simulations. The visual accuracy of such simulators is dependent on the user¿s reaction time. Static visual images that update at a rate of 25 Hz are perceived as real-time moving images. Hence, visualizing software requires fast algorithms to compute the deformation of soft tissue to facilitate a meaningful simulation. Furthermore, soft tissue behaviour should be modelled accurately while compatible with real-time computation. This work proposes a fast solver for the linearized finite element method (FEM) and validates the proposed algorithm with experimental results. The novelty of the method lies in the utilization of real-time force/displacement measurements that are embedded in the solution via the Kalman filter. A novel computational algorithm that utilizes the strength of the FEM in terms of accuracy and employs direct measurements from the manipulated tissue to overcome the slow computational process of the FEM is proposed in the first part of the thesis. As the behaviour of the mechanically loaded tissue can be regarded as linearly responding at each time step, a constant acceleration temporal discretization method, i.e., the Newmark-ß is employed. In real-time applications, the accuracy of the target variable highly depends on the accuracy of the inputs while differentiating noise from the signal is hardly ever possible. To address this problem, a Kalman filter-based method is developed. The proposed algorithm not only filters the noise from the measurements but also adapts the filter gain to the estimates of the target variable, i.e., the resulting tissue deformation. For a simulated tension test of a cubic model, the proposed algorithm achieves the update frequency of 63.3 Hz. This rate is a significant improvement in computational speed compared to the 5.8 Hz update rate by the classic FEM. Besides, this novel combination of the KF and the FEM makes it possible to expand the displacement estimates in the spatial domain when the measurements are only partially available at certain points. The performance of the above method is validated experimentally through a comparison with indentation tests on artificial human tissue-like material and with the FEM result under identical simulation conditions. The test is repeated on several samples, and the displacement variation from the FEM outcome is considered as the model error. Simulation results show that the proposed method achieves the deformation update frequency of 145.7 Hz compared to the 2.7 Hz from the reference FEM. The proposed method shows the same predictive ability, only 0.47% difference from FEM on average. Experimental validation of the proposed KF-FEM confirms that by consideration of both the measurement noise and the model error, the proposed method is capable of achieving high-frequency response without sacrificing the accuracy. Further to this, the experiments confirmed the linearized model response is reliable within the applied displacement range and therefore proving that KF can be employed. The developed KF-FEM was modified in the next study to address the problem resulting from inaccurate external loads measurements by the force sensors. In the modified version, both the external force, i.e., driving variable, and the displacement, i.e., driven variable, are taken as system states. It is considered that the uncertainty of the model input influences the accuracy of the system estimates. The modified model is calibrated to differentiate the system noise from the input noise. Numerical simulations were conducted on a liver shape geometrical model, and the simulation results demonstrate that more than 90% of the measurement noise is removed. The computational speed is also increased, delivering up to 89 Hz update rate. While the uncertainty of the external load is replicated in the displacements in an FEM solution, the developed algorithm can differentiate the measurement noise, including the displacement and external forces, from the system error, i.e., the FE model error. In the last study, the proposed model was developed to reflect the nonlinear behaviour of the manipulated tissue. The Central Difference time discretization method was used to model large deformations. A novel feature is that the Equation of motion is formulated within the element level rather than in the global spatial domain. This approach helped to improve the computational speed. Indentation with strains of slightly over 10% was simulated to assess the performance of the proposed model. The developed algorithm achieved the 33.85 Hz update frequency on a standard-issue PC and confirmed its suitability for real-time applications. Also, the proposed model achieved estimates with a maximum 5.75% mean absolute error (MAE) concerning the measurements while the classic FEM showed 6.20% MAE under identical simulation condition. Results confirm that deformation estimates for noisy boundary loads of the FEM can be improved with the help of direct measurements and yet be realistic in terms of real-time visual update. This study proposed a novel computational algorithm that achieved update frequencies of higher than 25 Hz to be perceived as real-time in human eyes. The developed KF-FEM model has also shown the potential of improving the FEM accuracy with the help of direct measurements. The proposed algorithm used partially available measurements and expanded its estimates in the spatial domain. The method was experimentally validated, and the model input uncertainty, as well as the nonlinear behaviour of the soft tissue, were assessed and verified

Book of Abstracts 15th International Symposium on Computer Methods in Biomechanics and Biomedical Engineering and 3rd Conference on Imaging and Visualization

In this edition, the two events will run together as a single conference, highlighting the strong connection with the Taylor & Francis journals: Computer Methods in Biomechanics and Biomedical Engineering (John Middleton and Christopher Jacobs, Eds.) and Computer Methods in Biomechanics and Biomedical Engineering: Imaging and Visualization (JoãoManuel R.S. Tavares, Ed.). The conference has become a major international meeting on computational biomechanics, imaging andvisualization. In this edition, the main program includes 212 presentations. In addition, sixteen renowned researchers will give plenary keynotes, addressing current challenges in computational biomechanics and biomedical imaging. In Lisbon, for the first time, a session dedicated to award the winner of the Best Paper in CMBBE Journal will take place. We believe that CMBBE2018 will have a strong impact on the development of computational biomechanics and biomedical imaging and visualization, identifying emerging areas of research and promoting the collaboration and networking between participants. This impact is evidenced through the well-known research groups, commercial companies and scientific organizations, who continue to support and sponsor the CMBBE meeting series. In fact, the conference is enriched with five workshops on specific scientific topics and commercial software.info:eu-repo/semantics/draf

Modelling Baroreceptors Function

Cardiovascular diseases form one of the most dangerous events that affect human life. They are usually the result of high blood pressure. Thus controlling blood pressure within patient specific healthy limits is a goal that we must target. There are two control loops for blood haemostasis inside the body either long term or short term. Baroreceptors control the short term blood pressure regulation. They are nerve ending that exist in certain locations within the blood vessels walls and they report blood pressure into the brain and the central nervous system. However the basics of their function are not yet known. We propose here that the baroreceptors work by converting circumferential and axial pressure into a stress into their respective direction and they start to send nerve signals based on a threshold of strain energy of the location they are embedded in. Thus baroreceptors A fibre is highly likely to exist in the stiffer adventitia, while the media will contain C fibres. This explains the reason behind having identical fibres with different threshold. We were able to arrive to this solution by getting a relationship between stress–strain relationship for the whole wall and for the arterial vessels. These findings are quiet significant as they allow a method to identify different stress in the arterial wall layers using whole wall experimental data and also as they were able to differentiate between different fibres based on their locations inside the arterial wall. A complete modelling of the baroreceptors function might lead to the formation of biosynthetic material that could interact with the body on the cellular level, so as to give humans the mean to the control of short term blood regulation thus preventing hypertension and its accompanying diseases such as atherosclerosis

Accurate determination and application of local strain for studying tissues with gradients in mechanical properties

Determination of the mechanical behavior of materials requires an understanding of deformation during loading. While this is traditionally accomplished in engineering by examining a force displacement curve for a whole sample, these techniques implicitly ignore local geometric complexities and local material inhomogeneities commonly found in biologic tissues. Techniques such as normalized cross correlation have been classically applied to address this issue and resolve deformation at the local level; however, these techniques have proven unreliable when deformations become large, if the sample undergoes a rotation, and/or if strain fields become incompatible (e.g. at or near failure). Presented here is a toolbox of techniques that addresses the limitations of the prior state-of-the-art for localized strain estimation. The first algorithm, termed 2D direct deformation estimation (2D-DDE), directly incorporates concepts from mechanics into non-rigid registration algorithms from computer vision, eliminating the need to consider displacement fields, as required for all of the prior state-of-the-art techniques. This results in not only an improvement in accuracy and precision of deformation estimation, but also relaxes compatibility of the deformation fields. A second algorithm, 2D Strain Inference with Measures of Probable Local Elevation (2D-SIMPLE), incorporates the results of 2D-DDE with results from algorithms that enforce strain compatibility to develop a robust detector of strain concentrations. While tracking local strain in a vinylidene chloride sheet in tension, 2D-SIMPLE detected strain concentrations which predicted the initiation of a crack in the material and the progression of the crack tip. The third and fourth algorithms generalize the two dimensional algorithms to analyze three dimensional deformations in volumetric images (3D-DDE and 3D-SIMPLE, respectively). Lastly, the 2D-DDE algorithm is modified to estimate two dimensional surface deformation from multi-view imaging systems. The robustness and adaptability of these techniques was then validated and demonstrated on a wide variety of biomedical applications. Using 2D-DDE, a microscale compliant region was discovered at the tendon-to-bone attachment, local heterogeneity of partially mineralized scaffolds was revealed, and gradients in stiffness of partially mineralized nano-fiber scaffolds were demonstrated. Using 2D-SIMPLE, mechanisms of embryonic wound healing and associated strain localizations were elucidated. 3D-DDE confirmed the existence of strain gradients across chordae tendineae in beating murine hearts as well as demonstrated dramatic localized changes in wall deformation before and after myocardial infarction in murine hearts. 2D-DDE was also used to develop a model system to study the effects of applied stress versus the effects of applied strain on cells. The model system was first theorized by considering a system in which gradients of cross sectional area or scaffold shape were composed with gradients in material stiffness. By combining these gradients in novel ways, it was theoretically determined that stress and strain could be locally isolated. A tensile bioreactor was constructed, techniques for fabricating scaffolds with gradients in stiffness and gradients in cross sectional area were developed, and theoretical strain gradients were confirmed experimentally using 2D-DDE. The model system was then validated for in vitro cell studies. Cell adhesion, proliferation, and viability following a seven day loading protocol were explored. Methods for determining single cell responses, which could be correlated back to a specific stress or strain states, were developed using immunocytochemistry and 2D-DDE approaches. Future studies will apply this model system to determine precise mechanotransduction responses of cells. These studies are critical to optimize stem cell tissue engineering strategies as well inform cell mechanobiology mechanisms

Mechanics of Heart Tube Formation in the Early Chick Embryo

The heart is the first functioning organ to form in the embryo. For decades, biologists have worked to identify many of the genetic and molecular factors involved in heart development, and over the years, these efforts have helped elucidate the vast biochemical signaling networks, which drive cardiac specification and differentiation in the embryo. Still, the biophysical mechanisms which link these molecular factors to actual, physical changes in cardiac morphology remain unclear. The aim of this thesis is to identify some of the mechanical forces which drive heart tube assembly in the early chick embryo. A unique feature of this work is the combination of mathematical modeling with ex ovo culture experiments. Head fold formation is the first step in this process. It sets the stage for early cardiac development by folding the: initially flat) heart fields out-of-plane, enabling them to form a tube along the ventral side of the embryo. Here, we show that head fold formation is driven by forces that originate in the ectoderm, forces that are typically associated with neurulation --- the formation of the neural tube. The primitive heart tube itself then forms as these bilateral heart fields move toward the midline and fuse to construct a straight, muscle-wrapped tube. We show that the endoderm plays a crucial mechanical role during this process. Instead of just serving as a passive, secretory substrate for the crawling mesodermal heart fields, the endoderm actively contracts to pull the heart fields toward the midline. We then investigate how this endodermal contraction is spatially distributed, and how different distributions of contraction might affect the observed morphogenetic deformations during heart tube formation. Our methods can be readily generalized to other morphogenetic processes, enabling us to investigate how physical forces are organized at the tissue-level to create biological form