On the Adjoint Operator in Photoacoustic Tomography

Photoacoustic Tomography (PAT) is an emerging biomedical "imaging from coupled physics" technique, in which the image contrast is due to optical absorption, but the information is carried to the surface of the tissue as ultrasound pulses. Many algorithms and formulae for PAT image reconstruction have been proposed for the case when a complete data set is available. In many practical imaging scenarios, however, it is not possible to obtain the full data, or the data may be sub-sampled for faster data acquisition. In such cases, image reconstruction algorithms that can incorporate prior knowledge to ameliorate the loss of data are required. Hence, recently there has been an increased interest in using variational image reconstruction. A crucial ingredient for the application of these techniques is the adjoint of the PAT forward operator, which is described in this article from physical, theoretical and numerical perspectives. First, a simple mathematical derivation of the adjoint of the PAT forward operator in the continuous framework is presented. Then, an efficient numerical implementation of the adjoint using a k-space time domain wave propagation model is described and illustrated in the context of variational PAT image reconstruction, on both 2D and 3D examples including inhomogeneous sound speed. The principal advantage of this analytical adjoint over an algebraic adjoint (obtained by taking the direct adjoint of the particular numerical forward scheme used) is that it can be implemented using currently available fast wave propagation solvers.Comment: submitted to "Inverse Problems

Quasi-static imaged-based immersed boundary-finite element model of human left ventricle in diastole

SUMMARY: Finite stress and strain analyses of the heart provide insight into the biomechanics of myocardial function and dysfunction. Herein, we describe progress toward dynamic patient-specific models of the left ventricle using an immersed boundary (IB) method with a finite element (FE) structural mechanics model. We use a structure-based hyperelastic strain-energy function to describe the passive mechanics of the ventricular myocardium, a realistic anatomical geometry reconstructed from clinical magnetic resonance images of a healthy human heart, and a rule-based fiber architecture. Numerical predictions of this IB/FE model are compared with results obtained by a commercial FE solver. We demonstrate that the IB/FE model yields results that are in good agreement with those of the conventional FE model under diastolic loading conditions, and the predictions of the LV model using either numerical method are shown to be consistent with previous computational and experimental data. These results are among the first to analyze the stress and strain predictions of IB models of ventricular mechanics, and they serve both to verify the IB/FE simulation framework and to validate the IB/FE model. Moreover, this work represents an important step toward using such models for fully dynamic fluid–structure interaction simulations of the heart

Exploring the relationship between the Engineering and Physical Sciences and the Health and Life Sciences by advanced bibliometric methods

We investigate the extent to which advances in the health and life sciences (HLS) are dependent on research in the engineering and physical sciences (EPS), particularly physics, chemistry, mathematics, and engineering. The analysis combines two different bibliometric approaches. The first approach to analyze the 'EPS-HLS interface' is based on term map visualizations of HLS research fields. We consider 16 clinical fields and five life science fields. On the basis of expert judgment, EPS research in these fields is studied by identifying EPS-related terms in the term maps. In the second approach, a large-scale citation-based network analysis is applied to publications from all fields of science. We work with about 22,000 clusters of publications, each representing a topic in the scientific literature. Citation relations are used to identify topics at the EPS-HLS interface. The two approaches complement each other. The advantages of working with textual data compensate for the limitations of working with citation relations and the other way around. An important advantage of working with textual data is in the in-depth qualitative insights it provides. Working with citation relations, on the other hand, yields many relevant quantitative statistics. We find that EPS research contributes to HLS developments mainly in the following five ways: new materials and their properties; chemical methods for analysis and molecular synthesis; imaging of parts of the body as well as of biomaterial surfaces; medical engineering mainly related to imaging, radiation therapy, signal processing technology, and other medical instrumentation; mathematical and statistical methods for data analysis. In our analysis, about 10% of all EPS and HLS publications are classified as being at the EPS-HLS interface. This percentage has remained more or less constant during the past decade