An efficient algorithm for the inverse problem in elasticity imaging by means of variational r-adaption.

A novel finite element formulation suitable for computing efficiently the stiffness distribution in soft biological tissue is presented in this paper. For that purpose, the inverse problem of finite strain hyperelasticity is considered and solved iteratively. In line with Arnold et al (2010 Phys. Med. Biol. 55 2035), the computing time is effectively reduced by using adaptive finite element methods. In sharp contrast to previous approaches, the novel mesh adaption relies on an r-adaption (re-allocation of the nodes within the finite element triangulation). This method allows the detection of material interfaces between healthy and diseased tissue in a very effective manner. The evolution of the nodal positions is canonically driven by the same minimization principle characterizing the inverse problem of hyperelasticity. Consequently, the proposed mesh adaption is variationally consistent. Furthermore, it guarantees that the quality of the numerical solution is improved. Since the proposed r-adaption requires only a relatively coarse triangulation for detecting material interfaces, the underlying finite element spaces are usually not rich enough for predicting the deformation field sufficiently accurately (the forward problem). For this reason, the novel variational r-refinement is combined with the variational h-adaption (Arnold et al 2010) to obtain a variational hr-refinement algorithm. The resulting approach captures material interfaces well (by using r-adaption) and predicts a deformation field in good agreement with that observed experimentally (by using h-adaption).

Efficient computation of the elastography inverse problem by combining variational mesh adaption and a clustering technique.

This paper is concerned with an efficient implementation suitable for the elastography inverse problem. More precisely, the novel algorithm allows us to compute the unknown stiffness distribution in soft tissue by means of the measured displacement field by considerably reducing the numerical cost compared to previous approaches. This is realized by combining and further elaborating variational mesh adaption with a clustering technique similar to those known from digital image compression. Within the variational mesh adaption, the underlying finite element discretization is only locally refined if this leads to a considerable improvement of the numerical solution. Additionally, the numerical complexity is reduced by the aforementioned clustering technique, in which the parameters describing the stiffness of the respective soft tissue are sorted according to a predefined number of intervals. By doing so, the number of unknowns associated with the elastography inverse problem can be chosen explicitly. A positive side effect of this method is the reduction of artificial noise in the data (smoothing of the solution). The performance and the rate of convergence of the resulting numerical formulation are critically analyzed by numerical examples.

Ultrasonic strain imaging and reconstructive elastography for biological tissue.

Mechanical properties of biological tissue represent important diagnostic information and are of histological and pathological relevance. In order to obtain non-invasively mechanical properties of tissue, we developed a real-time strain imaging system for clinical applications. The output data of this system also allow an inverse elastography approach leading to the spatial distribution of the relative elastic modulus of tissue. The internal displacement field of biological tissue is determined using the above mentioned strain imaging system by applying quasi-static compression to the considered tissue. Axial displacements are calculated by comparing echo signal sets obtained prior to and immediately following less than 0.1% compression, using the fast root seeking technique. Strain images representing mechanical tissue properties in a non-quantitative manner are displayed in real-time mode. For additional quantitative imaging, the stiffness distribution is calculated from the displacement field assuming the investigated material to be elastic, isotropic, and nearly incompressible. Different inverse problem approaches for calculating the shear modulus distribution using the internal displacement field have been implemented and compared. The results of an ongoing clinical study with more than 200 patients show, that our real-time strain imaging system is able to differentiate malignant and benign tissue areas in the prostate with a high degree of accuracy (sensitivity=76% and specificity=89%). The reconstruction approaches applied to the strain image data deliver quantitative tissue information and seem promising for an additional differential diagnosis of lesions in biological tissue. Our real-time system has the potential of improving diagnosis of prostate and breast cancer.

Technologies for haptic systems in telemedicine.

The ability to image the elastic properties of tissue is potentially useful in a variety of applications. The field of elastic imaging has grown in response to the potential use of such information in medical diagnosis. Real time ultrasound elastography represents a recent development in determining strain and elasticity distributions. Nevertheless, commonly used imaging techniques rely on the interpretation of two dimensional visual data displayed on a video screen. In reality however, physicians often prefer tactile exploration making the simultaneous portrayal of both video and haptic information most desirable. Since the 1970's many alphanumeric to tactile data conversion methods have been investigated, mainly with the ultimate aim of assisting the blind. More recently, interest has been directed toward the display of pictures on haptically explorable surfaces--Tactile imaging. Such a system would allow surgeons to examine hard sectors contained within soft tissue, and thereby assist in operations held remotely. The expansion of ultrasound elastography to 3D formats would mean the ability to haptically explore regions of the body normally inaccessible to human hands. For three-dimensional imaging the acquisition of sequential tomographic slices using Elastography, combined with image segmentation, enables the reconstruction, quantification and visualisation of tumour volumes. In a collaborative project between four research institutes, the aim is to produce a prototype three dimensional tactile displays comprising electrically switchable micromachined cells, whose mechanical moduli are governed by phase changes experienced by electrorheological and/or magnetorheological fluids. This will be integrated with a sensory ultrasonic elastography in order to present the human fingers with controllable surfaces capable of emulating biological tissue, muscle and bone.