The main objective of WP2 is the scientific validation of the technology and the development of an imaging software prototype based on its principles. Since the beginning of the project in April 2022, the partners involved in this work package have been working on the first two tasks dealing with FWI (Full Waveform Inversion) with uncertainty quantification and multiparameter extensions. Hereafter, our experts explain what these two tasks are about and how they approach them.
Uncertainty quantification in images
Most medical imaging studies rely on identifying regions of images which are “hypointensive” (i.e. darker than expected) or “hyperintensive” (i.e. lighter than expected). In contrast, a quantitative image must accurately measure a specific parameter. For example, quantitative Full-Waveform Inversion can measure parameters such as sound speed, attenuation, and density, simultaneously. Unfortunately, in most scientific disciplines, quantitative measurements are considered useless unless they contain an estimate of the variability, reliability, or uncertainty on the parameter. For example, a measurement of the diameter of the crater on the moon might be 6km, but this measurement is useless if the uncertainty is 13km; craters cannot measure less than 0km!
Uncertainty estimates are not typically provided in imaging science because traditional methods escalate either with the number of reconstructions or the volume of acquired data. This means that they take too long (e.g. Monte Carlo) or would be uncomfortable and unsafe for the patient (e.g. high scan time or higher doses of contrast). For this reason, we have developed Quantitative Stochastic Ultrasound Tomography, which incorporates a safe method to estimate uncertainty for less than 1% additional computational cost. We are currently validating the accuracy of this method, which will improve the quality of FWI measurements of sound speed, attenuation, and density. This will have a profound impact on US tomography of the breast and breast cancer screening, because knowledge of these parameters and their uncertainty will improve the quality of diagnostic information available to doctors.
Multiparameter Reconstruction of Breast Images
The propagation of ultrasound waves in biological tissue is subject to complex phenomena. In other words, ultrasound beams become highly distorted due to the heterogeneities and irregularities of the tissue. These variations are related to physical properties of the tissues which will provide doctors with further information about the breast and possible lesions detected. There are mathematical models that describe these propagation problems and are typically defined by a specific Partial Differential Equation (PDE) whose parameterization strongly depends on the tissue properties.
To solve this equation, computationally, we need to build an algorithm considering proper numerical techniques and ensuring low computing times and memory demands. With this aim, we explore the Pseudospectral (PS) methods that heavily exploit the efficient implementations of Fourier transform to result in low computing times. Reduction of memory demands is achieved by using minimum spatial grid resolution, which also guarantees optimal accuracy.
We rigorously study the main properties of our PS method, and analyze their dependency on the physical parameters comparing our results to others available in the literature.
Text authors: Carlos Spa (BSC), Oscar Bates (IC), Natalia Gutierrez (FW), Cristina Duran (FW)