Quantitative Tomography Using Coupled Physics of Waves

Project Information

QUANTOM

Grant agreement ID: 101001417

DOI

10.3030/101001417

EC signature date 8 February 2021

Start date 1 June 2021

End date 30 November 2026

Funded under

• EXCELLENT SCIENCE - European Research Council (ERC)

Total cost

€ 2 000 000,00

EU contribution

€ 2 000 000,00

Coordinated by

ITA-SUOMEN YLIOPISTO
Finland

Periodic Reporting for period 3 - QUANTOM (Quantitative Tomography Using Coupled Physics of Waves)

Reporting period: 2024-06-01 to 2025-11-30

Summary of the context and overall objectives of the project

Tomographic images are a valuable tool in various applications of medicine and biomedicine, industry and in security applications. Although efficient tomographic imaging techniques exist, development of new modalities that would overcome the limitations of the existing techniques are required. Overall, there is a need for development of new tomographic techniques that would provide quantitative information of unknown parameters of interest, such as tomographic images on the concentration of molecules. In particular, information on the reliability of the tomographic images is required.

The objective of the project is to develop quantitative tomographic imaging technique based on coupled physics of waves. In coupled physics imaging, contrast and resolution originating from different physical phenomena are combined. In the project, light, microwaves and ultrasound, i.e. waves, will be utilised through photoacoustic, thermoacoustic and acousto-optic effects. These techniques will be developed to produce tomographic images with an outstanding quantitative contrast in the sense of statistical information and modelling of uncertainties, combined with superior resolution and imaging depth.

Most tomographic imaging techniques are ill-posed problems that need to be approached in the framework of inverse problems. In the project, a Bayesian approach to ill-posed inverse problems, which supports the quantitative nature of the problem, will be taken. In the project, mathematical modelling and computational methods will be developed in close connection with experimental system development. The research is founded on a strong understanding of the underlying physics of coupled physics problems, knowledge on instrumentation on the related fields and experimental tomography, and state-of-the-art methods of computational inverse mathematics, that all come together in the PI’s research group.

Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far

Quantitative photoacoustic tomography (QPAT is an imaging methodology that exploits the photoacoustic effect with the aim of estimating distributions of optical parameters. The technique has two aspects: an acoustic part, where the initial acoustic pressure distribution is estimated from measured photoacoustic waves, and an optical part, where the distributions of the optical parameters are estimated from the initial pressure. We have approached these two inverse problems of QPAT in the framework of Bayesian inverse problems. In the acoustic inverse problem, we have developed a methodology for estimating the initial pressure and evaluating its reliability. The methodology has been evaluated using simulations and experimental measurements. In the optical inverse problem, we have studied estimating absorption and scattering from absorbed optical energy density. We have developed methodologies where the Monte Carlo method for light transport is utilised as a model for light propagation in the optical inverse problem of QPAT. Monte Carlo is a stochastic method where paths of photons are simulated as they undergo absorption and scattering events in a target. Due to this stochastic nature, also the search direction in a minimisation algorithm, that is used to solve the inverse problem, is stochastic. We have formulated an approach for solving the inverse problem and to overcome the challenges due to the stochastic nature of the problem. The approach has been evaluated with numerical simulations.

Furthermore, we have developed methodologies for diffuse optical tomography (DOT). DOT is an imaging technique aimed for estimating the optical parameters of a target from boundary measurements of near-infrared light. In DOT, we have developed a time-domain experimental DOT system and the related modelling based on nanosecond light sources. The system uses standard laboratory equipment for measuring the transmitted light, such as digital oscilloscopes, without a need for utilising time-gating and/or photon counting methods. The physics of the methodology was numerically simulated, and the performance of the experimental system was evaluated using phantom measurements.

One interest in our research has been utilisation of machine learning methods in inverse problems. We have developed methodologies that utilise machine learning approaches in the solution of the acoustic inverse problem of PAT and in DOT. We have studied, for example, compensating model uncertainties and evaluating the reliability of the estimated images. In PAT, a methodology where variational autoencoders are utilised such that estimates of the entire posterior distribution can be provided was developed. The approach was evaluated with numerical simulations, and it was found to provide accurate photoacoustic images together with estimates of their reliability.

Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far)

We developed a methodology where the Monte Carlo method for light transport is utilised in the inverse problem of quantitative photoacoustic tomography, and an approach for controlling the amount of the stochastic noise in the methodology. The same methodology can be extended also for other optical imaging modalities. One of the biggest challenges in biomedical optical imaging is imaging of targets of size within few millimetres. This regime is a so-called transport regime, where the imaged targets are too large for microscopy (that also has an additional challenge of not enabling imaging of living samples) and too small for utilising diffusion based light transport models. Therefore, a Monte Carlo based methodology, that has been developed in the project, can solve some bottlenecks that currently limit biomedical optical imaging in targets of size in the transport regime.

We developed and tested a methodology where variational autoencoders are utilised in photoacoustic tomography such that the methodology will provide estimates of the entire posterior distribution, that is the aim in Bayesian inverse problems and quantitative tomography, instead of only a qualitative image, that machine learning approaches conventionally do. The methodology was evaluated with numerical simulations. The results of the simulations also demonstrated the differences between conventional Bayesian approach and the developed methodology. The methodology will in general advance biomedical imaging community and inverse problems research.

In the second half of the project, we expect to extend the developed methodologies for realistic 3D geometries (by those parts where they are not already implemented) and evaluate the methodologies with experimental data. Furthermore, other tomography techniques in addition to QPAT and DOT will be studied. We expect to provide methodologies based on Bayesian inverse problems combined with experimental system development, uncertainty quantification, and machine learning for enabling quantitative tomography based on coupled physics of waves.

Expected value, standard deviation and a marginal distribution in a numerical phantom.