A Bayesian approach for energy-based estimation of acoustic aberrations in high intensity focused ultrasound treatment

High intensity focused ultrasound is a non-invasive method for treatment of diseased tissue that uses a beam of ultrasound to generate heat within a small volume. A common challenge in application of this technique is that heterogeneity of the biological medium can defocus the ultrasound beam. Here we reduce the problem of refocusing the beam to the inverse problem of estimating the acoustic aberration due to the biological tissue from acoustic radiative force imaging data. We solve this inverse problem using a Bayesian framework with a hierarchical prior and solve the inverse problem using a Metropolis-within-Gibbs algorithm. The framework is tested using both synthetic and experimental datasets. We demonstrate that our approach has the ability to estimate the aberrations using small datasets, as little as 32 sonication tests, which can lead to significant speedup in the treatment process. Furthermore, our approach is compatible with a wide range of sonication tests and can be applied to other energy-based measurement techniques

Tomografía computarizada: proceso de adquisición, tecnología y estado actual

Computed tomography is a noninvasive scan technique widely applied in areas such as medicine, industry, and geology. This technique allows the three-dimensional reconstruction of the internal structure of an object which is lighted with an X-rays source. The reconstruction is formed with two-dimensional cross-sectional images of the object. Each cross-sectional is obtained from measurements of physical phenomena, such as attenuation, dispersion, and diffraction of X-rays, as result of their interaction with the object. In general, measurements acquisition is performed with methods based on any of these phenomena and according to various architectures classified in generations. Furthermore, in response to the need to simulate acquisition systems for CT, software dedicated to this task has been developed. The objective of this research is to determine the current state of CT techniques, for this, a review of methods, different architectures used for the acquisition and some of its applications is presented. Additionally, results of simulations are presented. The main contributions of this work are the detailed description of acquisition methods and the presentation of the possible trends of the technique. La tomografía computarizada (CT) es una técnica de escaneo no invasivo ampliamente aplicada en sectores como la medicina, la industria y la geología. Esta técnica permite la reconstrucción tridimensional de la estructura interna de un objeto que es iluminado con una fuente de rayos-X. La reconstrucción se forma con imágenes bidimensionales de cortes transversales del objeto. Cada corte se obtiene a partir de las medidas de fenómenos físicos como la atenuación, la dispersión y la difracción de los rayos-X, como resultado de la interacción con el objeto. En general, la adquisición de las medidas se realiza con métodos basados en alguno de estos fenómenos y empleando diversas arquitecturas clasificadas en generaciones. Por otro lado, en respuesta a la necesidad de simular sistemas de adquisición para CT se ha desarrollado software dedicado a esta tarea. El objetivo de este artículo es determinar el estado actual de las técnicas de CT, para esto, se presenta una revisión de los métodos, las distintas arquitecturas usadas para la adquisición y algunas de sus aplicaciones. Adicionalmente, se presentan los resultados de simulaciones realizadas. Las principales contribuciones de este trabajo son la descripción detallada de los métodos de adquisición y la presentación de las posibles tendencias de la técnica en general.

Numerical Solution of Limited-Data Inverse Problems Arising from X-Ray Tomography and Acoustic Inverse Scattering

Inverse problems arise, for example, from various imaging applications in medicine and physics. Their inherent property is ill-posedness; even a very small error in the measurement data can lead to a large error in the reconstruction. To overcome this difficulty, regularization is necessary for the inversion. In this work three new computational regularization methods for limited-data inverse problems are introduced and studied. The problems of special interest are stationary and dynamic X-ray tomography (CT) with sparsely sampled X-ray projection data and acoustic inverse scattering with limited-aperture data. In the first article of this thesis we develop a computational reconstruction algorithm for solving stationary sparse-data CT problems. Sparse-data cases arise e.g. from the need to minimize radiation dose in medical imaging. The new reconstruction algorithm is based on total variation regularization, it preserves sharp features of the target and is suitable for large-scale problems such as 3D CT. Its performance is illustrated by numerical results computed from both simulated and real X-ray data. In the second and third articles we introduce an inversion method for dynamic CT application making use of a few fixed X-ray sources and detectors. In this application the attainable temporal resolution is high while the CT data measured at a single time step is extremely sparse. The inversion method is motivated by level set methods and it regularizes the problem in space-time so that certain regularity is required both in spatial and temporal directions. Some of its important theoretical aspects are analyzed, and a computational implementation of the method is tested using both simulated and real X-ray data. The new methodology provides whole new possibilities e.g. for 4D angiographic imaging with high temporal resolution. In the fourth article a numerical implementation of the so-called enclosure method by Masaru Ikehata is introduced and studied using simulated test data. The enclosure method is suitable for limited-aperture obstacle scattering problems, where one uses only one incident wave and measures the far field pattern of the scattered field on some possibly limited aperture. The name of the method comes from the fact that it finds the convex hull of the obstacle, rather than its precise shape. Numerical evidence presented suggests that the method can approximately recover the shape and position of an obstacle from noisy limited-aperture far field data.Väitöskirjassa tutkitaan röntgensäteillä ja akustisilla aalloilla tapahtuvan kuvantamisen matematiikkaa, erityisesti numeerisesta näkökulmasta. Nämä kuvantamissovellukset johtavat inversio-ongelmiin, tai käänteisiin ongelmiin, joiden ratkaisut ovat äärimmäisen herkkiä mittausdatassa oleville virheille. Siksi niiden ratkaiseminen käytännössä vaatii regularisointia. Erityisen kiinnostuksen kohteena työssä on rajoitetun datan ongelmat, joissa käytettävissä oleva mittausdata on vajavaista esimerkiksi geometristen rajoitteiden takia. Väitöskirjan ensimmäisessä artikkelissa esitellään uusi laskennallinen algoritmi, jonka avulla voidaan laskea käyttökelpoisia rekonstruktioita hyvin harvasta röntgendatasta. Harvan datan tapaus voi liittyä esimerkiksi säteilyannoksen minimointiin lääketieteellisessä röntgentomografiassa. Uusi algoritmi pohjautuu nk. totaalivariaatioregularisointiin, joka regularisoi tehokkaasti datan harvuuden aiheuttamia artefaktoja ja säilyttää poikkeuksellisen hyvin rekonstruktion terävät yksityiskohdat. Uusi algoritmi on laskennallisesti tehokas, joten sitä voidaan käyttää myös 3D-sovelluksissa. Toisessa ja kolmannessa artikkelissa esitellään uusi rekonstruktiomenetelmä ja -algoritmi dynaamiselle 4D-röntgentomografialle, jossa kuvannetaan ajassa muuttuvaa kohdetta käyttäen muutamaa kiinteästi asennettua röntgenlähdettä ja -ilmaisinta. Tällä kuvantamismenetelmällä saavutetaan suuri aikaresoluutio mutta yksittäisellä ajanhetkellä mitattu röntgendata on äärimmäisen harva. Uusi rekonstruktioalgoritmi on nk. tasa-arvojoukkomenetelmän motivoima ja se regularisoi ongelmaa aika-avaruudessa siten, että ratkaisulta vaaditaan sopivaa jatkuvuutta sekä ajan että paikan suhteen. Menetelmä osoittautui tehokkaaksi sekä simuloidulla että aidolla röntgendatalla, ja se tarjoaa aivan uusia mahdollisuuksia esimerkiksi verisuonten varjoainekuvantamiseen 4D:ssä korkealla aikaresoluutiolla. Neljännessä artikkelissa tutkitaan uutta rekonstruktioalgoritmia rajoitetun datan käänteiselle akustiselle sironnalle. Algoritmin pohjana on Masaru Ikehatan kehittämä ja teoreettisesti verifioima menetelmä, joka pystyy rekonstruoimaan tuntemattoman (este)sirottajan konveksin verhon käyttäen vain yhtä sisääntulevaa testiaaltoa ja mittaamalla sironneen kaukokentän rajoitetuissa suunnissa. Simuloidusta testidatasta laskettujen numeeristen tulosten perusteella menetelmä rekonstruoi kohtuullisella tarkkuudella sirottajan muodon ja sijainnin erittäin rajoittuneesta kohinaisesta kaukokenttädatasta

A Bayesian Approach for Energy-Based Estimation of Acoustic Aberrations in High Intensity Focused Ultrasound Treatment

High intensity focused ultrasound is a non-invasive method for treatment of diseased tissue that uses a beam of ultrasound to generate heat within a small volume. A common challenge in application of this technique is that heterogeneity of the biological medium can defocus the ultrasound beam. Here we reduce the problem of refocusing the beam to the inverse problem of estimating the acoustic aberration due to the biological tissue from acoustic radiative force imaging data. We solve this inverse problem using a Bayesian framework with a hierarchical prior and solve the inverse problem using a Metropolis-within-Gibbs algorithm. The framework is tested using both synthetic and experimental datasets. We demonstrate that our approach has the ability to estimate the aberrations using small datasets, as little as 32 sonication tests, which can lead to significant speedup in the treatment process. Furthermore, our approach is compatible with a wide range of sonication tests and can be applied to other energy-based measurement techniques