Thèses sur le sujet « Nonlinear ultrasound imaging »

The work presented in this thesis is focused on developing a method for imaging of nonlinear scattering from stiff particles using dual-frequency band pulses. The pulse complexes are comprised of a low-frequency manipulation pulse and a high-frequency imaging pulse where the the two pulses overlap in time and there is a frequency relationship of 1:8-10. It may be shown that the polarity of the nonlinear scattering follows the polarity of the low-frequency pulse, while linear scattering does not. By transmitting two such dual-frequency band pulses in each beam direction where the polarity of the low-frequency pulse is inverted from the first to the second, nonlinear scattering may be detected. The low-frequency pulse not only manipulates the scattering but also the propagation of the high-frequency imaging pulse. These nonlinear propagation effects will mask the nonlinear scattering and must be corrected for in order to suppress the linear scattering and detect the nonlinear scattering.In the first paper of this thesis, the nonlinear propagation effects using confocal low-frequency and high-frequency beams are investigated in a water tank setup. A dual-frequency band annular array, where the low-frequency element is place behind the high-frequency element, to form a stack, was used. When the high-frequency pulse is short compared to the low-frequency pulse period, the nonlinear propagation effects can be approximated by a nonlinear propagation delay and frequency shift. It is shown how the delay and frequency shift increases close to linearly with increasing manipulation pressure and how axis the profiles of the high-frequency beam are affected. On transmit, the size relationship between the low and high-frequency apertures can be varied, and it is shown how the nonlinear propagation effects is dependent on the array setup.By transmitting an unfocused low-frequency beam together with a focused high-frequency beam, the position of the high-frequency pulse relative to the low-frequency pulse can be kept close to constant over the whole imaging region. By placing the imaging pulse at the peak of the manipulation pulse, the frequency shift due to nonlinear propagation can be minimized. In the second paper, the suppression of linear scattering using such a beam setup and only correcting for the propagation delay is investigated. Applying a low-frequency pressure of 85 to 500 kPa, the linear scattering could be suppressed 35 to 17 dB. It is shown that there is an amplitude difference between the first and second received pulse which is due to diffraction differences of the first and second beam. Since the low-frequency beam is unfocused, the manipulation pressure will vary over the focused high-frequency beam and distort the spherical focusing. This distortion will be different for the first and second beam and produce different diffraction of the two beams, which will yield an amplitude difference. Frequency shift due to nonlinear propagation will also affect the diffraction but it is indicated that the nonlinear aberration is the dominating factor.In the third paper three different beamforming strategies for dual-frequency band imaging is investigated; 1. Focused low freq. + Focused high freq., 2. Unfocused low freq. + Focused high freq. and 1. Unfocused low freq. + Unfocused high freq. The nonlinear propagation delay and frequency shift are estimated and predicted based on the estimated low-frequency manipulation pressure experienced by the high-frequency pulse. There is good accordance between the estimated and predicted values until diffraction becomes significant. When diffraction becomes significant, differences in diffraction between the first and second pulse will also introduce a frequency shift and delay other than that generated by the nonlinear manipulation pressure. Differences in the pulse form of the first and second pulse is thus not only due to manipulation of the propagation of the high-frequency pulse by the low-frequency, but also by differences in diffraction.The nonlinear propagation and scattering are generated by equal processes but are different in the way that nonlinear propagation is an accumulative effect while scattering is a local effect. In the last part of the thesis the difference between nonlinear propagation and scattering is investigated using simulations, where the bandwidth of the high-frequency pulse relative to the center frequency of the manipulation pulse is varied. It is shown that when the high-frequency pulse is shorter in time than one period of the low-frequency pulse, the nonlinear propagation and scattering becomes different and the nonlinear scattering can be detected if the nonlinear propagation is corrected for.The correction of nonlinear propagation can be in the form of a filter, and a method for estimating this filter is also presented in the last part. Based on statistical analysis of the filter, it is shown that the average suppression of linear scattering using the proposed correction filter, is dependent on the homogeneity of the relation between the first and second pulse over the receive beam. Said in another way; if this relation is not constant over the receive beam, the optimal correction for a given signal segment is dependent on the unknown distribution of scatterers within the beam.The level of suppression of linear scattering using the proposed filter method will be dependent on the transmit beam setup. A simulation study where the effect of aperture size relationship between the low- and high-frequency beams and f-number of the high-frequency beam on the level of suppression of linear scattering is presented. In order to achieve a high degree of homogeneity, the diffraction of the HF and LF beams should be equal, which is not trivial to achieve in a medium with attenuation. Choosing the aperture sizes in order for the fresnel numbers to be equal for the two beams was thought to yield the optimal setup, but as attenuation affects the low and high-frequency pulses differently, this is not necessarily  true. The level of suppression of linear scattering increases when the the high-frequency aperture is increased, making the beam narrower, but the low-frequency aperture must also be increased accordingly.

In contrast enhanced ultrasound images (CEUS) that use microbubbles, nonlinear propagation of ultrasound creates artefacts which significantly impact the qualitative and quantitative assessments of tissue perfusion. Such artefact originates from tissue reflecting/scattering nonlinearly propagated ultrasound pulse. Consequently such tissue is misclassified as microbubbles which also generate nonlinear signals. This thesis reports the development and evaluation of an algorithm to reduce the nonlinear propagation artefact in CEUS. The method was evaluated in simulations, and on in vitro and in vivo data at both high and low ultrasound frequencies. Ways to further improve the performance of the method were also investigated. Firstly, the artefact correction algorithm was developed. The algorithm makes use of two independent datasets that are acquired simultaneously during CEUS; the Bmode image, which is dominated by tissue information, and the contrast specific image, which contains information on blood (signal) due to microbubbles, but confounded with some amount of tissue signals (artefact). The unwanted tissue contribution of the contrast specific image is reconstructed by estimating the two components that make up this contribution, namely, the underlying tissue distribution and the nonlinear point spread function (PSF) of the imaging system. To initially evaluate the algorithm, a simulation platform was developed to study artefact generation at various Mechanical Indices (MI), microbubble concentrations and frequencies. The algorithm was then evaluated using the simulation data. The results show that the algorithm is able to reduce the nonlinear propagation artefact at different MI, concentration and frequency under both ideal and noisy conditions. Next, artefact correction was applied to carotid artery imaging. The performance of the algorithm was evaluated using flow phantoms with large and small vessels containing microbubbles of various concentrations at different acoustic pressures. The algorithm significantly reduces nonlinear artefacts while maintaining the contrast signal from bubbles to increase the contrast to tissue ratio (CTR) by up to 11 dB. Contrast signal from a small vessel of 600 µm in diameter buried in tissue artefacts prior to correction is recovered after the correction. The algorithm was then evaluated using in vivo CEUS data acquired on patients’ carotid arteries. The algorithm is able to increase the CTR at the far-wall by up to 7.4 dB in vivo. Artefact correction was then improved by taking the spatial variance of the ultrasound field into account and improving the nonlinear PSF estimation. The new version of the algorithm was tested on in vitro and in vivo data and the improvements verified. The new version of the algorithm provides an additional increase in CTR by up to 5.4 dB in the far field, 4.3 dB at focus and 3.2 dB in the near field for the in vitro data over previous results. The additional increase in CTR for the in vivo data is up to 4 dB more in the near field and 5 dB more in the far field over the previous results. Nonlinear propagation correction was also applied to deep tissue imaging where lower ultrasound frequency than carotid imaging was used. The algorithm could suppress tissue signal more than 6 dB. However, due to the strong presence of the microbubbles in the B-mode image at low frequencies, the algorithm reduces microbubble signal by up to 2 dB. The resulting increase in CTR is up to 4 dB under specific imaging conditions. However, depending on the imaging geometry and acquisition settings used, it could fail to produce an increase in CTR. A possible future direction is to combine the algorithm with an attenuation correction method to improve perfusion quantification. The clinical efficacy of the combined nonlinear propagation and attenuation correction could be evaluated. Given that the method is purely post-processing, it is easier to implement it on current commercial scanners than some other existing techniques. The implementation of the algorithm using GPUs could be investigated and could possibly instigate translation into clinics.

L’imagerie ultrasonore harmonique, qui repose sur la non linéarité du milieu de propagation, est une technique d’imagerie clinique qui améliore la résolution des images. La mesure ultrasonore du paramètre local de non linéarité d'un milieu est une voie de recherche qui amènerait de nouvelles perspectives dans le domaine de la caractérisation des tissus. Cependant, l'accès à cette information se heurte à deux écueils : d'une part il n’existe pas actuellement de méthode de mesure de ce paramètre à partir du mode écho classique et d'autre part, les outils de simulation prenant en compte la non-linéarité du milieu sont peu développés. Une méthode de spectre angulaire a donc été proposée afin de calculer le champ de pression dans des milieux de non linéarité inhomogène. Ce champ de pression est ensuite utilisé pour engendrer des images échographiques contenant l’information harmonique. Cette méthode spectrale a été portée sur GPU afin d’accélérer le calcul et a été intégrée dans un logiciel libre : CREANUIS. Dans un deuxième temps, une extension d’une méthode comparative (ECM) a été proposée pour prendre en compte des milieux de non linéarité non homogène, fonctionnant en mode écho. Grâce aux outils de simulation développés, différentes configurations ont été utilisées pour la mise au point de l’ECM qui a ensuite été validée à partir d'objets tests et in vitro sur foies d’animaux. Même si la méthode de mesure présente une résolution relativement faible, les images obtenues démontrent le potentiel de l’imagerie du paramètre de non linéarité des tissus
Harmonic imaging, based on the propagated medium nonlinearity, is a clinical imaging technique which increases the resolution of ultrasound images. The ultrasound measure of the local nonlinear parameter brings new perspectives in term tissues characterization. However, access to this information suffers from two strong points: from one hand, there is no current measurement method of this parameter in echo mode configuration and on the other hand, the simulation tools taking into account the nonlinearity are not many developed. An angular spectrum method has been proposed to compute the nonlinear pressure field with inhomogeneous nonlinear parameter. This pressure field is then used to generate ultrasound images containing the harmonic component. This spectral approach has been implemented on a GPU in order to accelerate the computation and package in a free software made available to the scientific community under the name CREANUIS. In a second time, a extension of a comparative method (ECM) has been proposed to take into account media with inhomogeneous nonlinearity, working an echo mode configuration. Thanks the developed simulation tools, different configurations have been used to parameterize and to evaluate the ECM which has then be validated on test objects and in vitro animal’s livers. Even if the measure presents a relatively weak resolution, the obtained images demonstrated a high potential in the nonlinear parameter imaging of tissues

Models and methods for investigation of reverberations in nonlinear imaging techniques are presented in this thesis. Four independent papers provide insight on nonlinear propagation effects, a theoretical description of reverberations and the effects of reverberations on conventional and second-harmonic ultrasound imaging. Two papers, Paper A and C, describe methods used to investigate nonlinear distortion and reverberations, whereas Paper B and D concentrate on acoustic phenomena and performance of conventional and second-harmonic imaging. Paper A provides a comparison of Field II, the Texas code and Abersim; three freely available simulation tools. If analytic solutions exist, these are used as gold standards for the comparison, and when they do not; high resolution Field II or Texas code simulations are defined to be the gold standard. The comparison suggests that Abersim performs equivalent or better than the two other methods in solving diffraction, attenuation and nonlinear distortion. In Paper B, the effects of transmit beamforming and safety regulations on second-harmonic generation at two different frequencies are investigated. The safety regulations are imposed through a limitation of the maximum mechanical index of the transmit beam. Abersim is used as the simulation tool. The results suggest that the two frequencies perform equivalently when the transmit beamforming is equal in terms of wavelengths and the medium has a linear-in-frequency attenuation. Nonlinear frequency dependent attenuation and heterogeneous effects are suggested to be the main cause of the reduced improvements of second-harmonic imaging at higher frequencies. Paper C presents a time-domain Spectral Element Method for nonlinear propagation in a finite spatial domain. The method is shown to perform well when compared with analytic plane wave solutions and in a two-dimensional comparison with Abersim. The Spectral Element Method is suggested to be accurate for heterogeneous media, but this is not investigated or verified. The last paper concentrate on reverberations. A mathematical description of reverberations is presented along with a classification system. The main results state that reverberations always act in reciprocal pairs, and that secondharmonic suppression of reverberations is a combined effect of transmit beam intensity and a reverberation weight filter presented in the paper. The thesis provides insight on the description of reverberations and how they can be investigated. The influence of reverberations on ultrasound imaging is suggested to be more severe in applications where the object of interest is fully submerged in heterogeneous tissue. Deeper understanding of ultrasound acoustics may lead to new nonlinear imaging techniques where the noise contribution can be separated from the first-order echo. In turn, this might provide better gray scale images and ultrasound diagnoses.

The objective of this research is to develop large signal modeling and optimization methods for Capacitive Micromachined Ultrasonic Transducers (CMUTs), especially when they are used in an array configuration. General modeling and optimization methods that cover a large domain of CMUT designs are crucial, as many membrane and array geometry combinations are possible using existing microfabrication technologies. Currently, large signal modeling methods for CMUTs are not well established and nonlinear imaging techniques utilizing linear piezoelectric transducers are not applicable to CMUTs because of their strong nonlinearity. In this work, the nonlinear CMUT behavior is studied, and a feedback linearization method is proposed to reduce the CMUT nonlinearity. This method is shown to improve the CMUT performance for continuous wave applications, such as high-intensity focused ultrasound or harmonic imaging, where transducer linearity is crucial. In the second part of this dissertation, a large signal model is developed that is capable of transient modeling of CMUT arrays with arbitrary electrical terminations. The developed model is suitable for iterative design optimization of CMUTs and CMUT based imaging systems with arbitrary membrane and array geometries for a variety of applications. Finally, a novel multi-pulse method for nonlinear tissue and contrast agent imaging with CMUTs is presented. It is shown that the nonlinear content can be successfully extracted from echo signals in a CMUT based imaging system using a multiple pulse scheme. The proposed method is independent of the CMUT geometry and valid for large signal operation. Experimental results verifying the developed large signal CMUT array model, proposed gap feedback and multi-pulse techniques are also presented.

Les agents de contraste sont de petites bulles qui répondent non linéairement lorsqu’ils sont exposés à ultrasons. La réponse non-linéaire donne la possibilité d’images échographiques harmoniques qui a beaucoup d’avantages sur l’imagerie fondamentale. Toutefois, afin d’accroître l’échographie de contraste d’imagerie harmonique de performance nous devons d’abord comprendre la propagation non linéaire d’ultrasons. La non-linéarité du milieu déforme l’onde qui se propage, tels que les harmoniques commencent à se développer. La théorie qui a été prévue est la mise en œuvre, qui a permis une nouvelle méthode de modélisation de propagation des ultrasons non-linéaire. La connaissance acquise au cours de ce processus a été utilisée pour construire un deuxième signal à composantes multiples pour la réduction des harmoniques générées en raison des non-linéarités des tissus. En conséquence, la détection d’agents de contraste ultrasonore aux harmoniques a été augmentée. Une puissante technique d’imagerie échographique (Pulse inversion) a été renforcée avec le deuxième signal pour la réduction des harmoniques. Qu’est-ce qui a été appris pendant l’investigation : le pulse inversion technique a donné une nouvelle phase codée, appelée inversion de seconde harmonique. En outre, il a été noté que pour différents types de médias le niveau de distorsion de l’impulsion à ultrasons est différent. Cela dépend en grande partie du paramètre non linéaire B / A. Les travaux sur ce paramètre n’a pas été fini, mais il est quand même important de continuer dans cette direction puisque B / A imagerie avec des agents de contraste ultrasonore a beaucoup de potentiel
Ultrasound contrast agents are small micro bubbles that respond nonlinearly when exposed to ultrasound wave. The nonlinear response gives possibility of harmonic ultrasound images which has many advantages over fundamental imaging. However, to increase ultrasound contrast harmonic imaging performance we must first understand nonlinear propagation of ultrasound wave. Nonlinear propagation distorts the propagating wave such that higher harmonics appear as the wave is propagating. The theory that was laid down, was allowed implementing a new method of modelling nonlinear ultrasound propagation. The knowledge obtained during this process was used to construct a multiple component second harmonic reduction signal for reduction of their harmonics generated due to the tissue nonlinearities. As a consequence detection of ultrasound contrast agents at higher harmonics was increased. Further more, a powerful ultrasound imaging technique called Pulse Inversion, was further enhanced with multiple component second harmonic reduction signal. What was learned during investigation of the Pulse Inversion, technique lead to a new phase coded ultrasound contrast harmonic method called second harmonic inversion;. Also it was noted that for different type of media the level of distortion of ultrasound pulse is different. It depends largely on the nonlinear parameter B / A. Although the work on this parameter has not been finished it is very important to continue in this direction since B / A imaging with ultrasound contrast agents has a lot of potential

Evolution of vulnerable carotid plaques are crucial reason for cerebral ischemic strokes and identifying them in the early stage can become very important in avoiding the risk of stroke. In order to improve the identification and quantification accuracy of infancy plaques better visualization techniques are needed. Improving the visualization and quantification of neovascularization in carotid plaque using contrast enhanced ultrasound imaging still remains a challenging task. In this thesis work, three optimization techniques are proposed, which showed an improvement in the sensitivity of contrast agents when compared to the conventional clinical settings and insonation strategies. They are as follows:1) Insonation at harmonic specific (2nd harmonic) resonance frequency instead of resonance frequency based on maximum energy absorption provides enhanced nonlinear contribution.2) At high frequency ultrasound imaging, shorter pulse length will provide improved harmonic signal content when compared to longer pulse lengths. Applying this concept to multi- pulse sequencing (Pulse Inversion and Cadence contrast pulse sequencing) resulted in increased magnitude of the remaining harmonic signal after pulse summations.3) Peak negative pressure optimization of Pulse Inversion and Cadence contrast pulse sequencing was showed to further enhance the nonlinear content of the backscattered signal from contrast microbubbles without increasing the safety limits, defined by the mechanical index.The results presented in this thesis are based on computational modeling (Bubblesim software) and as a future continuation we plan to verify the simulation results with vitro studies.

Utilisés dans de nombreux domaines d'applications, les ultrasons se révèlent être sensibles aux propriétés visco-élastiques des milieux traversés. L'investigation spatiale et temporelle des propriétés visco-élastiques des matériaux par méthodes ultrasonores permet notamment le contrôle de l'intégrité de structures ainsi que le suivi de processus. Un dispositif auto-calibrée en émission-réception, basé sur l'application du principe de réciprocité, a été développé pour la mesure du paramètre non linéaire B/A. Cette mesure repose sur une étude harmonique des signaux ultrasonores se propageant dans le milieu. L’instrumentation ultrasonore mise en œuvre a été choisie pour assurer une mesure rapide en émission-réception du paramètre B/A imposant un choix technologique spécifique. L'évolution au cours du temps des paramètres acoustiques dans les matériaux de type sol-gel fait apparaitre un temps caractéristique lié à la structuration du matériau (gélification). Les temps de gélification extraits des mesures permettant de retrouver la loi d'Arrhenius cohérente avec celle obtenue par des méthodes rhéologiques conventionnelles. Une image du paramètre non linéaire a été réalisée sur un fantôme contenant deux fluides non miscibles (eau et huile de silicone). A travers ces deux applications, nous montrons l'efficacité du système de mesure du paramètre non linéaire dans le cadre du suivi d'un matériau en évolution ainsi qu'en imagerie
Used in many application areas, ultrasound proved to be sensitive to determine viscoelastic properties. The spatial and temporal investigation of viscoelastic properties of materials by ultrasonic methods can be used to monitor structure integrity and processes. A self-calibrated method, based on reciprocity principle has been developed for measuring the nonlinear parameter B/A. Instrumentation has been development to ensure the rapid determination of the parameter B/A imposing a specific technology. The time evolution of the acoustic parameters of sol-gel materials shows a characteristic time related to the structuration of the material (Arrhnius law). A picture of the nonlinear parameter was performed on a phantom containing two immiscible fluids (water and silicone oil). Through these two examples, the effectiveness of the nonlinear parameter measurements has shown in the follow-up of a material changes as well as imaging

Neste trabalho é apresentada uma nova modalidade de imagens elastográficas baseada na emissão acústica, quando um meio é submetido à radiação ultrassônica. Esta técnica está sendo denominada de Acustografia por Pulso/Emissão (APE). Características não-lineares da propagação acústica de ondas ultrassônicas, e a resposta mecânica vibracional, foram utilizadas como artifício para geração de imagens com frequências da ordem de quilohertz (kHz), a partir da excitação com ondas ultrassônicas na ordem de megahertz. Para produzir imagens com essa nova modalidade, simuladores de tecido biológicos foram construídos com diferenças de rigidez localizadas, e submetidos a uma radiação ultrassônica focalizada (MHz). O som emitido devido a interação da onda ultrassônica com a região de interesse era gravado e processado de modo a associar a cada pequena porção do tecido a um valor relacionado a rigidez para a formação da imagem. Os resultados mostraram que o método pode produzir imagens associadas às alterações viscoelásticas das amostras. A resolução espacial mostrou-se fortemente ligada a morfologia do campo acústico de excitação, sendo possível detectar estruturas da ordem de 0,25 mm isoladamente. A técnica de aquisição, desenvolvida e apresentada neste trabalho, é similar a técnica de vibroacustografia todavia, com uma instrumentação reduzida e com a possibilidade de obtenção de mais informações da estrutura do meio material, a partir dos fenômenos não lineares observados. Estudos pilotos de aplicação desta nova técnica e com a vibroacustografia, foram realizados e comparados para a avaliação de potenciais aplicações, por exemplo, na avaliação do sinal acústico diante de mudanças nas propriedades viscoelásticas do meio induzidas por mudança de temperatura; formação de imagens em meios com inclusões isoecogênicas e com rigidez ligeiramente diferentes; geração de imagens de estrutura óssea in vitro.
In this work is presented a new modality of elastography images based on the acoustic emission when a material medium was subjected to a ultrasound radiation.This tecnique Nonlinearity behavior of the acoustic wave propagation and the vibrational mechanical response were used to produce images from kilohertz frequencies when the sample was excited by ultrasound waves in megahertz. To produce images with this modality, tissue mimicking phantoms were made with stiffness in homogeneities and subjected a focused ultrasound radiation pulses. The sound emitted due the interaction of the ultrasound wave with the region of interest was recorded and processed in order to associate each small portion of the tissue to a value for image formation. The results showed that this method can produce images associated to the viscoelastic changes of the samples. The spatial resolution have showed strongly linked to the morphology of the excitation acoustic field, this way was possible to detect isolated structures in order of 0.25 mm. The acquisiton technique developed and presented in this work is similar to the vibroacoustography technique, however with reduced instrumentation setup and with the possibility to acquire further information about the structure of the material from the nonlinear phenomenal. Preliminary studies of this new technique and the vibroacoustography were made and compared to evaluate the potential applications, for example, in the evalution of the acoustic signal behavior due changes in the viscoelastic properties changes induced by temperature variations; image formation in the medium with lightly stiffness inclusions; generation of the images of bone structure in vitro.

Microbubble contrast agents for ultrasound are widely used in numerous medical applications, both diagnostic and therapeutic. Due to their size, similar to that of red blood cells, microbubbles are able to traverse the entire vascular bed, enabling their utilization for applications such as tumour diagnosis. Vaporizable submicron droplets of liquid perfluoro- carbon potentially represent a new generation of extravascular contrast agents for ultrasound. Droplets of a few hundred nanometers in diameter have the ability to extravasate selectively in regions of tumour growth while staying intravascular in healthy tissues. Upon extravasation, these droplets may be vaporized with ultrasound and converted into gas bubbles. In this thesis we argue that vaporized submicron perfluorocarbon droplets possess the necessary stability and acoustic characteristics to be potentially applicable as a new gener- ation of extravascular ultrasound contrast agents. We examine, separately, the ultrasound conditions necessary for vaporization of the droplets into microbubbles, the size and stability of these bubbles following vaporization, on timescales ranging from nanoseconds to minutes, and the bubbles’ acoustic response to incident diagnostic ultrasound. We show that submicron droplets may be vaporized into bubbles of a few microns in diameter using single ultrasound pulse within the diagnostic range. The efficiency of conversion is shown to be on the order of at least 10% of the exposed droplets converting into stable microbubbles. The bubbles are shown to be stabilized by the original coating material encapsulating the droplet precursors, and be stable for at least minutes following vaporization. Finally, vaporized droplets are shown to be echogenic, with acoustic characteristics comparable to these of the commercially available ultrasound contrast agents. The results presented here show that vaporized droplets possess the necessary stability properties and echogenicity required for successful application as contrast agents, suggesting potential for their future translation into clinical practice.

碩士
國立中正大學
資訊工程研究所
103
Ministry of Health and Welfare showed that the main cause of death in Taiwan and around the world is cardiovascular disease, and the resulted number of death is increasing. Most cardiovascular diseases are closely related to atherosclerosis. Since the carotid is the main blood supply channel to the brain, its atherosclerosis will cause stroke and is worthy of monitoring. Ultrasound imaging is a cheap and risk-free method to examine the carotid wall for any abnormality. Most methods for estimating the carotid stiffness is to calculate the ratio of lumen diameter (area) and blood pressure between the systolic and diastolic period, but the accuracy and stability would be influenced by many factors. Some studies showed that the stiffness can be assessed by calculating the approximate entropy (ApEn) of that long-term cross section change of carotid. The ApEn and cross-ApEn are nonlinear analysis methods that have been used to analyze many kinds of physiological signals to distinguish abnormality from the normal states. Our goals are two-folded. The first is to verify if the nonlinear analysis results of long term carotid diameter change will be influenced by different image segmentation methods or other factors. The second is to evaluate if the nonlinear analysis can make significant difference between normal and abnormal carotid movements. Our experimental results show that both ApEn and cross-ApEn can make significant difference between normal subjects and carotid atherosclerosis patients, but ApEn will be biased by the heart rate. It works only when the heart rate is normalized before comparisons between groups. Different image segmentation methods will not deviate both entropy calculations.

The focus of the thesis is on the development of a few stochastic search schemes for inverse problems and their applications in medical imaging. After the introduction in Chapter 1 that motivates and puts in perspective the work done in later chapters, the main body of the thesis may be viewed as composed of two parts: while the first part concerns the development of stochastic search algorithms for inverse problems (Chapters 2 and 3), the second part elucidates on the applicability of search schemes to inverse problems of interest in tomographic imaging (Chapters 4 and 5). The chapter-wise contributions of the thesis are summarized below. Chapter 2 proposes a Monte Carlo stochastic filtering algorithm for the recursive estimation of diffusive processes in linear/nonlinear dynamical systems that modulate the instantaneous rates of Poisson measurements. The same scheme is applicable when the set of partial and noisy measurements are of a diffusive nature. A key aspect of our development here is the filter-update scheme, derived from an ensemble approximation of the time-discretized nonlinear Kushner Stratonovich equation, that is modified to account for Poisson-type measurements. Specifically, the additive update through a gain-like correction term, empirically approximated from the innovation integral in the filtering equation, eliminates the problem of particle collapse encountered in many conventional particle filters that adopt weight-based updates. Through a few numerical demonstrations, the versatility of the proposed filter is brought forth, first with application to filtering problems with diffusive or Poisson-type measurements and then to an automatic control problem wherein the exterminations of the associated cost functional is achieved simply by an appropriate redefinition of the innovation process. The aim of one of the numerical examples in Chapter 2 is to minimize the structural response of a duffing oscillator under external forcing. We pose this problem of active control within a filtering framework wherein the goal is to estimate the control force that minimizes an appropriately chosen performance index. We employ the proposed filtering algorithm to estimate the control force and the oscillator displacements and velocities that are minimized as a result of the application of the control force. While Fig. 1 shows the time histories of the uncontrolled and controlled displacements and velocities of the oscillator, a plot of the estimated control force against the external force applied is given in Fig. 2. (a) (b) Fig. 1. A plot of the time histories of the uncontrolled and controlled (a) displacements and (b) velocities. Fig. 2. A plot of the time histories of the external force and the estimated control force Stochastic filtering, despite its numerous applications, amounts only to a directed search and is best suited for inverse problems and optimization problems with unimodal solutions. In view of general optimization problems involving multimodal objective functions with a priori unknown optima, filtering, similar to a regularized Gauss-Newton (GN) method, may only serve as a local (or quasi-local) search. In Chapter 3, therefore, we propose a stochastic search (SS) scheme that whilst maintaining the basic structure of a filtered martingale problem, also incorporates randomization techniques such as scrambling and blending, which are meant to aid in avoiding the so-called local traps. The key contribution of this chapter is the introduction of yet another technique, termed as the state space splitting (3S) which is a paradigm based on the principle of divide-and-conquer. The 3S technique, incorporated within the optimization scheme, offers a better assimilation of measurements and is found to outperform filtering in the context of quantitative photoacoustic tomography (PAT) to recover the optical absorption field from sparsely available PAT data using a bare minimum ensemble. Other than that, the proposed scheme is numerically shown to be better than or at least as good as CMA-ES (covariance matrix adaptation evolution strategies), one of the best performing optimization schemes in minimizing a set of benchmark functions. Table 1 gives the comparative performance of the proposed scheme and CMA-ES in minimizing a set of 40-dimensional functions (F1-F20), all of which have their global minimum at 0, using an ensemble size of 20. Here, 10 5 is the tolerance limit to be attained for the objective function value and MAX is the maximum number of iterations permissible to the optimization scheme to arrive at the global minimum. Table 1. Performance of the SS scheme and Chapter 4 gathers numerical and experimental evidence to support our conjecture in the previous chapters that even a quasi-local search (afforded, for instance, by the filtered martingale problem) is generally superior to a regularized GN method in solving inverse problems. Specifically, in this chapter, we solve the inverse problems of ultrasound modulated optical tomography (UMOT) and diffraction tomography (DT). In UMOT, we perform a spatially resolved recovery of the mean-squared displacements, p r of the scattering centres in a diffusive object by measuring the modulation depth in the decaying autocorrelation of the incident coherent light. This modulation is induced by the input ultrasound focussed to a specific region referred to as the region of interest (ROI) in the object. Since the ultrasound-induced displacements are a measure of the material stiffness, in principle, UMOT can be applied for the early diagnosis of cancer in soft tissues. In DT, on the other hand, we recover the real refractive index distribution, n r of an optical fiber from experimentally acquired transmitted intensity of light traversing through it. In both cases, the filtering step encoded within the optimization scheme recovers superior reconstruction images vis-à-vis the GN method in terms of quantitative accuracies. Fig. 3 gives a comparative cross-sectional plot through the centre of the reference and reconstructed p r images in UMOT when the ROI is at the centre of the object. Here, the anomaly is presented as an increase in the displacements and is at the centre of the ROI. Fig. 4 shows the comparative cross-sectional plot of the reference and reconstructed refractive index distributions, n r of the optical fiber in DT. Fig. 3. Cross-sectional plot through the center of the reference and reconstructed p r images. Fig. 4. Cross-sectional plot through the center of the reference and reconstructed n r distributions. In Chapter 5, the SS scheme is applied to our main application, viz. photoacoustic tomography (PAT) for the recovery of the absorbed energy map, the optical absorption coefficient and the chromophore concentrations in soft tissues. Nevertheless, the main contribution of this chapter is to provide a single-step method for the recovery of the optical absorption field from both simulated and experimental time-domain PAT data. A single-step direct recovery is shown to yield better reconstruction than the generally adopted two-step method for quantitative PAT. Such a quantitative reconstruction maybe converted to a functional image through a linear map. Alternatively, one could also perform a one-step recovery of the chromophore concentrations from the boundary pressure, as shown using simulated data in this chapter. Being a Monte Carlo scheme, the SS scheme is highly parallelizable and the availability of such a machine-ready inversion scheme should finally enable PAT to emerge as a clinical tool in medical diagnostics. Given below in Fig. 5 is a comparison of the optical absorption map of the Shepp-Logan phantom with the reconstruction obtained as a result of a direct (1-step) recovery. Fig. 5. The (a) exact and (b) reconstructed optical absorption maps of the Shepp-Logan phantom. The x- and y-axes are in m and the colormap is in mm-1. Chapter 6 concludes the work with a brief summary of the results obtained and suggestions for future exploration of some of the schemes and applications described in this thesis.