Standard source method in passive acoustic thermal tomography

Potentialities of passive acoustic thermal tomography in reconstructing the 2D temperature distribution in a human body are studied. Special attention is given to the estimation of the maximal temperature value. A method for its exact reconstruction is proposed. The method uses the assumption that the temperature distribution is formed by a local heat source and is based on the selection of the parameters of such a source by the minimization of the residual of the measured and hypothetical values of the acoustic brightness temperature. The accuracy of the determination of the maximal in-depth temperature by different methods is analyzed by numerical simulation. It is demonstrated that the proposed method provides a higher accuracy than Tikhonov’s methods of global and local regularization, especially with a heat source at great depth. The proposed method is shown to cause no systematic error in the reconstruction of temperature peaks at great depth. The possibility of reconstructing a two-peak temperature distribution by the proposed method is demonstrated.     

Experimental studies of passive correlation tomography of incoherent acoustic sources in the megahertz frequency band

Correlation properties of thermal acoustic radiation in the megahertz frequency band are studied experimentally. The amplitudes of correlation peaks measured at the sum of the delays that correspond to the direct signal propagation between the piezoelectric transducers are found to depend on the relative transducer positions. This effect is explained by a possible difference between the receive patterns of the transducers and the patterns of their intrinsic thermal radiation. The correlation of signals received from a spatial region heated above the ambient medium is measured. The correlation between the received signals is found to depend on the time of heating of the emitter’s working medium. Numerical calculation of temperature distributions and the allowance for the decorrelation effect due to the spatial extent of the source provide a quantitative agreement between the theoretical and experimental results. Estimates of the spatial resolution achievable with the given experimental configuration show that it is close to the coherence length of the received radiation.     

声速不均匀介质的光声成像重建算法

为提高声速不均匀介质的光声成像精度,提出一种基于反卷积的光声成像重建算法.本算法不需预先知道介质的声速分布.先通过探测到的光声信号构造出一个新函数,并用不同位置探测到的光声信号间的相关性来估计空间两点间的声波传播时间,以补偿声速的不均匀性.然后基于反卷积方法由该函数解出待测组织内的电磁波吸收分布.仿真研究结果表明,当介质声速差异在10%以内时,重建图像能正确反映待测目标的大小、位置和电磁波吸收系数,算法具有良好的抗噪性能.由于生物软组织内的声速差异一般小于10%,因此本算法是一种有效的光声成像重建算法.     

The directivity pattern of an interferometer for measuring thermal acoustic radiation

The directivity patterns of a pair of piezoelectric transducers for measuring the spatial correlation function of sound pressures produced by sources of thermal acoustic radiation in the megahertz frequency range are calculated. Sources in the form of a heated plane or strip are considered. The signal detection by two circular or rectangular piezoelectric transducers and by focusing transducers is studied. It is demonstrated that, for measuring the correlation function, the piezoelectric transducers must partially overlap. To determine the directivity pattern with a strong dependence on the distance between the heated object and the pair of piezoelectric transducers, focusing piezoelectric transducers should be used. The results obtained offer possibilities for a noninvasive measurement of the absorption coefficient of a medium and also for the realization of the previously proposed [20] passive acoustic thermotomograph, which does not use a priori information on the absorption coefficient of the medium.     

多轴差分吸收光谱断层扫描重建烟羽空间分布

为了实现烟羽二维空间分布的精确重建, 建立了被动多轴差分吸收光谱断层扫描系统,实现了多台被动多轴差分吸收光谱系统对废气烟羽空间分布的测量。首先,介绍了多轴差分吸收光谱系统及其反演气体浓度的机理。接着,使用代数迭代算法对不同的重建模型,采用不同的扫描光路进行了重建模拟,并设计了重建程序。然后,对数值模拟仿真结果进行了分析比较。最后,搭建了多轴差分吸收光扫描系统平台,进行了外场试验。数值模拟的结果显示：MAX-DOAS层析技术能精确的重建出烟羽模型的二维空间分布,四光源光路的重建误差约是双光源光路重建误差的三分之一,四光源重建时间约是双光源重建时间的四分之一,且双峰模型的重建误差大于单峰模型的重建误差。外场试验的结果显示：重建图像的积分数据与多轴差分吸收光谱测得的投影数据是一致的,说明重建出的烟羽空间分布符合实际情况。研究表明,数值模拟的结果与外场试验的结果具有一致性。     

Maximum likelihood estimates in correlation acoustic thermotomography

Informative capabilities of active—passive acoustic thermotomography that allows a separate reconstruction of the local values of intrinsic and background temperature, absorption coefficient, and ultrasonic velocity are discussed. An iterative procedure based on the maximum likelihood method that provides unbiasedness of estimates is proposed for the correlation processing of a large body of experimental data. The sensitivity of a thermotomographic system is connected to the limitations imposed on the accumulation factor by actual experimental conditions. A sensitivity enhancement is possible at the cost of loosening the requirements on the resolution of the image under reconstruction. Results of numerical simulation of a thermotomographic experiment in narrowband and broadband modes of operation are presented.     

声学CT复杂温度场重建研究

为提高声学CT复杂温度场重建能力,提出一种利用Markov径向基函数逼近和Tikhonov正则化的温度场重建算法,简称MTR算法。该算法首先用Markov径向基函数的线性组合,逼近介质中的复杂声速场分布,然后利用介质中多路径声波传播时间和Tikhonov正则化法,求解声速场分布,进而利用声速与温度的关系获得温度分布。对单热点、三热点和五热点温度场模型进行了仿真重建,结果表明MTR算法热点定位精度高,重建误差小。开发了声学CT温度场重建实验系统,用电加热器在内装1200 kg大豆的实验粮仓中形成热点,MTR重建结果能正确反映热点位置,热点温度重建误差1.3%。可见,MTR算法复杂温度场重建能力强,可望用于实际储粮温度分布监测。      

基于电阻抗层析成像的高强度聚焦超声温度监测技术

作为一种对正常组织无损伤且不易引起癌细胞转移的非入侵肿瘤治疗手段,高强度聚焦超声(HIFU)治疗过程中焦域的温度监测是实现剂量精准控制的关键.本文基于生物组织的温度-电阻抗的关系,将电阻抗层析成像(EIT)和HIFU治疗相结合,提出了一种利用组织焦平面的表面电压实现电阻抗重构的检测技术.建立了HIFU治疗和EIT综合系统模型,在考虑组织的声吸收条件下,对三维Helmholtz方程在柱坐标下的声场计算进行了二维简化,并引入Pennes生物热传导方程来计算HIFU焦域的声压和温升分布特性;引入生物组织的温度-电阻抗关系,基于麦克斯韦电磁场理论,建立了具有温度分布HIFU焦域的电流和电压计算模型,利用恒流注入的边界条件实现电场计算,获得焦平面的表面电压分布.在数值计算中,利用实验聚焦换能器参数,模拟了在固定声功率下组织焦域的声场和温度场分布,以及中心和偏心聚焦条件下不同治疗时刻的电导率分布;然后通过对称电极的循环电流注入,计算了组织模型焦平面内的电流密度和电势分布,获得了焦平面圆周分布的表面电极电压;进一步采用修正的牛顿-拉夫逊算法,利用32×32的表面电极电压实现了焦平面内电导率分布的重建.结果表明,基于温度-电阻抗关系的EIT电导率重建技术不但能准确定位HIFU焦域中心,还能恢复HIFU治疗中焦域的温度分布,证明了EIT用于HIFU治疗中温度监测的可行性,为其疗效评估和剂量控制提供了一种无创电阻抗测量和成像新方法.     

光声信号的声透镜层析成像研究

提出了一种用声透镜实现光声层析成像的新模式。从理论上计算出了声透镜的响应，测出了已知声场中标准物像面处的声场分布。考虑到圆形活塞振源的指向性，对代表物成像进行了理论修正，并与实验结果做了对比分析。研究表明，利用声透镜可以实现光声层析成像，并经图像重构得到了生物组织中异物的光声图像，横向、纵向分辨力较高。     

Focused array transducer for two-dimensional optoacoustic tomography

Optoacoustic (OA) imaging utilizes short laser pulses to create acoustic sources in tissue and time resolved detection of generated pressure profiles for image reconstruction. The ultrasonic transients provide information on the distribution of optical absorption coefficient that can be useful for early cancer diagnostics. In this work a new design of wide-band array transducer is developed and tested. The array consists of 32 focused piezo-elements made of PVDF slabs imposed on a cylindrical surface. A single array element response to an OA signal coming from arbitrarily located point source is investigated theoretically and experimentally. The measured signals correspond well to numerically calculated ones. Focal zone maps of the elements with aperture angles 30 degrees and 60 degrees are presented and discussed; the resolution in direction perpendicular to the imaging plane is determined. Point spread function of the whole array is calculated using experimentally obtained signals from the sources located at different distances from the array. Backprojection algorithm is employed for reconstruction of the optoacoustic images. It is shown that the spatial resolution of the images yielded by the proposed array increases significantly compared to previous transducer designs.     

Passive broadband acoustic thermometry

The 1D internal (core) temperature profiles for the model object (plasticine) and the human hand are reconstructed using the passive acoustothermometric broadband probing data. Thermal acoustic radiation is detected by a broadband (0.8–3.5 MHz) acoustic radiometer. The temperature distribution is reconstructed using a priori information corresponding to the experimental conditions. The temperature distribution for the heated model object is assumed to be monotonic. For the hand, we assume that the temperature distribution satisfies the heat-conduction equation taking into account the blood flow. The average error of reconstruction determined for plasticine from the results of independent temperature measurements is 0.6 K for a measuring time of 25 s. The reconstructed value of the core temperature of the hand (36°C) generally corresponds to physiological data. The obtained results make it possible to use passive broadband acoustic probing for measuring the core temperatures in medical procedures associated with heating of human organism tissues.     

快速傅里叶算法在哈特曼夏克传感器波前重构算法中的应用

提出了一种应用快速傅里叶变换算法提高哈特曼－夏克波前传感器波前重构实时性的快速算法，在根据波前斜率值应用最小二乘法估计波前相位的过程中，应用快速傅里叶变换算法进行方程的对角化和相位值的解耗，算法精站度，稳定，空间分辨率越高，算法实时性的优越性就越显著。     

球面近场声全息中的阵列传声器分布与球面数值积分

球形传声器阵列是实现封闭空间三维声场重构的测量前端,传声器在球形阵列面上的分布对三维声场重构的精度有重要影响。针对球面近场声全息方法,结合I.H.Sloan,Spherical t-designs,J.Fliege等球面数值积分法,检验传声器数目、传声器几何位置分布、积分权重、波数、基函数扩展项数、声场重构半径等参数对声场重构精度的影响。结果表明:Spherical t-designs球面数值积分法与其它积分法相比,在声场重构误差接近的情形下,允许传声器的数目和位置布置有更多的选择,并且在传声器数目一定时,各点积分权重相等,使得球面近场声全息中球面数值积分计算相对简单。      

Acoustic thermometric reconstruction of a time-varying temperature profile

The time-varying temperature profiles were reconstructed in an experiment using a thermal acoustic radiation receiving array containing 14 sensors. The temperature was recovered by performing similar experiments using plasticine, as well as in vivo with a human hand. Plasticine preliminarily heated up to 36.5°C and a human hand were placed into water for 50 s at a temperature of 20°C. The core temperature of the plasticine was independently measured using thermocouples. The spatial resolution of the reconstruction in the lateral direction was determined by the distance between neighboring sensors and was equal to10 mm; the averaging time was 10 s. The error in reconstructing the core temperature determined in the experiment with plasticine was 0.5 K. The core temperature of the hand changed with time (in 50 s it decreased from 35 to 34°C) and space (the mean square deviation was 1.5 K). The experiment with the hand revealed that multichannel detection of thermal acoustic radiation using a compact 45 × 36 mm array to reconstruct the temperature profile could be performed during medical procedures.     

Spatial resolution limits for the reconstruction of acoustic source strength by inverse methods

One method for deducing the strength of an acoustic source distribution from measurement of the radiated field involves the inversion of the matrix of frequency response functions relating the field measurement points to the strengths of a number of point sources used to represent the source distribution. In practice, the frequency response function matrix to be inverted may very often be ill-conditioned. This ill-conditioning will also often result in an ill-posed problem and thus regularization algorithms are used to produce reasonable solutions. For this purpose, Tikhonov regularization has been applied, and generalized cross-validation (GCV) has been introduced as an effective method for determining the proper amount of regularization without prior knowledge of either the source distribution or the contaminating errors. In the present work, the emphasis is placed on the relationship between the spatial resolution of the reconstructed source distribution and the small singular values of the frequency response function matrix to be inverted. However, the use of Tikhonov regularization often suppresses the effect of small singular values and these are in turn often associated with high spatial frequencies of the source distribution. Thus, the process of regularization produces a useful estimate of the acoustic source strength distribution but with a limited spatial resolution. Furthermore, in the field of Fourier acoustics, the spatial resolution of the reconstructed source distribution is usually limited by the wavelength of the radiation. This paper expresses the relationship between estimation accuracy, spatial resolution, noise-level and source/sensor geometry, when a range of inverse sound radiation problems are regularised using Tikhonov regularization with GCV. The results presented form the basis of guidelines that enable the reconstruction of acoustic source strength with a resolution that is finer than the intrinsic half-wavelength limit.     

Separation of chiral molecules by temperature programmed desorption

The Monte Carlo simulation method was used to model thermal desorption of a pair of enantiomers from a solid surface with a chiral periodic pattern of active sites. The main objective of the study was to determine the optimal number of the active sites and their spatial distribution within the unit cell of the surface to achieve the most efficient separation of the enantiomers. For that purpose we tested the series of chiral patterns which were found previously for the equilibrium adsorption. Temperature programmed desorption spectra were calculated using a square lattice of adsorption sites in which the active sites were distributed spatially according to the candidate patterns. Additionally, influence of relaxation of the adsorbed layer on the relative shift of the TPD peaks of the enantiomers was assessed and the key factors affecting the chiral separation were identified.     

Comparison of the efficiencies of Fourier and wavelet expansions in passive acoustic thermal tomography

A comparison of the accuracy achieved in temperature-distribution reconstruction by the Fourier and wavelet expansions in passive acoustic tomography is carried out. Since the use of focused ultrasound in hyperthermia leads to local heating of the tissue, the wavelet representation of such temperature distributions with local fluctuations is more compact than their Fourier representation. It is demonstrated that the compactness of the wavelet representation provides an opportunity to reduce considerably the number of unknown quantities in solving the inverse problem of acoustic thermal tomography and to increase the accuracy of the temperature-distribution reconstruction in comparison with the case of using the Fourier representation. A method for choosing a compact wavelet basis for temperature distributions obtained in the hyperthermia process is proposed.     

一种考虑声线弯曲的温度场重建算法

声波在非均匀温度场中传播时会由于声波的折射而产生声线弯曲现象。为提高非均匀温度场声学CT (Computer Tomography)重建精度,提出一种考虑声线弯曲的重建算法。首先用最小二乘法获得一个不考虑声线弯曲的重建温度场,然后用打靶-插值法确定本征声线出射角,用三角形前向展开法追踪声线,获得此温度场中声波发射/接收器间的本征声线,建立本征声线上声波传播时间与温度分布间的关系,进而实现考虑声线弯曲的最小二乘法温度场重建。单峰、双峰温度场仿真重建结果表明:所采用的本征声线追踪法计算简单运行速度快;考虑声线弯曲后,可明显提高温度场重建精度。因此所提重建算法能更好地适应实际温度场重建需求。      

基于波叠加法的近场声全息空间分辨率增强方法

提出一种基于波叠加法的近场声全息空间分辨率增强方法. 该方法在波叠加法的基础上,利用全息面声压信号求得布置在全息面附近的虚源面上的简单源源强,再根据求得的简单源源强实现对全息面声压的插值,进而利用插值后的全息面声压数据进行重建. 该方法可以提高近场声全息重建图像的空间分辨率,减少测量工作量,简化测量过程. 通过仿真对影响插值结果的参数进行了分析,给出了合理的选取范围;通过仿真和实验研究验证了该方法的有效性. 关键词： 波叠加法 近场声全息 空间分辨率     

Application of the nonregularization method to solving the inverse problem of passive acoustic thermotomography on the wavelet basis

A comparative analysis of reconstruction quality is performed for the reconstruction of the temperature distribution under hyperthermia by the regularization and nonregularization methods, which are used for solving the systems of linear equations following from the statement of the ill-posed inverse problem of passive acoustic thermotomography. The basis functions are chosen to be wavelets, which allows a compact representation of the temperature peak under reconstruction. It is shown that, when deep-seated parts of tissue are heated, the nonregularization method gives a much smaller systematic error of temperature reconstruction at the focusing point. At the same time, the random error of reconstruction increases. The nonregularization method of reconstruction can be used in combination with regularization for monitoring hyperthermia procedures in oncology to obtain more detailed information on the in-depth temperature.