X-ray computerized tomography (CT) and acoustic CT are two main medical imaging modalities based on two intrinsically different physical phenomena. X-ray CT is based on x-ray’s attenuation when x-ray passes through medium. It has been well known that the Radon transform is the imaging theory for x-ray CT. Photoacoustic CT is a type of acoustic CT, which is based on differentiating electromagnetic energy absorption among media. In 1998 a new 3D reconstruction concept, the P-transform, was proposed to serve the imaging theory for photoacoustic CT. In this paper it was rigorously proved that both x-ray CT and photoacoustic CT are governed by a unified imaging theory. 3D data acquisition can be completed in 2p stereoangle. This new imaging theory realized, in part, the dream of all physicists, including Albert Einstein, who have long believed that our world is ultimately governed by few simple rules.
Photoacoustic phenomenon has been investigated. An experimental protocol using photoacoustic principle has been proposed to image the regional distribution of electromagnetic energy absorption density in an object. This paper presents a rigorous method for photoacoustic image reconstruction. It is proved that photoacoustic image reconstruction is intrinsically a three-dimensional (3D) procedure. The spatial smear function (SSF) is introduced. An example using synthetic data proves the validity of photoacoustic image reconstruction theory proposed by the paper. The example shows that even the first order approximation of photoacoustic image reconstruction gives good agreement with the reality. It is also seen from the example that the accuracy and noise immunity of the reconstruction procedure depend on the experimental arrangement.
Photoacoustic imaging theory is presented based on fundamental physical processes involved in photoacoustic phenomena. Excessive pressure is used to characterize the photoacoustic signal. A solution to photoacoustic pressure derived for liquids is investigated under a rapid heating condition. Photoacoustic image reconstruction theory is proposed for short, square heating pulses. The limitation of the reconstruction theory is discussed. Relationship of the photoacoustic image reconstruction and the Radon transform is presented. The local radiation absorption energy density is determined by the reconstruction theory for three- and two- dimensional cases and for complete or partial data acquisition. The accurate solution is an infinite series. The general formulas of the zero- and first order approximations for three- and two-dimensional cases are provided. A computer simulation for a two-dimensional case exhibits good agreement between the first order approximation and true value.
Photoacoustic signals generated by breasts irradiated with short microwave, infrared or optical pulses could be used to detect breast cancer. Since radiation at this spectrum is non-ionizing, the photoacoustic approach provides a special safety feature. The purpose of the paper is to present a means to predict photoacoustic pressure signals for different breast phantoms and irradiation conditions. The photoacoustic wave equation was derived for linear, non-viscous liquid media. The equation was solved assuming uniform acoustic properties in an infinite medium. Compressed breast phantoms were used as the objects of simulation. The spatial dependence of electromagnetic energy absorption was given by another research paper of this conference. The time dependence of the absorption was assumed to be either uniform or bell- shaped. Photoacoustic pressure signals received by transducers at different locations were calculated numerically.
The simulation of energy deposition within the compressed human breast following its illumination with a short duration pulse of near-infrared light is examined. Different scattering and absorption conditions are studied: homogeneous scattering with homogeneous absorption, homogeneous scattering with heterogeneous absorption (i.e., the introduction of an abnormality), and heterogeneous scattering with homogeneous absorption. Some of the results were used in a companion paper for the simulation of photoacoustic ultrasonic waves resulting from the quick absorption of energy by a region exhibiting increased differential absorption over that of immediately adjacent areas. A method for simulating heterogenous scattering properties is introduced. It is observed that changes in the scattering coefficient within a region do not influence the absorption patterns of the region.
This investigation describes the design and performance of two, water-immersed, microwave applicators (433 MHz) for use with photoacoustic ultrasonography (PAUS). A cylindrical, open-aperture waveguide was chosen because it could be integrated easily into our PAUS instrumentation. The microwave flux distributions for two microwave applicators were measured using a specially-constructed temperature probe, consisting of an optical fiber with a temperature-sensitive phosphor that was placed inside a thin, polyethylene tube filled with 0.5 M saline. Using this instrumentation, we mapped the microwave flux distribution for each applicator. The physical characteristics of these applicators are discussed.
Recent theoretical calculations by our group (2134-14) indicate that regional optical absorption of radiation within highly scattering media, such as biologic tissue, can be localized by detecting photo-acoustic waves that are produced during regional, optical absorption. This paper reports our initial experimental verification that measurable ultrasonic waves are produced when differential optical absorption takes place within turbid media simulating biologic tissue. For these experiments, an aquarium filled with a 0.5% intralipid solution was used to simulate the scattering properties of biologic tissue. Regional, optical absorption was produced by suspending black, latex spheres (3 - 10 mm diameter) within the intralipid bath. A broadband, xenon flash lamp (1 microsecond(s) ec rise time) was used for one set of experiments and a Nd:YAG laser ((lambda) equals 1064 nm, pulse width < 10 ns) was used for another set. A variety of focused, ultrasound transducers (0.5 - 2.5 MHz) were used successfully to detect and localize photo-acoustic waves. Lateral scanning of the transducers was used to localize the position of the absorption cells with a spatial resolution approximately 1 mm.
Localizing optical absorption within biologic tissue is compromised by the ubiquitous scattering of light that takes place within such tissues. As an alternative to purely optical detection schemes, regional absorption of optical radiation can be detected and localized within highly scattering tissues by detecting the acoustic waves that are produced whenever differential absorption of radiation takes place within such tissues. When the source of optical radiation is delivered in pulses of <EQ 1 microsecond(s) ec duration, the acoustic waves that are produced lie in the medical ultrasonic frequency range, and can be localized using conventional ultrasonic transducers and reconstruction methodology. Localizing such acoustic waves is not adversely affected by optical scattering. This paper introduces a simplistic theory of acoustic wave production within turbid media. The relationships among the irradiating optical pulse power, regional absorption, and strength of acoustic wave production are developed. Estimates of contrast and spatial resolution are presented, assuming a conventional, focused ultrasound transducer and translational scanning are used. Initial theoretical work indicates that optical absorption can be localized with millimeter spatial resolution for 10% absorption or less in biologic tissues as thick as 6.0 cm using safe levels of optical radiation.
Electromagnetic energy that is carried by light is converted to thermodynamic and mechanical forms of energy, i.e., heat and kinetic energy, when light interacts with tissue. The conversion efficiency from the absorbed radiative energy by an object into the kinetic energy is an important issue in the study of laser-tissue interactions, because the kinetic energy is the source of acoustic signals. Based on the first law of thermodynamics and some simplified assumptions, an expression for the conversion efficiency of optical to kinetic energy has been derived for an isolated, uniformly absorbing sphere. If there is no phase transition, the rule of thumb is that the converted kinetic energy is proportional to the square of the total absorbed radiative energy per unit time, and the square of the linear thermal expansion coefficient; and, it is inversely proportional to the product of the density, radius and the square of the specific heat of the sphere. This result will be used to optimize a design for photo-acoustic measurement of the optical absorption properties of phantoms and biological tissues in vivo.
A new approach to solve the radiative transport equation for time-resolved spectroscopy is presented. A new phase function that shows much better agreement with Mie theory than Henyey-Greenstein's phase function is introduced. Initial laser beams are properly modeled. For every small time increment, precise and analytical solutions are found to satisfy the radiative transport equation for the uniform field, wide beam, and narrow beam. Computer simulations give promising results. Different conditions of initial beams, media, and medium abnormalities are discussed. A strategy for using the semianalytical solutions to reconstruct the regional distribution of the scattering attenuation coefficient and future work are described.
Biological tissues produce high levels of optical scattering in the visible and near-infrared. A phase function is often used to characterize the scattering properties of the media. Henyey- Greenstein's phase function has been widely adopted by researchers in the biomedical optics field. A new scattering phase function is proposed to approximate phase functions strictly derived from Mie scattering theory. The new phase function demonstrates much better agreement with Mie theory than Henyey-Greenstein's phase function. In calculation of light propagation within biological media using the radiative transport equation, the phase function plays an even more important role. Using the new phase function as the integral kernel in the radiative transport equation, an analytical expression for the integral term of the equation is obtained for highly aligned beams. This may lead to a semi-analytical solution to the time- dependent radiative transport equation for time-resolved spectroscopy.
This article proposes a new approach to the `forward problem' by directly solving the radiative transport equation. A new phase function introduced by the authors' previous work has been used in the new approach in a simplified form. A function modeling the spatial, directional and temporal distributions of the incident laser pulse is proposed. For every small time increment, analytical approximation solutions to the time-dependent radiative transport equation are formulated. Preliminary results of computer simulation of the approach are provided.
A mathematical model is proposed describing time-resolved output measurements obtained on the surface of a diffusely scattering body due to an input pulse of near-IR light at a different location also on the surface. Such measurements can be obtained using a pulsed near-IR laser coupled with a CCD streak camera. The scattering body is assumed to exhibit homogenous scattering and spatially varying absorption. Using this model, an iterative algorithm is derived using maximum likelihood methods that allows the reconstruction of the spatial absorption pattern from a set of time-resolved tomographic measurements. The methodology places no restrictions upon the time-of-arrival of the detected photons, thus permitting the entire time-resolved signal to be used in the reconstruction process. The reconstruction algorithm is easily initialized and preliminary results indicate that stable reconstructions can be performed.
Researchers in biomedical optics use either the photon diffusion model or the Monte Carlo simulation to approach the `forward problem' of image reconstruction of the optical diffusion tomography for turbid media. Solving the photon transport equation is an alternate method to solve the `forward problem,' and might be more accurate because light propagation in turbid media is supposed to be better depicted by the photon transport equation than the other two methods. A solution to the time-dependent integro-differential equation has been found, using a hybrid (finite-difference and analytic) method. When the spatial and directional distributions of the initial light beam are given, analytical solutions to the photon transport equation are obtained for following discrete instances. This new approach has potential application to the time-resolved optical diffusion tomography as a more accurate solution to the `forward problem.'