Temporal Point Spread Function Research Articles

Monte Carlo modeling of temporal point spread functions and sensitivity functions for mesoscopic time-resolved fluorescence molecular tomography

The paper describes a TurbidMC code that implements a perturbative Monte Carlo method to model temporal point spread functions and sensitivity functions for time-resolved fluorescence molecular tomography (FMT). The code is aimed at working with a particular FMT method published earlier (Ref. [22]) which defines the specificity of sensitivity function calculation. The method solves the inverse problem first for a generalized fluorescence parameter distribution function and then calculates separate distributions for the fluorophore absorption coefficient and the fluorescence lifetime. The proper operation of the code was verified through a comparison between fluorescence temporal point spread functions from test calculations and data from experiments where a phantom with a fluorophore was scanned with a three-channel probe in the mesoscopic reflectance regime. An example is given on the reconstruction of fluorescence parameter distributions. It shows that the sensitivity functions are calculated correctly.

Expressions of the peak time for time-domain boundary measurements of diffuse light

Light propagation through diffusive media can be described by the diffusion equation in a space–time domain. Furthermore, fluorescence can be described by a system of coupled diffusion equations. This paper analyzes time-domain measurements. In particular, the temporal point-spread function is measured at the boundary of a diffusive medium. Moreover, the temporal profile of fluorescence is considered. In both cases, we refer to the maximum temporal position of measured light as the peak time. In this paper, we provide proofs of the existence and uniqueness of the peak time and give explicit expressions of the peak time. The relationship between the peak time and the object position in a medium is clarified.

Utilising nanosecond sources in diffuse optical tomography

Diffuse optical tomography (DOT) use near-infrared light for imaging optical properties of biological tissues. Time-domain (TD) DOT systems use pulsed lasers and measure time-varying temporal point spread function (TPSF), carrying information from both superficial and deep layers of imaged target. In this work, feasibility of nanosecond scale light pulses as sources for TD-DOT is studied. Nanosecond sources enable using relatively robust measurement setups with standard analogue-to-digital converter waveform digitizers, such as digital oscilloscopes. However, this type of systems have some properties, such as variations in source pulses and limited temporal sampling, that could limit their usage. In this work, these different aspects and possible limitations were studied with simulations and experiments. Simulations showed that information carried by TD data of diffuse medium is on low frequencies. This enables usage of relatively slow response time measurement electronics, and image processing using Fourier-transformed TD data. Furthermore, the temporal sampling in measurements needs to be high enough to capture the TPSF, but this rate can be achieved with standard digital oscilloscopes. It was shown that, although variations in light pulses of nanosecond lasers are larger than those of picosecond sources, these variations do not affect significantly on image quality. Overall, the simulations demonstrated the capability of nanosecond sources to be utilised in TD-DOT in diffuse medium. In this work, a prototype TD-DOT experimental system utilising a high-energy nanosecond laser was constructed. The system is relatively robust consisting of a nanosecond Nd:YAG laser combined with optical parametric oscillator for light input and optical fibres for guiding the light, and avalanche photodetector and high-bandwidth oscilloscope for TPSF measurements. The system was used in both absolute and difference imaging of two phantoms. The experiments verified that both absorbing and scattering objects can be reconstructed with good accuracy with TD-DOT using a nanosecond laser.

Functional Time Domain Diffuse Correlation Spectroscopy.

Time-domain diffuse correlation spectroscopy (TD-DCS) offers a novel approach to high-spatial resolution functional brain imaging based on the direct quantification of cerebral blood flow (CBF) changes in response to neural activity. However, the signal-to-noise ratio (SNR) offered by previous TD-DCS instruments remains a challenge to achieving the high temporal resolution needed to resolve perfusion changes during functional measurements. Here we present a next-generation optimized functional TD-DCS system that combines a custom 1,064 nm pulse-shaped, quasi transform-limited, amplified laser source with a high-resolution time-tagging system and superconducting nanowire single-photon detectors (SNSPDs). System characterization and optimization was conducted on homogenous and two-layer intralipid phantoms before performing functional CBF measurements in six human subjects. By acquiring CBF signals at over 5 Hz for a late gate start time of the temporal point spread function (TPSF) at 15 mm source-detector separation, we demonstrate for the first time the measurement of blood flow responses to breath-holding and functional tasks using TD-DCS.

Laplace-domain diffuse optical measurement

Time-domain diffuse optical measurement systems determine depth-resolved absorption changes by using the time of flight distribution of the detected photons. It is well known that certain feature data, such as the Laplace transform of the temporal point spread function, is sufficient for image reconstruction and diffuse optical sensing. Conventional time-domain systems require the acquisition of full temporal profiles of diffusive photons and then numerically compute the feature dataset, for example, Laplace transformed intensities for imaging applications. We have proposed a novel method for directly obtaining the Laplace transform data. Our approach can significantly improve the data acquisition speed for time-domain diffuse optical imaging. We also demonstrated that the use of negative Laplace parameters can provide enhanced sensitivity to perturbations located in deep regions.

Reconstruction of high-resolution early-photon tomography based on the first derivative of temporal point spread function.

For fluorescence molecular tomography, higher spatial resolution can be achieved using minimally scattered early photons. Conventional reconstruction methods of early photon tomography (EPT) are based on the integral of temporal point spread function (TPSF), which may lead to poor image quality due to systematic noise and time mismatch between the TPSF data and forward model. The derivative of the rising portion of TPSF is proposed to be used in EPT to increase the performance of reconstruction because the derivative is less sensitive to noise and time mismatch than the integral. A method based on projected Tikhonov regularization with the reconstructed result of steepest descent algorithm as a priori information is developed. Using the derivative of TPSF, the method can achieve high spatial resolution in phantom experiments and is capable of separating targets with an edge-edge distance of 1.5mm.

混沌激光相关法实现时间点扩展函数的测量

混沌激光相关法实现时间点扩展函数的测量

Time-resolved near infrared light propagation using frequency domain superposition.

Time-resolved temporal point spread function (TPSF) measurement of near infrared spectroscopic (NIRS) data allows the estimation of absorption and reduced scattering properties of biological tissues. Such analysis requires an iterative calculation of the theoretical TPSF curve using mathematical and computational models of the domain being imaged which are computationally complex and expensive. In this work, an efficient methodology for representing the TPSF data using a superposition of cosines calculated in frequency domain is presented. The proposed method is outlined and tested on finite element realistic models of the human neck and head. Using an adult head model containing ~140k nodes, the TPSF calculation at each node for one source is accelerated from 3.11 s to 1.29 s within an error limit of ± 5% related to the time domain calculation method.

Recovering temporal PSF using ToF camera with delayed light emission

Recovering temporal point spread functions (PSFs) is important for various applications, especially analyzing light transport. Some methods that use amplitude-modulated continuous wave time-of-flight (ToF) cameras are proposed to recover temporal PSFs, where the resolution is several nanoseconds. Contrarily, we show in this paper that sub-nanosecond resolution can be achieved using pulsed ToF cameras and an additional circuit. A circuit is inserted before the illumination so that the emission delay can be controlled by sub-nanoseconds. From the observations of various delay settings, we recover temporal PSFs of the sub-nanosecond resolution. We confirm the effectiveness of our method via real-world experiments.

Time-domain diffuse correlation spectroscopy.

Physiological monitoring of oxygen delivery to the brain has great significance for improving the management of patients at risk for brain injury. Diffuse correlation spectroscopy (DCS) is a rapidly growing optical technology able to non-invasively assess the blood flow index (BFi) at the bedside. The current limitations of DCS are the contamination introduced by extracerebral tissue and the need to know the tissue's optical properties to correctly quantify the BFi. To overcome these limitations, we have developed a new technology for time-resolved diffuse correlation spectroscopy. By operating DCS in the time domain (TD-DCS), we are able to simultaneously acquire the temporal point-spread function to quantify tissue optical properties and the autocorrelation function to quantify the BFi. More importantly, by applying time-gated strategies to the DCS autocorrelation functions, we are able to differentiate between short and long photon paths through the tissue and determine the BFi for different depths. Here, we present the novel device and we report the first experiments in tissue-like phantoms and in rodents. The TD-DCS method opens many possibilities for improved non-invasive monitoring of oxygen delivery in humans.

Fluorescence lifetime measurements in heterogeneous scattering medium.

Fluorescence lifetime in heterogeneous multiple light scattering systems is analyzed by an algorithm without solving the diffusion or radiative transfer equations. The algorithm assumes that the optical properties of medium are constant in the excitation and emission wavelength regions. If the assumption is correct and the fluorophore is a single species, the fluorescence lifetime can be determined by a set of measurements of temporal point-spread function of the excitation light and fluorescence at two different concentrations of the fluorophore. This method is not dependent on the heterogeneity of the optical properties of the medium as well as the geometry of the excitation–detection on an arbitrary shape of the sample. The algorithm was validated by an indocyanine green fluorescence in phantom measurements and demonstrated by an in vivo measurement.

Early-photon guided reconstruction method for time-domain fluorescence lifetime tomography

A reconstruction method guided by early-photon fluorescence yield tomography is proposed for time-domain fluorescence lifetime tomography (FLT) in this study. The method employs the early-arriving photons to reconstruct a fluorescence yield map, which is utilized as a priori information to reconstruct the FLT via all the photons along the temporal-point spread functions. Phantom experiments demonstrate that, compared with the method using all the photons for reconstruction of fluorescence yield and lifetime maps, the proposed method can achieve higher spatial resolution and reduced crosstalk between different targets without sacrificing the quantification accuracy of lifetime and contrast between heterogeneous targets.

Estimating the absorption coefficient of the bottom layer in four-layered turbid mediums based on the time-domain depth sensitivity of near-infrared light reflectance

Expanding our previously proposed "time segment analysis" for a two-layered turbid medium, this study attempted to selectively determine the absorption coefficient (μa) of the bottom layer in a four-layered human head model with time-domain near-infrared measurements. The difference curve in the temporal profiles of the light attenuation between an object and a reference medium, which are obtained from Monte Carlo simulations, is divided into segments along the time axis, and a slope for each segment is calculated to obtain the depth-dependent μa(μaseg). The reduced scattering coefficient (μs') of the reference is determined by curve fitting with the temporal point spread function derived from the analytical solution of the diffusion equation to the time-resolved reflectance of the object. The deviation of μaseg from the actual μa is expressed by a function of the ratio of μaseg in an earlier time segment to that in a later segment for mediums with different optical properties and thicknesses of the upper layers. Using this function, it is possible to determine the μa of the bottom layer in a four-layered epoxy resin-based phantom. These results suggest that the method reported here has potential for determining the μa of the cerebral tissue in humans.

Improving the depth sensitivity of time-resolved measurements by extracting the distribution of times-of-flight.

Time-resolved (TR) techniques provide a means of discriminating photons based on their time-of-flight. Since early arriving photons have a lower probability of probing deeper tissue than photons with long time-of-flight, time-windowing has been suggested as a method for improving depth sensitivity. However, TR measurements also contain instrument contributions (instrument-response-function, IRF), which cause temporal broadening of the measured temporal point-spread function (TPSF) compared to the true distribution of times-of-flight (DTOF). The purpose of this study was to investigate the influence of the IRF on the depth sensitivity of TR measurements. TPSFs were acquired on homogeneous and two-layer tissue-mimicking phantoms with varying optical properties. The measured IRF and TPSFs were deconvolved using a stable algorithm to recover the DTOFs. The microscopic Beer-Lambert law was applied to the TPSFs and DTOFs to obtain depth-resolved absorption changes. In contrast to the DTOF, the latest part of the TPSF was not the most sensitive to absorption changes in the lower layer, which was confirmed by computer simulations. The improved depth sensitivity of the DTOF was illustrated in a pig model of the adult human head. Specifically, it was shown that dynamic absorption changes obtained from the late part of the DTOFs recovered from TPSFs acquired by probes positioned on the scalp were similar to absorption changes measured directly on the brain. These results collectively demonstrate that this method improves the depth sensitivity of TR measurements by removing the effects of the IRF.

A three-dimensional finite element model and image reconstruction algorithm for time-domain fluorescence imaging in highly scattering media

In this work, development and evaluation of a three-dimensional (3D) finite element model (FEM) based on the diffusion approximation of time-domain (TD) near-infrared fluorescence light transport in biological tissue is presented. This model allows both excitation and fluorescence temporal point-spread function (TPSF) data to be generated for heterogeneous scattering and absorbing media of arbitrary geometry. The TD FEM is evaluated via comparisons with analytical and Monte Carlo (MC) calculations and is shown to provide a quantitative accuracy which has less than 0.72% error in intensity and less than 37 ps error for mean time. The use of the Born–Ratio normalized data is demonstrated to reduce data mismatch between MC and FEM to less than 0.22% for intensity and less than 22 ps in mean time. An image reconstruction framework, based on a 3D FEM formulation, is outlined and simulation results based on a heterogeneous mouse model with a source of fluorescence in the pancreas is presented. It is shown that using early photons (i.e. the photons detected within the first 200 ps of the TPSF) improves the spatial resolution compared to using continuous-wave signals. It is also demonstrated, as expected, that the utilization of two time gates (early and latest photons) can improve the accuracy both in terms of spatial resolution and recovered contrast.

Pseudo-random single photon counting: a high-speed implementation

Pseudo-random single photon counting (PRSPC) is a new time-resolved optical measurement method which combines the spread spectrum time-resolved method with single photon counting. A pseudo-random bit sequence is used to modulate a continuous wave laser diode, while single photon counting is used to build up the optical signal in response to the modulated excitation. Periodic cross-correlation is performed to obtain the temporal profile of the subject of interest. Compared with conventional time-correlated single photon counting (TCSPC), PRSPC enjoys many advantages such as low cost and high count rate without compromising the sensitivity and time-resolution. In this paper, we report a PRSPC system that can be used for high-speed acquisition of the temporal point spread function of diffuse photons. It can reach a photon count rate as high as 3 Mcps (counts per second). Phantom experiments have been conducted to demonstrate the system performance.

Perturbation theory for the diffusion equation by use of the moments of the generalized temporal point-spread function III Frequency-domain and time-domain results

We study the performance of a previously proposed perturbation theory for the diffusion equation in frequency and time domains as they are known in the field of near infrared spectroscopy and diffuse optical tomography. We have derived approximate formulas for calculating higher order self- and mixed path length moments, up to the fourth order, which can be used in general diffusive media regardless of geometry and initial distribution of the optical properties, for studying the effect of absorbing defects. The method of Padé approximants is used to extend the validity of the theory to a wider range of absorption contrasts between defects and background. By using Monte Carlo simulations, we have tested these formulas in the semi-infinite and slab geometries for the cases of single and multiple absorbing defects having sizes of interest (d=4-10 mm, where d is the diameter of the defect). In frequency domain, the discrepancy between the two methods of calculation (Padé approximants and Monte Carlo simulations) was within 10% for absorption contrasts Deltamu(a)<or=0.2 mm(-1) for alternating current data, and usually to within 1 degrees for Deltamu(a)<or=0.1 mm(-1) for phase data. In time domain, the average discrepancy in the temporal range of interest (a few nanoseconds) was 2%-3% for Deltamu(a)<or=0.06 mm(-1). The proposed method is an effective fast forward problem solver: all the time-domain results presented in this work were obtained with a computational time of less than about 15 s with a Pentium IV 1.66 GHz personal computer.

Design of an Advanced Time-Domain Diffuse Optical Tomography System

This paper describes the design of an improved multichannel time-domain diffuse optical tomography (TD-DOT) system. For the spread spectrum TD-DOT, the image quality depends on the stability of the time-resolved signals, which can be affected by fluctuation in the source modulation depth and drift in the detector gain. A microcontroller-based bias controller is designed to lock the bias of a Mach-Zehnder intensity modulator at the positive quadrature point. With additional temperature stabilization over the avalanche photodiodes, the temporal stability of the time-resolved signals has been significantly improved-the fluctuations of the temporal point spread function have been limited to ±2% for a testing period of a few hours. The image quality and reproducibility have been substantially improved with the stabilized signals.

Analytical Method for the Fast Time-Domain Reconstruction of Fluorescent Inclusions In Vitro and In Vivo

A novel time-domain optical method to reconstruct the relative concentration, lifetime, and depth of a fluorescent inclusion is described. We establish an analytical method for the estimations of these parameters for a localized fluorescent object directly from the simple evaluations of continuous wave intensity, exponential decay, and temporal position of the maximum of the fluorescence temporal point-spread function. Since the more complex full inversion process is not involved, this method permits a robust and fast processing in exploring the properties of a fluorescent inclusion. This method is confirmed by in vitro and in vivo experiments.

Comparisons of motion‐blur assessment strategies for newly emergent LCD and backlight driving technologies

Abstract— Compared to the conventional cathode‐ray‐tube TV, the conventional liquid‐crystal TV has the shortcoming of motion blur. Motion blur can be characterized by the motion‐picture response‐time metric (MPRT). The MPRT of a display can be measured directly using a commercial MPRT instrument, but it is expensive in comparison with a photodiode that is used in temporal‐response (temporal luminance transition) measurements. An alternative approach is to determine the motion blur indirectly via the temporal point‐spread function (PSF), which does not need an accurate tracking mechanism as required for the direct “spatial” measurement techniques. In this paper, the measured motion blur is compared by using both the spatial‐tracking‐camera approach and the temporal‐response approach at various backlight flashing widths. In comparison to other motion‐blur studies, this work has two unique advantages: (1) both spatial and temporal information was measured simultaneously and (2) several temporal apertures of the display were used to represent different temporal PSFs. This study shows that the temporal method is an attractive alternative for the MPRT instrument to characterize the LCD's temporal performance.