Estimation of kinetic model parameters in fluorescence optical diffusion tomography

Indirect and direct estimation of pharmacokinetic parameters in dynamic diffuse fluorescence tomography by adaptive extended Kalman filtering

Pharmacokinetic parameter estimation with the support of dynamic diffuse fluorescence tomography (DFT) can provide helpful diagnostic information for tumor differentiation and monitoring. Adaptive extended Kalman filtering (AEKF) as a nonlinear filter method has the merits of high quantitativeness, noise robustness, and initialization independence. In this paper, indirect and direct AEKF schemes combining with a commonly used two-compartment model were studied to estimate the pharmacokinetic parameters based on our self-designed dynamic DFT system. To comprehensively compare the performances of both schemes, the selection of optimal noise covariance matrices affecting estimation results was first studied, then a series of numerical simulations with the metabolic time ranged from 4.16 min to 38 min was carried out and quantitatively evaluated. The comparison results show that the direct AEKF outperforms the indirect EKF in estimation accuracy at different metabolic velocity and demonstrates stronger stability at the large metabolic velocity. Furtherly, the in vivo experiment was conducted to achieve the indocyanine green pharmacokinetic-rate images in the mouse liver. The experimental results confirmed the capability of both schemes to estimate the pharmacokinetic-rate images and were in agreement with the theory predictions and the numerical simulation results.

Multiresolution Localization with Temporal Scanning for Super-Resolution Diffuse Optical Imaging of Fluorescence

A super-resolution optical imaging method is presented that relies on the distinct temporal information associated with each fluorescent optical reporter to determine its spatial position to high precision with measurements of heavily scattered light. This multiple-emitter localization approach uses a diffusion equation forward model in a cost function, and has the potential to achieve micron-scale spatial resolution through centimeters of tissue. Utilizing some degree of temporal separation for the reporter emissions, position and emission strength are determined using a computationally efficient time stripping multiresolution algorithm. The approach circumvents the spatial resolution challenges faced by earlier optical imaging approaches using a diffusion equation forward model, and is promising for in vivo applications. For example, in principle, the method could be used to localize individual neurons firing throughout a rodent brain, enabling direct imaging of neural network activity.

Parameterized level-set based pharmacokinetic fluorescence optical tomography using the regularized Gauss-Newton filter

Pharmacokinetic tomography is emerging as an important methodology for detecting abnormalities in tissue based upon spatially varying estimation of the pharmacokinetic rates governing the leakage of an injected fluorophore between blood plasma and tissue. We present a shape-based reconstruction framework of a compartment-model based formulation of this dynamic fluorescent optical tomography problem to solve for the pharmacokinetic rates and concentrations of the fluorophore from time-varying log intensity measurements of the optical signal. The compartment-model based state variable model is set up in a radial basis function parameterized level set setting. The state (concentrations) and (pharmacokinetic) parameter estimation problem is solved with an iteratively regularized Gauss-Newton filter in a trust-region framework. Reconstructions obtained using this scheme for noisy data obtained from cancer mimicking numerical phantoms of near/sub-cm sizes show a good localization of the affected regions and reasonable estimates of the pharmacokinetic rates and concentration curves.

Assessing indocyanine green pharmacokinetics in mouse liver with a dynamic diffuse fluorescence tomography system

Fluorescence pharmacokinetic rates in tissues can provide additional specific and quantitative physiological and pathological information for evaluating organ function. This modality requires a highly sensitive diffuse fluorescence tomography (DFT) working in dynamic way to finally extract the pharmacokinetic rates from the measured pharmacokinetics-associated temporally varying boundary intensity, normally with the support of a priori anatomy. This paper is devoted to study pharmacokinetics of indocyanine green (ICG) in mouse liver based on synergistic dynamic-DFT and X-ray computer tomography (XCT): A highly sensitive dynamic DFT system of CT-scanning mode working with parallel 4 photomultiplier-tube photon-counting channels generates informative and instantaneous sampling datasets; An XCT system provides priori information of the target localization for improvement of the reconstruction quality; An analysis procedure extracts the pharmacokinetic rates from the reconstructed ICG concentration-time curves, using the Gauss-Newton scheme for fitting to a 2-compartment model. The uptake and excretion rates of ICG which were obtained in livers of 10 healthy mice in the in vivo experiments can be used to quantitatively evaluate liver function. The results can validate the effectiveness of both the imaging measurements system and pharmacokinetic analysis method.

Excitation-resolved multispectral method for imaging pharmacokinetic parameters in dynamic fluorescent molecular tomography

Imaging of the pharmacokinetic parameters in dynamic fluorescence molecular tomography (DFMT) can provide three-dimensional metabolic information for biological studies and drug development. However, owing to the ill-posed nature of the FMT inverse problem, the relatively low quality of the parametric images makes it difficult to investigate the different metabolic processes of the fluorescent targets with small distances. An excitation-resolved multispectral DFMT method is proposed; it is based on the fact that the fluorescent targets with different concentrations show different variations in the excitation spectral domain and can be considered independent signal sources. With an independent component analysis method, the spatial locations of different fluorescent targets can be decomposed, and the fluorescent yields of the targets at different time points can be recovered. Therefore, the metabolic process of each component can be independently investigated. Simulations and phantom experiments are carried out to evaluate the performance of the proposed method. The results demonstrated that the proposed excitation-resolved multispectral method can effectively improve the reconstruction accuracy of the parametric images in DFMT.

Automatic selection of regularization parameters for dynamic fluorescence molecular tomography: a comparison of L-curve and U-curve methods

Dynamic fluorescence molecular tomography (FMT) is a promising technique for the study of the metabolic process of fluorescent agents in the biological body in vivo, and the quality of the parametric images relies heavily on the accuracy of the reconstructed FMT images. In typical dynamic FMT implementations, the imaged object is continuously monitored for more than 50 minutes. During each minute, a set of the fluorescent measurements is acquired and the corresponding FMT image is reconstructed. It is difficult to manually set the regularization parameter in the reconstruction of each FMT image. In this paper, the parametric images obtained with the L-curve and U-curve methods are quantitatively evaluated through numerical simulations, phantom experiments and in vivo experiments. The results illustrate that the U-curve method obtains better accuracy, stronger robustness and higher noise-resistance in parametric imaging. Therefore, it is a promising approach to automatic selection of the regularization parameters for dynamic FMT.

Fast direct reconstruction strategy of dynamic fluorescence molecular tomography using graphics processing units

Dynamic fluorescence molecular tomography (DFMT) is a valuable method to evaluate the metabolic process of contrast agents in different organs in vivo, and direct reconstruction methods can improve the temporal resolution of DFMT. However, challenges still remain due to the large time consumption of the direct reconstruction methods. An acceleration strategy using graphics processing units (GPU) is presented. The procedure of conjugate gradient optimization in the direct reconstruction method is programmed using the compute unified device architecture and then accelerated on GPU. Numerical simulations and in vivo experiments are performed to validate the feasibility of the strategy. The results demonstrate that, compared with the traditional method, the proposed strategy can reduce the time consumption by ∼90% without a degradation of quality.

Direct reconstruction in CT-analogous pharmacokinetic diffuse fluorescence tomography: two-dimensional simulative and experimental validations

We present a generalized strategy for direct reconstruction in pharmacokinetic diffuse fluorescence tomography (DFT) with CT-analogous scanning mode, which can accomplish one-step reconstruction of the indocyanine-green pharmacokinetic-rate images within in vivo small animals by incorporating the compartmental kinetic model into an adaptive extended Kalman filtering scheme and using an instantaneous sampling dataset. This scheme, compared with the established indirect and direct methods, eliminates the interim error of the DFT inversion and relaxes the expensive requirement of the instrument for obtaining highly time-resolved date-sets of complete 360 deg projections. The scheme is validated by two-dimensional simulations for the two-compartment model and pilot phantom experiments for the one-compartment model, suggesting that the proposed method can estimate the compartmental concentrations and the pharmacokinetic-rates simultaneously with a fair quantitative and localization accuracy, and is well suitable for cost-effective and dense-sampling instrumentation based on the highly-sensitive photon counting technique.

Performance Enhancement of Pharmacokinetic Diffuse Fluorescence Tomography by Use of Adaptive Extended Kalman Filtering

Due to both the physiological and morphological differences in the vascularization between healthy and diseased tissues, pharmacokinetic diffuse fluorescence tomography (DFT) can provide contrast-enhanced and comprehensive information for tumor diagnosis and staging. In this regime, the extended Kalman filtering (EKF) based method shows numerous advantages including accurate modeling, online estimation of multiparameters, and universal applicability to any optical fluorophore. Nevertheless the performance of the conventional EKF highly hinges on the exact and inaccessible prior knowledge about the initial values. To address the above issues, an adaptive-EKF scheme is proposed based on a two-compartmental model for the enhancement, which utilizes a variable forgetting-factor to compensate the inaccuracy of the initial states and emphasize the effect of the current data. It is demonstrated using two-dimensional simulative investigations on a circular domain that the proposed adaptive-EKF can obtain preferable estimation of the pharmacokinetic-rates to the conventional-EKF and the enhanced-EKF in terms of quantitativeness, noise robustness, and initialization independence. Further three-dimensional numerical experiments on a digital mouse model validate the efficacy of the method as applied in realistic biological systems.

Bayesian Framework Based Direct Reconstruction of Fluorescence Parametric Images

Fluorescence imaging has been successfully used in the study of pharmacokinetic analysis, while dynamic fluorescence molecular tomography (FMT) is an attractive imaging technique for three-dimensionally resolving the metabolic process of fluorescent biomarkers in small animals in vivo. Parametric images obtained by combining dynamic FMT with compartmental modeling can provide quantitative physiological information for biological studies and drug development. However, images obtained with conventional indirect methods suffer from poor image quality because of failure in utilizing the temporal correlations of boundary measurements. Besides, FMT suffers from low spatial resolution due to its ill-posed nature, which further reduces the image quality. In this paper, we propose a novel method to directly reconstruct parametric images from boundary measurements based on maximum a posteriori (MAP) estimation with structural priors in a Bayesian framework. The proposed method can utilize structural priors obtained from an X-ray computed tomography system to mitigate the ill-posedness of dynamic FMT inverse problem, and use direct reconstruction strategy to make full use of temporal correlations of boundary measurements. The results of numerical simulations and in vivo mouse experiments demonstrate that the proposed method leads to significant improvements in the reconstruction quality of parametric images as compared with the conventional indirect method and a previously developed direct method.

Acceleration of dynamic fluorescence molecular tomography with principal component analysis

Dynamic fluorescence molecular tomography (FMT) is an attractive imaging technique for three-dimensionally resolving the metabolic process of fluorescent biomarkers in small animal. When combined with compartmental modeling, dynamic FMT can be used to obtain parametric images which can provide quantitative pharmacokinetic information for drug development and metabolic research. However, the computational burden of dynamic FMT is extremely huge due to its large data sets arising from the long measurement process and the densely sampling device. In this work, we propose to accelerate the reconstruction process of dynamic FMT based on principal component analysis (PCA). Taking advantage of the compression property of PCA, the dimension of the sub weight matrix used for solving the inverse problem is reduced by retaining only a few principal components which can retain most of the effective information of the sub weight matrix. Therefore, the reconstruction process of dynamic FMT can be accelerated by solving the smaller scale inverse problem. Numerical simulation and mouse experiment are performed to validate the performance of the proposed method. Results show that the proposed method can greatly accelerate the reconstruction of parametric images in dynamic FMT almost without degradation in image quality.

Compressed-sensing-based fluorescence molecular tomographic image reconstruction with grouped sources

BACKGROUND

Although the quality of reconstructed results can be improved with the increment of the number of measurements, the scale of the matrices involved in the reconstruction of fluorescence molecular tomography (FMT) will become larger, which leads to the poor efficiency of the process of tomographic image reconstruction. In this paper, we proposed a new method for image reconstruction of FMT based on compressed sensing, in which a scheme of grouped sources is incorporated.

METHODS

The forward equations are implemented using the finite element method (FEM). The reconstruction model is formulated under the framework of compressed sensing theory. The regularization term and the total variation penalty are incorporated in the objective function. During the reconstruction of FMT, the sources are divided into two groups for iteration in turn. One group of sources is employed in the first iteration of inverse problem, and the other group is employed in the next iteration.

RESULTS

Simulation results demonstrate that the computation time and mean square error (MSE) of the reconstruction with our algorithm are less than those with the traditional method. The proposed algorithm can reconstruct the target with enhanced contrast and more accurate shape.

CONCLUSIONS

The proposed algorithm can significantly improve the speed and accuracy of the reconstruction of FMT. Furthermore, our compressed-sensing-based method can reduce the number of measurements.

In vivo mouse fluorescence imaging for folate-targeted delivery and release kinetics

Many cancer cells over-express folate receptors, and this provides an opportunity for both folate-targeted fluorescence imaging and the development of targeted anti-cancer drugs. We present an optical imaging modality that allows for the monitoring and evaluation of drug delivery and release through disulfide bond reduction inside a tumor in vivo for the first time. A near-infrared folate-targeting fluorophore pair was synthesized and used to image a xenograft tumor grown from KB cells in a live mouse. The in vivo results are shown to be in agreement with previous in vitro studies, confirming the validity and feasibility of our method as an effective tool for preclinical studies in drug development.

Quality and precision of parametric images created from PET sinogram data by direct reconstruction: proof of concept

We have previously implemented the direct reconstruction of dense kinetic model parameter images ("parametric images") from sinogram data, and compared it to conventional image domain kinetic parameter estimation methods . Although it has been shown that the direct reconstruction algorithm estimates the kinetic model parameters with lower root mean squared error than the conventional image domain techniques, some theoretical obstacles remain. These obstacles include the difficulty of evaluating the accuracy and precision of the estimated parameters. In image domain techniques, the reconstructed time activity curve (TAC) and the model predicted TAC are compared, and the goodness-of-fit is evaluated as a measure of the accuracy and precision of the estimated parameters. This approach cannot be applied to the direct reconstruction technique as there are no reconstructed TACs. In this paper, we propose ways of evaluating the precision and goodness-of-fit of the kinetic model parameters estimated by the direct reconstruction algorithm. Specifically, precision of the estimates requires the calculation of variance images for each parameter, and goodness-of-fit is addressed by reconstructing the difference between the measured and the fitted sinograms. We demonstrate that backprojecting the difference from sinogram space to image space creates error images that can be examined for goodness-of-fit and model selection purposes. The presence of nonrandom structures in the error images may indicate an inadequacy of the kinetic model that has been incorporated into the direct reconstruction algorithm. We introduce three types of goodness-of-fit images. We propose and demonstrate a number-of-runs image as a means of quantifying the adequacy or deficiency of the model. We further propose and demonstrate images of the F statistic and the change in the Akaike Information Criterion as devices for identifying the statistical advantage of one model over another at each voxel. As direct reconstruction to parametric images proliferates, it will be essential for imagers to adopt methods such as those proposed herein to assess the accuracy and precision of their parametric images.

Region-based reconstruction method for fluorescent molecular tomography

A common difficulty for the traditional methods of fluorescent molecular tomographic (FMT) reconstruction is that only a small amount of measurements can be used to recover the image comprised of a large number of pixels. This difficulty not only leads to expensive computational cost but also likely results in an unstable solution prone to be affected by the noise in the measurement data. In this paper, we propose a region-based method for reducing the unknowns, where the target areas are determined by searching for the nearest neighbor nodes. In this method, the Hessian matrix of the second-order derivatives is incorporated to speed up the optimization process. An iteration strategy of multi-wavelength measurement is introduced to further improve the accuracy of inverse solutions. Simulation results demonstrate that the proposed approach can significantly speed up the reconstruction process and improve the image quality of FMT.

Direct reconstruction of pharmacokinetic-rate images of optical fluorophores from NIR measurements

In this paper, we present a new method to form pharmacokinetic-rate images of optical fluorophores directly from near infra-red (NIR) boundary measurements. We first derive a mapping from spatially resolved pharmacokinetic rates to NIR boundary measurements by combining compartmental modeling with a diffusion based NIR photon propagation model. We express this mapping as a state-space equation. Next, we introduce a spatio-temporal prior model for the pharmacokinetic-rate images and combine it with the state-space equation. We address the image formation problem using the extended Kalman filtering framework. We analyze the computational complexity of the resulting algorithms and evaluate their performance in numerical simulations. An important feature of our approach is that the reconstruction of fluorescence concentrations and compartmental modeling are combined into a single step 1) to take advantage of the inherent temporal correlations in dynamic NIR measurements, and 2) to incorporate spatio-temporal a priori information on pharmacokinetic-rate images. Simulation results show that the resulting algorithms are more robust and lead to higher signal-to-noise ratio as compared to existing approaches where the reconstruction of concentrations and compartmental modeling are treated separately. Additionally, we reconstructed pharmacokinetic-rate images using in vivo data obtained from three patients with breast tumors. The reconstruction results show that the pharmacokinetic rates of indocyanine green are higher inside the tumor region as compared to the surrounding tissue.

A survey of approaches for direct parametric image reconstruction in emission tomography

The quantitative data obtained by emission tomography are decoded using a number of techniques and methods in sequence to provide physiological information. Conventionally, the data are reconstructed to produce a series of static images. Then, pharmacokinetic modeling techniques are applied, and kinetic parameters that have physiological or functional significance are derived. Although it is possible to optimize each estimation step in this process, many simplifying assumptions have to be introduced to make the methods that are used practicable. Published research has shown that if the kinetic parameters are estimated directly from the measured data, the parametric images will have higher quality and lower mean-squared error than if this was done indirectly. This review highlights some aspects of the methods that have been proposed for such direct estimation of pharmacokinetic information from raw emission data.

Reconstruction of spatially resolved pharmacokinetic rate images of fluorescence agents in FDOT

In this work, we propose a method to reconstruct spatially resolved pharmacokinetic rate images of fluorescence agents directly from the boundary photon flux measurements. We use a compartmental modeling scheme to model the pharmacokinetics of fluorescence agents. We coupled this model with the fluorescence diffuse optical tomography (FDOT) forward model to form a state space model which is then iteratively solved by extended Kalman filtering (EKF) algorithm. As an example, we used a two-compartment model for indocyanine green (ICG) pharmacokinetics. To validate the proposed method, we tested our approach using a simulation study. Reconstructed pharmacokinetic rate images with correct localization of heterogeneities and high reconstruction accuracy show that the proposed algorithm can be used for tumor detection, tumor diagnosis, drug delivery and feasibility studies.

Dynamic optical imaging of vascular and metabolic reactivity in rheumatoid joints

Dynamic optical imaging is increasingly applied to clinically relevant areas such as brain and cancer imaging. In this approach, some external stimulus is applied and changes in relevant physiological parameters (e.g., oxy- or deoxyhemoglobin concentrations) are determined. The advantage of this approach is that the prestimulus state can be used as a reference or baseline against which the changes can be calibrated. Here we present the first application of this method to the problem of characterizing joint diseases, especially effects of rheumatoid arthritis (RA) in the proximal interphalangeal finger joints. Using a dual-wavelength tomographic imaging system together with previously implemented model-based iterative image reconstruction schemes, we have performed initial dynamic imaging case studies on a limited number of healthy volunteers and patients diagnosed with RA. Focusing on three cases studies, we illustrated our major finds. These studies support our hypothesis that differences in the vascular reactivity exist between affected and unaffected joints.