Alexander X. Cong

Practical reconstruction method for bioluminescence tomography

Bioluminescence tomography (BLT) is used to localize and quantify bioluminescent sources in a small living animal. By advancing bioluminescent imaging to a tomographic framework, it helps to diagnose diseases, monitor therapies and facilitate drug development. In this paper, we establish a direct linear relationship between measured surface photon density and an unknown bioluminescence source distribution by using a finite-element method based on the diffusion approximation to the photon propagation in biological tissue. We develop a novel reconstruction algorithm to recover the source distribution. This algorithm incorporates a priori knowledge to define the permissible source region in order to enhance numerical stability and efficiency. Simulations with a numerical mouse chest phantom demonstrate the feasibility of the proposed BLT algorithm and reveal its performance in terms of source location, density, and robustness against noise. Lastly, BLT experiments are performed to identify the location and power of two light sources in a physical mouse chest phantom.

A finite-element-based reconstruction method for 3D fluorescence tomography

In this paper, we propose a dual-excitation-mode methodology for three-dimensional (3D) fluorescence molecular tomography (FMT). For this modality, an effective reconstruction algorithm is developed to reconstruct fluorescent yield and lifetime using finite element techniques. In the steady state mode, a direct linear relationship is established between measured optical data on the body surface of a small animal and the unknown fluorescent yield inside the animal, and the reconstruction of fluorescent yield is formulated as a linear least square minimization problem. In the frequency domain mode, based on localization results of the fluorescent probe obtained using the first mode, the reconstruction of fluorescent lifetime is transformed into a relatively simple optimization problem. This algorithm helps overcome the ill-posedness with FMT. The effectiveness of the proposed method is numerically demonstrated using a heterogeneous mouse chest phantom, showing good accuracy, stability, noise characteristics and computational efficiency.

Multispectral Bioluminescence Tomography: Methodology and Simulation

Bioluminescent imaging has proven to be a valuable tool for monitoring physiological and pathological activities at cellular and molecular levels in living small animals. Using biological techniques, target cells can be tagged with reporters encoding several kinds of luciferase enzymes, which generate characteristic photons in a wide spectrum covering the infrared range. Part of the diffused light can reach the body surface of the small animal, be separated into several spectral bands using appropriate filters, and collected by a sensitive CCD camera. Here we present a bioluminescence tomography (BLT) method for a bioluminescent source reconstruction from multispectral data measured on the external surface, and demonstrate the advantages of multispectral BLT in a numerical study using a heterogeneous mouse chest phantom. The results show that the multispectral approach significantly improves the accuracy and stability of the BLT reconstruction even if the data are highly noisy.

A practical method to determine the light source distribution in bioluminescent imaging

Optical signatures of tumor cells may be generated by expression of reporter genes encoding bioluminescent/fluorescent proteins. Bioluminescent imaging is a novel technique that identifies such light sources from the light flux detected on the surface of a small animal. This technique can effectively evaluate tumor cell growth and regression in response to various therapies in medical research, drug development and gene therapy. In this paper, the diffusion approximation is employed to describe the propagation of photons through biological tissues. Then, a practical method is proposed for localizing and quantifying bioluminescent sources from external bioluminescent signals. This method incorporates prior knowledge on permissible source regions, and transforms the inverse bioluminescent problem into a finite element-based constrained optimization procedure. This approach is validated and evaluated with ideal and noise data in numerical simulation.

Differential Evolution Approach for Regularized Bioluminescence Tomography

Bioluminescence tomography (BLT) is an inverse source problem that localizes and quantifies bioluminescent probe distribution in 3-D. The generic BLT model is ill-posed, leading to nonunique solutions and aberrant reconstruction in the presence of measurement noise and optical parameter mismatches. In this paper, we introduce the knowledge of the number of bioluminescence sources to stabilize the BLT problem. Based on this regularized BLT model, we develop a differential evolution-based reconstruction algorithm to determine the source locations and strengths accurately and reliably. Then, we evaluate this novel approach in numerical, phantom, and mouse studies.

Flux vector formulation for photon propagation in the biological tissue

We present a generalized delta-Eddington phase function to simplify the radiative transfer equation to an integral equation with respect to the photon flux vector. The solution of the integral equation is highly accurate to model the photon propagation in the biological tissue over a broad range of optical parameters, especially in the visible light spectrum where the diffusion approximation breaks down. The methodology is validated in the Monte Carlo simulation and can be applied in various optical imaging applications.

Integral equations of the photon fluence rate and flux based on a generalized Delta-Eddington phase function

We present a generalized Delta-Eddington phase function to simplify the radiative transfer equation to integral equations with respect to both photon fluence rate and flux vector. The photon fluence rate and flux can be solved from the system of integral equations. By comparing to the Monte Carlo simulation results, the solutions of the system of integral equations accurately model the photon propagation in biological tissue over a wide range of optical parameters.

Monte Carlo fluorescence microtomography

Fluorescence microscopy allows real-time monitoring of optical molecular probes for disease characterization, drug development, and tissue regeneration. However, when a biological sample is thicker than 1 mm, intense scattering of light would significantly degrade the spatial resolution of fluorescence microscopy. In this paper, we develop a fluorescence microtomography technique that utilizes the Monte Carlo method to image fluorescence reporters in thick biological samples. This approach is based on an l(0)-regularized tomography model and provides an excellent solution. Our studies on biomimetic tissue scaffolds have demonstrated that the proposed approach is capable of localizing and quantifying the distribution of optical molecular probe accurately and reliably.

Geometrical modeling using multiregional marching tetrahedra for bioluminescence tomography

Localization and quantification of the light sources generated by the expression of bioluminescent reporter genes is an important task in bioluminescent imaging of small animals, especially the generically engineered mice. To employ the Monte Carlo method for the light-source identification, the surfaces that define the anatomic structures of the small experimental animal is required; to perform finite element-based reconstruction computation, the volumetric mesh is a must. In this work, we proposed a Multiregional Marching Tetrahedra (MMT) method for extracting the surface and volumetric meshes from segmented CT/micro-CT (or MRI) image volume of a small experimental animal. The novel MMT method extracts triangular surface mesh and constructs tetrahedra/prisms volumetric finite element mesh for all anatomic components, including heart, liver, lung, bones etc., within one sweep over all the segmented CT slices. In comparison with the well-established Marching Tetrahedra (MT) algorithm, our MMT method takes into consideration of two more surface extraction cases within each tetrahedron, and guarantees seamless connection between anatomical components. The surface mesh is then smoothed and simplified, without losing the seamless connections. The MMT method is further enhanced to generate volumetric finite-element mesh to fill the space of each anatomical component. The mesh can then be used for finite element-based inverse computation to identify the light sources.

Improving the accuracy of the diffusion model in highly absorbing media

The diffusion approximation of the Boltzmann transport equation is most commonly used for describing the photon propagation in turbid media. It produces satisfactory results in weakly absorbing and highly scattering media, but the accuracy lessens with the decreasing albedo. In this paper, we presented a method to improve the accuracy of the diffusion model in strongly absorbing media by adjusting the optical parameters. Genetic algorithm-based optimization tool is used to find the optimal optical parameters. The diffusion model behaves more closely to the physical model with the actual optical parameters substituted by the optimized optical parameters. The effectiveness of the proposed technique was demonstrated by the numerical experiments using the Monte Carlo simulation data as measurements.