Genetically engineered mouse model(GEMM) that develops pancreatic ductal adenocarcinoma (PDAC) offers an experimental system to advance our understanding of radiotherapy (RT) for pancreatic cancer. Cone beam CT (CBCT)-guided small animal radiation research platform (SARRP) has been developed to mimic the RT used for human. However, we recognized that CBCT is inadequate to localize the PDAC growing in low image contrast environment. We innovated bioluminescence tomography (BLT) to guide SARRP irradiation for in vivo PDAC. Before working on the complex PDAC-GEMM, we first validated our BLT target localization using subcutaneous and orthotopic pancreatic tumor models. Our BLT process involves the animal transport between the BLT system and SARRP. We inserted a titanium wire into the orthotopic tumor as the fiducial marker to track the tumor location and to validate the BLT reconstruction accuracy. Our data shows that with careful animal handling, minimum disturbance for target position was introduced during our BLT imaging procedure(<0.5mm). However, from longitudinal 2D bioluminescence image (BLI) study, the day-to-day location variation for an abdominal tumor can be significant. We also showed that the 2D BLI in single projection setting cannot accurately capture the abdominal tumor location. It renders that 3D BLT with multipleprojection is needed to quantify the tumor volume and location for precise radiation research. Our initial results show the BLT can retrieve the location at 2mm accuracy for both tumor models, and the tumor volume can be delineated within 25% accuracy. The study for the subcutaneous and orthotopic models will provide us valuable knowledge for BLTguided PDAC-GEMM radiation research.
The proposed image reconstruction method exploits the spectrally dependent absorption properties of biological tissue and quantum dots for recovering the three-dimensional reporter distribution. Only a single light source with macro-illumination needs to be used for the purpose of light emission stimulation and image reconstruction. The light propagation in strongly absorbing tissue is modeled with the simplified spherical harmonics (SPN) equations.
Hyperspectral excitation-resolved fluorescence tomography (HEFT) exploits the spectrally-dependent absorption
properties of biological tissue for recovering the unknown three-dimensional (3D) fluorescent reporter distribution inside
tissue. Only a single light source with macro-illumination and wavelength-discrimination is required for the purpose of
light emission stimulation and 3D image reconstruction. HEFT is built on fluorescent sources with a relatively broad
spectral absorption profile (quantum dots) and a light propagation model for strongly absorbing tissue between
wavelengths 560 nm and 660 nm (simplified spherical harmonics - SPN, - equations). The measured partial current of
fluorescence light is cast into an algebraic system of equations, which is solved for the unknown quantum dot
distribution with an expectation-maximization (EM) method. HEFT requires no source-detector multiplexing for 3D
image reconstruction and, hence, offers a technologically simple design.
A computer-aided interpretation approach is proposed to detect rheumatic arthritis (RA) in human finger joints using optical tomographic images. The image interpretation method employs a classification algorithm that makes use of a so-called self-organizing mapping scheme to classify fingers as either affected or unaffected by RA. Unlike in previous studies, this allows for combining multiple image features, such as minimum and maximum values of the absorption coefficient for identifying affected and not affected joints. Classification performances obtained by the proposed method were evaluated in terms of sensitivity, specificity, Youden index, and mutual information. Different methods (i.e., clinical diagnostics, ultrasound imaging, magnet resonance imaging, and inspection of optical tomographic images), were used to produce ground truth benchmarks to determine the performance of image interpretations. Using data from 100 finger joints, findings suggest that some parameter combinations lead to higher sensitivities, while others to higher specificities when compared to single parameter classifications employed in previous studies. Maximum performances are reached when combining the minimum/maximum ratio of the absorption coefficient and image variance. In this case, sensitivities and specificities over 0.9 can be achieved. These values are much higher than values obtained when only single parameter classifications were used, where sensitivities and specificities remained well below 0.8.
The procedures we propose make possible the mapping of two-dimensional (2-D) bioluminescence image (BLI) data onto a skin surface derived from a three-dimensional (3-D) anatomical modality [magnetic resonance (MR) or computed tomography (CT)] dataset. This mapping allows anatomical information to be incorporated into bioluminescence tomography (BLT) reconstruction procedures and, when applied using sources visible to both optical and anatomical modalities, can be used to evaluate the accuracy of those reconstructions. Our procedures, based on immobilization of the animal and a priori determined fixed projective transforms, should be more robust and accurate than previously described efforts, which rely on a poorly constrained retrospectively determined warping of the 3-D anatomical information. Experiments conducted to measure the accuracy of the proposed registration procedure found it to have a mean error of 0.36±0.23 mm. Additional experiments highlight some of the confounds that are often overlooked in the BLT reconstruction process, and for two of these confounds, simple corrections are proposed.
KEYWORDS: 3D modeling, Data modeling, Monte Carlo methods, Absorption, Spherical lenses, Optical properties, Bioluminescence, Photon transport, Diffusion, 3D image processing
A three dimensional (3D) photon transport model has been developed based on the frequency domain simplified
spherical harmonics approximation (SPN) to the Radiative Transport Equation. Based on preliminary Monte Carlo
studies, it is shown that for problems exhibiting strong absorption, the solutions using the 7th order SPN model (N = 7) are
significantly more accurate than those from a standard Diffusion (SP1) based solver. This advance is of particular
interest in the field of bioluminescent imaging where the peak emission of light emitting molecular markers are closer to
the visible range (500 - 650 nm) corresponding to strong absorption due to hemoglobin.
We developed a method for solving the fluorescence equation of radiative transfer in the frequency domain on blockstructured
grids. In this way fluorescence light propagation in arbitrarily shaped tissue can be modeled with high
accuracy without compromising on the convergence speed of these codes. The block-structure grid generator is
developed as a multi-purpose tool that can be used with many numerical schemes. We present results from numerical
studies that show that it is possible to resolve curved boundaries with grids that maintain much of the intrinsic structure
of Cartesian grids. The natural ordering of this grid allows for simplified algorithms. In simulation studies we found that
we can reduce the error in boundary fluence by a factor of five by using a two-level block structured grid. The increase
in computational cost is only two-fold. We compare benchmark solutions to results with various levels of refinement,
boundary conditions, and different geometries.
A recent research study has shown that combining multiple parameters, drawn from optical tomographic images,
leads to better classification results to identifying human finger joints that are affected or not affected
by rheumatic arthritis RA. Building up on the research findings of the previous study, this article presents an
advanced computer-aided classification approach for interpreting optical image data to detect RA in finger joints.
Additional data are used including, for example, maximum and minimum values of the absorption coefficient
as well as their ratios and image variances. Classification performances obtained by the proposed method were
evaluated in terms of sensitivity, specificity, Youden index and area under the curve AUC. Results were compared
to different benchmarks ("gold standard"): magnet resonance, ultrasound and clinical evaluation. Maximum accuracies
(AUC=0.88) were reached when combining minimum/maximum-ratios and image variances and using
ultrasound as gold standard.
This research study explores the combined use of more than one parameter derived from optical tomographic images to increase diagnostic accuracy which is measured in terms of sensitivity and specificity. Parameters considered include, for example, smallest or largest absorption or scattering coefficients or the ratios thereof in an image region of interest. These parameters have been used individually in a previous study to determine if a finger joint is affected or not affected by rheumatoid arthritis. To combine these parameters in the analysis we employ here a vector quantization based classification method called Self-Organizing Mapping (SOM). This method allows producing multivariate ROC-curves from which sensitivity and specificities can be determined. We found that some parameter combinations can lead to higher sensitivities whereas others to higher specificities when compared to singleparameter classifications employed in previous studies. The best diagnostic accuracy, in terms of highest Youden index, was achieved by combining three absorption parameters [maximum(µa), minimum(µa), and the ratio of minimum(µa) and maximum(µa)], which result in a sensitivity of 0.78, a specificity of 0.76, a Youden index of 0.54, and an area under the curve (AUC) of 0.72. These values are higher than for previously reported single parameter classifications with a best sensitivity and specificity of 0.71, a Youden index of 0.41, and an AUC of 0.66.
We found that using more than one parameter derived from optical tomographic images can lead to better image classification results compared to cases when only one parameter is used.. In particular we present a multi-parameter classification approach, called self-organizing mapping (SOM), for detecting synovitis in arthritic finger joints based on sagittal laser optical tomography (SLOT). This imaging modality can be used to determine various physical parameters such as minimal absorption and scattering coefficients in an image of the proximal interphalengeal joint. Results were compared to different gold standards: magnet resonance imaging, ultra-sonography and clinical evaluation. When compared to classifications based on single-parameters, e.g., absorption minimum only, the study reveals that multi-parameter classifications lead to higher classification sensitivities and specificities and statistical significances with p-values <5 per cent. Finally, the data suggest that image analyses are more reliable and avoid ambiguous interpretations when using more than one parameter.
The underlying mathematical model for bioluminescence tomography (BLT) is an ill-posed inverse source problem,
which can be cast into an optimization problem of a χ2-error function. The error function quantifies the discrepancy
between the measured and predicted partial current of bioluminescent light at the tissue boundary. In this work, the
predicted partial current has been calculated prior to image reconstruction by solving the equation of radiative transfer
(ERT) for a set of source basis functions of the entire tissue domain. A global optimization technique based on
stochastic sampling principles probes the global parameter space of bioluminescent source distributions composed of
source basis functions. The stochastic approach avoids a premature convergence, which can be caused, e.g., by a narrow
or a shallow surface landscape of the χ2-error function. Initial reconstruction results are compared to gradient-based
image reconstructions.
Imaging of dynamic changes in blood parameters, functional brain imaging, and tumor imaging are the most advanced application areas of diffuse optical tomography (DOT). When dealing with the image reconstruction problem one is faced with the fact that near-infrared photons, unlike X-rays, are highly scattered when they traverse biological tissue. Image reconstruction schemes are required that model the light propagation inside biological tissue and predict measurements on the tissue surface. By iteratively changing the tissue-parameters until the predictions agree with the real measurements, a spatial distribution of optical properties inside the tissue is found. The optical properties can be related to the tissue oxygenation, inflammation, or to the fluorophore concentration of a biochemical marker. If the model of light propagation is inaccurate, the reconstruction process will lead to an inaccurate result as well. Here, we focus on difficulties that are encountered when DOT is employed for functional imaging of small tissue volumes, for example, in cancer studies involving small animals, or human finger joints for early diagnosis of rheumatoid arthritis. Most of the currently employed image reconstruction methods rely on the diffusion theory that is an approximation to the equation of radiative transfer. But, in the cases of small tissue volumes and tissues that contain low scattering regions diffusion theory has been shown to be of limited applicability Therefore, we employ a light propagation model that is based on the equation of radiative transfer, which promises to overcome the limitations.
Small animal models are employed to simulate disease in humans and to study its progression, what factors are
important to the disease process, and to study the disease treatment. Biomedical imaging modalities such as magnetic
resonance imaging (MRI) and Optical Tomography make it possible to non-invasively monitor the progression of
diseases in living small animals and study the efficacy of drugs and treatment protocols. MRI is an established imaging
modality capable of obtaining high resolution anatomical images and along with contrast agents allow the studying of
blood volume. Optical tomography, on the other hand, is an emerging imaging modality, which, while much lower in
spatial resolution, can separate the effects of oxyhemoglobin, deoxyhemoglobin, and blood volume with high temporal
resolution. In this study we apply these modalities to imaging the growth of kidney tumors and then there treatment by
an anti-VEGF agent. We illustrate how these imaging modalities have their individual uses, but can still supplement
each other and cross validation can be performed.
Inflammatory processes as they occur during rheumatoid arthritis (RA) lead to changes in the optical properties of joint tissues and fluids. These changes occur early on in the disease process and can potentially be used as diagnostic parameter. In this work we report on in vivo studies involving 12 human subjects, which show the potential of diffuse optical tomographic techniques for the diagnosis of inflammatory processes in proximal interphalangeal (PIP) joints.
Diffuse optical tomography is emerging as a viable new biomedical imaging modality. Using near-infrared light this technique probes absorption as well as scattering properties of biological tissues. First commercial instruments are now available that combined with appropriate image reconstruction scheme allow to obtain cross sectional views of various body parts. The main applications are currently brain, breast, limb and joint imaging. While the spatial resolution is limited compared to other imaging modalities such as MRI or X-ray tomography, diffuse optical tomography provides for a fast, inexpensive, acquisition of a variety of physiological parameters that are otherwise not accessible. We present here a brief overview over the current state-of-the-art technology and some of its main applications.
Optical fluorescence tomography recovers the spatial distribution of light emitting fluorophores inside a highly scattering medium. The quantification of a non-uniform quantum yield and fluorophore absorption distribution is of major interest in molecular imaging of biological tissue. We have developed a fluorescence image reconstruction code that is based on the particle transport equation. Since the algorithm does not rely on the diffusion approximation it promises to yield more accurate results in highly absorbing media or media with small geometries. We show that the code can be employed in a two-stage reconstruction process to obtain images of the fluorophore absorption and of the quantum yield.
The equation of radiative transfer can take into account the anisotropic scattering behavior of photons and anisotropic sources for modeling the light propagation in tissue. This is an important aspect when small tissue geometries are considered. In this case the solutions of the commonly applied diffusion approximation may provide only insufficiently accurate results. We numerically solve the equation of radiative transfer by means of a finite-difference discrete-ordinates technique. However, strong anisotropically scattering media require many discrete ordinates, which lead to a large computational burden. In this study we implemented a Delta-Eddington method that allows using only a small number of discrete ordinates, and the solution can be obtained at a lesser computational costs.
There has been considerable discussion concerning the effects of the cerebrospinal fluid on measurements of blood-related parameters in the human brain, and if diffusion-theory-based image reconstruction algorithms can accurately account for the light propagation in the head. All of these studies have been performed either with synthetic data generate from numerical models or from phantom studies. We present here the first comparative study that involves clinical data from optical tomographic measurements. Data obtained from the human forehead during a Valsalva maneuver were input to two different model-based iterative image reconstruction algorithms recently developed in our laboratories. One code is based on the equation of radiative transfer, while the other algorithm uses a diffusion model to describe the light propagation in the head. Both codes use finite-element formulations of the respective theories and were used to obtain three-dimensional volumetric images of oxy, dexoy and total hemoglobin. The reconstructed overall spatial heterogeneity in changes of these parameters is similar using both algorithms. The two codes differ mostly in the amplitude of the observed changes. In general the transport based codes reconstructs changes 10-40% stronger than the diffusion code.
The system theory was developed from the combination of the operational calculus of N. Wiener and the transfer theory of K. Kuepfmueller. The system theory is the basic for the optical transfer function. With the introduction of a so- called transfer (or system) function, the question arose how to apply this theory to problems in optical tissue diagnostics.
Diffuse optical tomography (DOT) can be considered as an optimization problem, in which the minimum of an objective function is sought. The objective function is typically some measure of the difference between the predicted and experimentally obtained detector readings. Most of the optimization techniques that are currently applied in optical tomography employ so-called gradient methods. These methods start from an initial guess of the distribution of optical properties and iteratively update this initial guess along the gradient of the objective function. It is well known that the success of gradient techniques depends strongly on the initial guess. If the guess is not chosen appropriately, the algorithm may not converge or may converge to a local minimum. Evolution strategies are global optimization techniques that depend much less on initial guesses. The drawback of evolution-based codes is that they are computationally expensive. In this work we introduce a hybrid approach that combines the advantages of gradient techniques and evolution strategies. The hybrid algorithm is less dependent on an initial guess and overcomes the computational burden connected to evolution strategies.
In diffuse optical diffuse tomography (DOT) one attempts to reconstruct cross-sectional images of various body parts given data from near-infrared transmission measurements. The cross- sectional images, display the spatial distribution of optical properties, such as the absorption coefficient (mu) (alpha ), the scattering coefficient (mu) s, or a combination thereof. Most of the currently employed imaging algorithms are model- based iterative image reconstruction (MOBIIR) schemes that employ information about the gradient of a suitably defined objective function with respect to the optical properties. In this approach the image reconstruction problem is considered as a nonlinear optimization problem, where the unknowns are the values of optical properties throughout the medium to be reconstructed. It is well known that gradient-based schemes are inefficient in areas where the gradient is close to zero. These schemes often get caught in local minima close to the starting point of the search and have problems finding the global minimum. To overcome this problem, we propose to employ optimization algorithms that make use of evolution strategies. These schemes are in general much better suited to find global minima and may be a better choice for the image reconstruction problem in diffuse optical tomography.
Optical Tomography (OT) can provide useful information about the interior distribution of optical properties in various body parts, such as the brain, breast, or finger joints. This novel medical imaging modality uses measured transmission intensities of near infrared light that are detected on accessible surfaces. Image reconstruction schemes compute from the measured data cross sectional images of the optical properties throughout the body. The image quality and the computational speed largely depend on the employed reconstruction method. Of considerable interest are currently so-called model-based iterative image reconstruction schemes, in which the reconstruction problem is formulated as an optimization problem. The correct image equals the spatial distribution of optical properties that leads to a minimum of a user-defined objective function. In the past several groups have developed steepest-gradient-descent (SGD) techniques and conjugate-gradient (CG) methods, which start from an initial guess and search for the minimum. These methods have shown some good initial results, however, they are known to be only slowly converging. To alleviate this disadvantage we have implemented in this work a quasi-Newton (QN) method. We present numerical results that show that QN algorithms are superior to CG techniques, both in terms of conversion time and image quality.
Currently available image reconstruction schemes for photon migration tomography are based on the diffusion approximation for light propagation in turbid media. We have shown in previous works that these schemes fail to describe the light propagation in very low scattering media such as the cerebrospinal fluid of the brain or the synovial fluid of finger joints. Therefore, we have developed a reconstruction algorithm that is based on the equation of radiative transfer. This equation describes the photon propagation in turbid media most accurately without any assumptions regarding the optical properties. Analytical solutions for complex geometries and heterogeneous media are not available. Thus, a numerical method is considered, which is based on a finite-difference formulation of the time-dependent transport equation. The reconstruction code consists of three major parts: (1) a forward model based that predicts detector readings based on the equation of radiative transfer , (2) an objective function that describes the differences between the measured and the predicted data, and (3) an updating scheme that uses the gradient of the objective function to perform a line minimization to get new guesses of the optical properties. Based on a new guess of the optical properties a new forward calculation is performed. The reconstruction process is completed when the minimum of the objective function is found.
KEYWORDS: Optical properties, Image restoration, Sensors, Reconstruction algorithms, Diffusion, Tissues, Optical tomography, Data modeling, Absorption, Signal to noise ratio
It is well known that the reconstruction problem in optical tomography is ill-posed. Therefore, the choice of an appropriate regularization method is of crucial importance for any successful image reconstruction algorithm. In this work we approach the regularization problem within a gradient-based image iterative reconstruction (GIIR) scheme. The image reconstruction is considered as a minimization of an appropriately defined objective function. The objective function can be separated into a least-square-error term, which compares predicted and actual detector readings, and additional penalty terms that may contain additional a priori information about the system. For the efficient minimization of this objective function the gradient with respect to the spatial distribution of optical properties is calculated. Besides presenting the underlying concepts in our approach to the regularization problem, we will show numerical results that demonstrate how prior knowledge can improve the reconstruction results.
Rheumatoid arthritis (RA) is one of the most common diseases of human joints. This progressive disease is characterized by an inflammation process that originates in the inner membrane (synovalis) of the capsule and spreads to other parts of the joint. In early stages the synovalis thickness and the permeability of this membrane changes. This leads to changes in the optical parameters of the synovalis and the synovial fluid (synovia), which occupies the space between the bones. The synovia changes from a clear yellowish fluid to a turbid grayish substance. In this work we present 2 and 3-dimensional reconstruction schemes for optical tomography of the finger joints. Our reconstruction algorithm is based on the diffusion approximation and employs adjoint differentiation techniques for the gradient calculation of the objective function with respect to the spatial distribution of optical properties. In this way, the spatial distribution of optical properties within the joints is reconstructed with high efficiency and precision. Volume information concerning the synovial space and the capsula are provided. Furthermore, it is shown that small changes of the scattering coefficients can be monitored. Therefore, optical tomography has the potential of becoming a useful tool for the early diagnosis and monitoring of disease progression in RA.
Our aim is to reconstruct the optical parameters in a slice of a finger joint phantom for further investigations about rheumatoid arthritis (RA). Therefore, we have developed a flexible NIR scanning system in order to collect amplitude and phase delay of photon density waves in frequency-domain. A cylindrical finger joint phantom was embedded in a container of Intralipid solution due to the application of an inverse method for infinite geometry. The joint phantom was investigated by a laser beam obtaining several projections. The average optical parameters of each projection was calculated. Using different reconstruction techniques, e.g. ART and SIRT with a special projection operator, we reconstructed the optical parameters in a slice. The projection operator can be heuristically described by a photon path density function of a homogeneous media with infinite geometry. Applied to an object with an unknown distribution of optical parameters it calculates the expectation value of the investigated object. The potentials and limits of these fast reconstruction methods will be presented.
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