Abhinav K. Jha

Simulating Silicon Photomultiplier Response to Scintillation Light

The response of a Silicon Photomultiplier (SiPM) to optical signals is affected by many factors including photon-detection efficiency, recovery time, gain, optical crosstalk, afterpulsing, dark count, and detector dead time. Many of these parameters vary with overvoltage and temperature. When used to detect scintillation light, there is a complicated non-linear relationship between the incident light and the response of the SiPM. In this paper, we propose a combined discrete-time discrete-event Monte Carlo (MC) model to simulate SiPM response to scintillation light pulses. Our MC model accounts for all relevant aspects of the SiPM response, some of which were not accounted for in the previous models. We also derive and validate analytic expressions for the single-photoelectron response of the SiPM and the voltage drop across the quenching resistance in the SiPM microcell. These analytic expressions consider the effect of all the circuit elements in the SiPM and accurately simulate the time-variation in overvoltage across the microcells of the SiPM. Consequently, our MC model is able to incorporate the variation of the different SiPM parameters with varying overvoltage. The MC model is compared with measurements on SiPM-based scintillation detectors and with some cases for which the response is known a priori. The model is also used to study the variation in SiPM behavior with SiPM-circuit parameter variations and to predict the response of a SiPM-based detector to various scintillators.

Three-dimensional Neumann-series approach to model light transport in nonuniform media

We present the implementation, validation, and performance of a three-dimensional (3D) Neumann-series approach to model photon propagation in nonuniform media using the radiative transport equation (RTE). The RTE is implemented for nonuniform scattering media in a spherical harmonic basis for a diffuse-optical-imaging setup. The method is parallelizable and implemented on a computing system consisting of NVIDIA Tesla C2050 graphics processing units (GPUs). The GPU implementation provides a speedup of up to two orders of magnitude over non-GPU implementation, which leads to good computational efficiency for the Neumann-series method. The results using the method are compared with the results obtained using the Monte Carlo simulations for various small-geometry phantoms, and good agreement is observed. We observe that the Neumann-series approach gives accurate results in many cases where the diffusion approximation is not accurate.

Simulating photon-transport in uniform media using the radiative transport equation: a study using the Neumann-series approach

We present the implementation, validation, and performance of a Neumann-series approach for simulating light propagation at optical wavelengths in uniform media using the radiative transport equation (RTE). The RTE is solved for an anisotropic-scattering medium in a spherical harmonic basis for a diffuse-optical-imaging setup. The main objectives of this paper are threefold: to present the theory behind the Neumann-series form for the RTE, to design and develop the mathematical methods and the software to implement the Neumann series for a diffuse-optical-imaging setup, and, finally, to perform an exhaustive study of the accuracy, practical limitations, and computational efficiency of the Neumann-series method. Through our results, we demonstrate that the Neumann-series approach can be used to model light propagation in uniform media with small geometries at optical wavelengths.

A clustering algorithm for liver lesion segmentation of diffusion-weighted MR images

In diffusion-weighted magnetic resonance imaging, accurate segmentation of liver lesions in the diffusion-weighted images is required for computation of the apparent diffusion coefficient (ADC) of the lesion, the parameter that serves as an indicator of lesion response to therapy. However, the segmentation problem is challenging due to low SNR, fuzzy boundaries and speckle and motion artifacts. We propose a clustering algorithm that incorporates spatial information and a geometric constraint to solve this issue. We show that our algorithm provides improved accuracy compared to existing segmentation algorithms.

Task-based evaluation of segmentation algorithms for diffusion-weighted MRI without using a gold standard

In many studies, the estimation of the apparent diffusion coefficient (ADC) of lesions in visceral organs in diffusion-weighted (DW) magnetic resonance images requires an accurate lesion-segmentation algorithm. To evaluate these lesion-segmentation algorithms, region-overlap measures are used currently. However, the end task from the DW images is accurate ADC estimation, and the region-overlap measures do not evaluate the segmentation algorithms on this task. Moreover, these measures rely on the existence of gold-standard segmentation of the lesion, which is typically unavailable. In this paper, we study the problem of task-based evaluation of segmentation algorithms in DW imaging in the absence of a gold standard. We first show that using manual segmentations instead of gold-standard segmentations for this task-based evaluation is unreliable. We then propose a method to compare the segmentation algorithms that does not require gold-standard or manual segmentation results. The no-gold-standard method estimates the bias and the variance of the error between the true ADC values and the ADC values estimated using the automated segmentation algorithm. The method can be used to rank the segmentation algorithms on the basis of both the ensemble mean square error and precision. We also propose consistency checks for this evaluation technique.

Value of Intratumoral Metabolic Heterogeneity and Quantitative 18F-FDG PET/CT Parameters to Predict Prognosis in Patients With HPV-Positive Primary Oropharyngeal Squamous Cell Carcinoma

Objective The aim of this study was to evaluate the impact of intratumoral metabolic heterogeneity and quantitative FDG PET/CT imaging parameters for predicting patient outcomes in primary oropharyngeal squamous cell cancer (OPSCC). Patients and Methods We retrospectively investigated 105 patients with HPV-positive OPSCC. SUVmax and metabolic tumor volume (MTV) were measured for the primary tumors and when available for the metastatic sites. Primary tumor intratumoral metabolic heterogeneity was calculated as the area under a cumulative SUV volume histograms curve (AUC-CSH). The median follow-up time was 35.4 months (range, 3–92 months). Outcome end point was event-free survival (EFS). Kaplan-Meier survival plots and Cox regression analyses were performed. Results Of the 105 patients included, 19 patients relapsed and 11 deceased during the study period. AUC-CSH indexes were associated with EFS using PET gradient-based (P = 0.034) and 50% threshold (P = 0.02) segmentation methods, on multivariate analysis. Kaplan-Meier survival analysis using optimum cutoff of 16.7 SUVmax and 12.7 mL total MTV were significant predictors of EFS. Combining SUVmax and AUC-CSH index in 3 subgroups, patients with higher intratumoral heterogeneity and higher SUVmax were associated with worse outcome (log-rank, P = 0.026). Similarly, patients with higher intratumoral heterogeneity tumors and higher MTV had worse prognosis (log-rank, P = 0.022). Conclusions Intratumoral metabolic heterogeneity using FDG PET was a prognostic factor for EFS in patients with primary HPV (+) OPSCC. The combined predictive effect of FDG avidity, metabolic tumor burden, and intratumoral heterogeneity provided prognostic survival information in these patients.

Singular value decomposition for photon-processing nuclear imaging systems and applications for reconstruction and computing null functions

Recent advances in technology are enabling a new class of nuclear imaging systems consisting of detectors that use real-time maximum-likelihood (ML) methods to estimate the interaction position, deposited energy, and other attributes of each photon-interaction event and store these attributes in a list format. This class of systems, which we refer to as photon-processing (PP) nuclear imaging systems, can be described by a fundamentally different mathematical imaging operator that allows processing of the continuous-valued photon attributes on a per-photon basis. Unlike conventional photon-counting (PC) systems that bin the data into images, PP systems do not have any binning-related information loss. Mathematically, while PC systems have an infinite-dimensional null space due to dimensionality considerations, PP systems do not necessarily suffer from this issue. Therefore, PP systems have the potential to provide improved performance in comparison to PC systems. To study these advantages, we propose a framework to perform the singular-value decomposition (SVD) of the PP imaging operator. We use this framework to perform the SVD of operators that describe a general two-dimensional (2D) planar linear shift-invariant (LSIV) PP system and a hypothetical continuously rotating 2D single-photon emission computed tomography (SPECT) PP system. We then discuss two applications of the SVD framework. The first application is to decompose the object being imaged by the PP imaging system into measurement and null components. We compare these components to the measurement and null components obtained with PC systems. In the process, we also present a procedure to compute the null functions for a PC system. The second application is designing analytical reconstruction algorithms for PP systems. The proposed analytical approach exploits the fact that PP systems acquire data in a continuous domain to estimate a continuous object function. The approach is parallelizable and implemented for graphics processing units (GPUs). Further, this approach leverages another important advantage of PP systems, namely the possibility to perform photon-by-photon real-time reconstruction. We demonstrate the application of the approach to perform reconstruction in a simulated 2D SPECT system. The results help to validate and demonstrate the utility of the proposed method and show that PP systems can help overcome the aliasing artifacts that are otherwise intrinsically present in PC systems.

Diffusion MRI with Semi-Automated Segmentation Can Serve as a Restricted Predictive Biomarker of the Therapeutic Response of Liver Metastasis.

PURPOSE To assess the value of semi-automated segmentation applied to diffusion MRI for predicting the therapeutic response of liver metastasis. METHODS Conventional diffusion weighted magnetic resonance imaging (MRI) was performed using b-values of 0, 150, 300 and 450s/mm(2) at baseline and days 4, 11 and 39 following initiation of a new chemotherapy regimen in a pilot study with 18 women with 37 liver metastases from primary breast cancer. A semi-automated segmentation approach was used to identify liver metastases. Linear regression analysis was used to assess the relationship between baseline values of the apparent diffusion coefficient (ADC) and change in tumor size by day 39. RESULTS A semi-automated segmentation scheme was critical for obtaining the most reliable ADC measurements. A statistically significant relationship between baseline ADC values and change in tumor size at day 39 was observed for minimally treated patients with metastatic liver lesions measuring 2-5cm in size (p=0.002), but not for heavily treated patients with the same tumor size range (p=0.29), or for tumors of smaller or larger sizes. ROC analysis identified a baseline threshold ADC value of 1.33μm(2)/ms as 75% sensitive and 83% specific for identifying non-responding metastases in minimally treated patients with 2-5cm liver lesions. CONCLUSION Quantitative imaging can substantially benefit from a semi-automated segmentation scheme. Quantitative diffusion MRI results can be predictive of therapeutic outcome in selected patients with liver metastases, but not for all liver metastases, and therefore should be considered to be a restricted biomarker.

An ideal-observer framework to investigate signal detectability in diffuse optical imaging

With the emergence of diffuse optical tomography (DOT) as a non-invasive imaging modality, there is a requirement to evaluate the performance of the developed DOT systems on clinically relevant tasks. One such important task is the detection of high-absorption signals in the tissue. To investigate signal detectability in DOT systems for system optimization, an appropriate approach is to use the Bayesian ideal observer, but this observer is computationally very intensive. It has been shown that the Fisher information can be used as a surrogate figure of merit (SFoM) that approximates the ideal observer performance. In this paper, we present a theoretical framework to use the Fisher information for investigating signal detectability in DOT systems. The usage of Fisher information requires evaluating the gradient of the photon distribution function with respect to the absorption coefficients. We derive the expressions to compute the gradient of the photon distribution function with respect to the scattering and absorption coefficients. We find that computing these gradients simply requires executing the radiative transport equation with a different source term. We then demonstrate the application of the SFoM to investigate signal detectability in DOT by performing various simulation studies, which help to validate the proposed framework and also present some insights on signal detectability in DOT.

Joint reconstruction of activity and attenuation map using LM SPECT emission data

Attenuation and scatter correction in single photon emission computed tomography (SPECT) imaging often requires a computed tomography (CT) scan to compute the attenuation map of the patient. This results in increased radiation dose for the patient, and also has other disadvantages such as increased costs and hardware complexity. Attenuation in SPECT is a direct consequence of Compton scattering, and therefore, if the scattered photon data can give information about the attenuation map, then the CT scan may not be required. In this paper, we investigate the possibility of joint reconstruction of the activity and attenuation map using list- mode (LM) SPECT emission data, including the scattered-photon data. We propose a path-based formalism to process scattered-photon data. Following this, we derive analytic expressions to compute the Cram´er-Rao bound (CRB) of the activity and attenuation map estimates, using which, we can explore the fundamental limit of information-retrieval capacity from LM SPECT emission data. We then suggest a maximum-likelihood (ML) scheme that uses the LM emission data to jointly reconstruct the activity and attenuation map. We also propose an expectation-maximization (EM) algorithm to compute the ML solution.