Abstract: Frequency combs generated by coherent stimulated emission have revolutionized the precision at which we are able to measure time, frequency, and distance. Directly measuring the frequency of the radiation offers a much higher resolution, as time can be measured with a higher accuracy than distance, and conversion between frequency and wavelength can be done without much concern for accuracy degradation. FC generation in the visible and near-IR have enjoyed much progress in the last decade however there is still a lack of viable methods for producing FCs in the mid-IR and THz spectrum. Typically, combs are generated with mode-locked pulses or sending coherent light through a non-linear resonator, however there is a lack of materials available to achieve this in the longer wavelengths. Current approaches for FCs at longer wavelength typically include non-linear frequency conversion, which suffers from low conversion efficiency. Quantum Cascade lasers (QCLs) are a ubiquitous source of coherent radiation in the mid-infrared to THz regions of the spectrum. However, passive mode-locking is hard to achieve in QCLs because of their inherently low gain recovery time, due to intersubband operation, on the order of 1ps when compared to the round trip time on the order of 100ps. Despite the difficulty of actively or passively locking QCLs, experimental evidence has shown that frequency combs are indeed generated by free-running QCLs [1,2], i.e. no additional active or passive elements. Given proper dispersion compensation and a broadband gain medium the QCL generates coherent frequency combs with a frequency modulated phase relation.
In an attempt to explicate this behavior, a theoretical, frequency-domain model was developed via a perturbative solution of the Maxwell Bloch equation in the frequency domain, illustrating that frequency modulation is indeed a natural consequence of spatial hole burning in an inhomogeneously broadened gain medium (the origin of multi-mode lasing) and a short gain recovery time, which favors constant intensity. This combination of multi-mode operation with constant intensity is a signature of frequency modulation. The theoretical model predicts a pseudo-random frequency modulation of the laser with a general period of oscillations equal to the gain recovery time and an amplitude equal to the gain bandwidth. The work proposed here attempts to explain the necessity of a pseudo-random FM signal as well as take into account spectral hole burning which was excluded in the FD model.
This time domain model is developed using the Optical Bloch Equations (OBE). Initially the question of coherence must be investigated. It is our hypothesis that the dynamics of the laser, in fact, do not rely on coherent processes. In order to prove this, we compare the OBE under a full coherent interaction with a modified rate equation that is an approximation of the OBE. We operate under the assumption that the time rate of change is slower than the loss of coherence. This approximation greatly lightens the computational load, allowing for a more realistic model (more inhomogeneously broadened spectral bins, a longer cavity length, etc.). With the validation of this assumption we assert that the operation regime with the most stimulated emission will result in the lowest threshold, rationalizing the necessity of a pseudo random frequency modulation signal. In order to achieve this, we input various forms of an FM signal into a model utilizing real world specifications of both mid-infrared and THz QCLs. We show that indeed, with an FM signal similar to that produced in the FD model, the gain provided by the active medium peaks for a very random signal that fully spans the gain bandwidth, we trace the root cause of this to be spatial hole burning. Further experimental results have shown that under certain conditions the QCLs exhibit amplitude modulation as well as frequency modulation. In order to keep our model current, we develop analytical solutions for spatial hole burning in the cavity and investigate under what conditions of AM and FM is the spatial hole burning reduced.
Title: Dose Optimization for Pediatric Renal SPECT Imaging
Abstract: Like any real-world problem, the design of an imaging system always requires tradeoffs. For medical imaging modalities using ionization radiation, a major tradeoff is between diagnostic image quality (IQ) and risk to the patient from absorbed radiation dose. In nuclear medicine, reducing the radiation dose to the patient will always result in increased Poisson noise in the image. At the same time, reducing the radiation dose (RD), below some level at least, will always result in reduced risk of adverse effects to the patient. The overall goal of this research is to propose a rigorous IQ-RD tradeoff analysis method for pediatric nuclear medicine renal imaging. However, the methodologies developed in this proposal can also be applied to other nuclear medicine imaging applications and other important medical modalities involving ionization radiation such as computed tomography and planar X-rays.
Balancing the tradeoffs between RD and IQ is especially important for children, as they are often considered more vulnerable to radiation than adults. In nuclear medicine imaging, reducing the RD requires reducing the administered activity (AA). Lower AA results in increased Poisson noise in the images or requires longer acquisition durations to maintain the noise level. In pediatric nuclear medicine, it is desirable to use the lowest AA and the shortest acquisition duration that gives sufficient IQ for clinical diagnosis. In current clinical practice, AA for pediatric molecular imaging is often based on the North American consensus guidelines (U.S.) and the European pediatric dosage card (Europe). Both of these dosing guidelines involve scaling the adult AA by patient weight subject to upper and lower constraints on the AA. However, these guidelines were developed based on expert consensus or rough estimates (estimated count rates) of IQ rather than rigorous, objective measures of performance on the diagnostic task.
In this research, we propose a general framework for optimizing RD with task-based assessment of IQ. Here, IQ is defined as an objective measure of the user performing the diagnostic task that the images were acquired to answer. Specifically, we propose to establish relationships between AA, acquisition duration, measures of body habitus, and IQ for pediatric patients undergoing renal molecular imaging procedures. To investigate IQ as a function of renal defect detectability, we have developed a projection image database modeling imaging of 99mTc-DMSA, a renal function agent. The database uses a highly-realistic population of pediatric phantoms with anatomical and body morphological variations. Using the developed projection image database, we have explored patient factors that affect IQ and are currently in the process of determining relationships between IQ and AA (IQ-AA curve) in terms of these found factors. Our preliminary data have shown that the current weight-based guidelines, based on scaling the AA by patient weight, are not optimal in the sense that they do not give the same image quality for patients with the same weight. Furthermore, we have found that factors that are more local to the target organ may be more robust than weight for estimating the AA needed to provide a constant IQ across a population of patients. In the case of renal imaging, we have discovered that girth is more robust than weight in predicting AA needed to provide a desired IQ. In addition, in order to simulate a full clinical multi-slice detection task (just like what a nuclear medicine physician would do), we propose to develop a CNN-based model observer. We will perform human observer studies to verify and calibrate the developed model observers used to generate the IQ-AA curves. The results of this proposal will provide the data needed by standards bodies to develop improved dosing guidelines for pediatric molecular imaging that result in more consistent image quality and absorbed dose.
Title: Modeling Cellular Events: Chemotaxis and Aneuploidy
Abstract: Biology is the ‘study of complex natural things’ and the biologists are mostly interested in details of those complexity in a system. But often a simpler mathematical model is proved to be very efficient in deciphering the underlying basic working principle of the system. Despite the usefulness, these models are often criticized for not being able to explain the sufficient details of the wide range of experimental observations of different cases of pharmacological/genetic perturbations.