Derek W. Austin

Frequency domain analysis of noise in simple gene circuits

Recent advances in single cell methods have spurred progress in quantifying and analyzing stochastic fluctuations, or noise, in genetic networks. Many of these studies have focused on identifying the sources of noise and quantifying its magnitude, and at the same time, paying less attention to the frequency content of the noise. We have developed a frequency domain approach to extract the information contained in the frequency content of the noise. In this article we review our work in this area and extend it to explicitly consider sources of extrinsic and intrinsic noise. First we review applications of the frequency domain approach to several simple circuits, including a constitutively expressed gene, a gene regulated by transitions in its operator state, and a negatively autoregulated gene. We then review our recent experimental study, in which time-lapse microscopy was used to measure noise in the expression of green fluorescent protein in individual cells. The results demonstrate how changes in rate constants within the gene circuit are reflected in the spectral content of the noise in a manner consistent with the predictions derived through frequency domain analysis. The experimental results confirm our earlier theoretical prediction that negative autoregulation not only reduces the magnitude of the noise but shifts its content out to higher frequency. Finally, we develop a frequency domain model of gene expression that explicitly accounts for extrinsic noise at the transcriptional and translational levels. We apply the model to interpret a shift in the autocorrelation function of green fluorescent protein induced by perturbations of the translational process as a shift in the frequency spectrum of extrinsic noise and a decrease in its weighting relative to intrinsic noise.

Design and Performance of a New SPECT Detector for Multimodality Small Animal Imaging Platforms

A new detector for single photon emission computed tomography (SPECT) has been developed for the Siemens microCATreg II and Inveon Multimodality preclinical imaging systems. The detector provides an active imaging area of 15 cm times 15 cm. We review the design of this new SPECT detector and present some key performance characteristics. Integral and differential uniformity were 3.7% and 3.0%, respectively. Mean energy resolution for 99mTc (140 keV) was 12.5%. Sensitivity as high as 1400 cps/MBq was measured for 99mTc on a dual-detector system, and a spatial resolution of 0.7 mm (FWHM) was obtained using 0.5 mm single pinhole collimators. Additionally, we present data from representative preclinical SPECT studies acquired with single and multi-pinhole collimators and multiple isotopes. Reconstructed images demonstrate that this detector is capable of high-resolution SPECT for multimodality small animal imaging.

Modeling of the Point Spread Function by Numerical Calculations in Single-Pinhole and Multipinhole SPECT Reconstruction

In conventional reconstruction of single photon emission computed tomography (SPECT) data acquired with a single-pinhole or multipinhole system, the point spread function (PSF) may be either approximated by some analytical equations or substituted by the sensitivity function, which is the integral of the PSF. We have developed a method to numerically calculate the PSF for a pinhole system in order to improve image resolution over a sensitivity-function-based method. The method calculates the probability of photon penetration through the pinhole edges using a ray-tracing approach. To calculate the transmission by the collimator plate along each ray, we trace the ray through the collimator by analytical calculations. The PSF is calculated for only one detector angle, and a Gaussian rotator is used to rotate the image grid for other detector angles in the iterative reconstruction. To evaluate our method, we measured the sensitivities of four keel-edged single-pinhole plates and scanned an ultramicro Derenzo phantom on a single-pinhole system and a five-pinhole system and performed two mouse bone scans on the five-pinhole system using the 140 keV photons of Tc-99m. The numerical calculations of sensitivities for the single-pinhole plates agreed well with the measurements. Results for both types of data scans showed that modeling of the PSF improved image resolution. In conclusion, we found that modeling of the PSF by numerical calculations increases the resolution of reconstruction for single-pinhole and multipinhole SPECT imaging.

A New Highly Versatile Multimodality Small Animal Imaging Platform

A new, highly versatile multi-modality small animal imaging platform, the Siemens Inveon Multimodality (MM) scanner, has been developed. This platform supports any combination of X-ray micro-CT, single-photon computed tomography (SPECT) and positron emission tomography (PET) modalities on a single gantry. Each modality within the system is designed to be configured with a different level of imaging performance based on the needs of the application. From a single control workstation, the end-user has the ability to tune the system configuration for each modality in terms of resolution, field-of-view (FOV), sensitivity, etc., as needed for the target application. The scanner platform is ergonomically designed to allow efficient access to the animal and employs a unique cable management device to allow more effective use of physiologic monitoring and anesthesia systems within a user-accessible X-ray shielded cabinet. The motivation for this versatile platform design is to accommodate a wide range of multi-modality imaging applications from mouse to small primate, each with performance parameters that can be tuned as driven by the target anatomy or biological process being studied within the animal.

A data acquisition and Event Processing Module for small animal SPECT imaging

The Quicksilver event processing module (EPM) designed for the Siemens Inveon Dedicated PET (Positron Emission Tomography) preclinical scanner, has been leveraged in the development of a new SPECT (Single Photon Emission Computed Tomography) EPM module. This new module is used in Inveon SPECT systems and provides 16 channels of high speed data acquisition and event processing functions. Fifteen of these channels are used for processing 7 X signals, 7 Y signals and a SUM signal all received from the SPECT detector electronics. Custom mixed-signal CMOS ASICs and high speed ADCs are utilized to provide the front-end analog portion of the data acquisition. A high performance FPGA provides the digital portion of the data acquisition running at 100 MHz and the subsequent event processing. This FPGA also provides multiple high speed serial data channels for external interconnection. These interconnections allow the module to be replicated as needed in a distributed parallel processing architecture for flexible, high performance SPECT imaging. The module also provides controllable high voltage needed to bias the SPECT detectors. A four head Nal(Tl) based SPECT system is currently being built using one SPECT EPM per SPECT head.

Automated Least-Squares Calibration of the Coregistration Parameters for a Micro PET-CT System

PET-CT coregistration parameters can be derived from PET and CT images of a four-point-source calibration phantom for a micro PET-CT scanner. An automated segmentation method has been developed, based on thresholding and application of constraints on the sizes of point sources in the images. After point sources are identified on PET and CT images, coregistration is performed using an analytic rigid-body registration algorithm which is based on singular value decomposition and minimization of the coregistration error. The coregistration parameters thus derived can then be applied to coregister other PET and CT images from the same system. Twenty PET-CT images of the calibration phantom at various locations and/or orientations were obtained on a Siemens Inveon® Multi-Modality scanner. We tested the use of from 1 to 10 data sets to derive the coregistration parameters, and found that the coregistration accuracy improves with increasing number of data sets until it stabilizes. Coregistration of PET-CT images with an accuracy of 0.33±0.11 mm has been achieved by this method on the Inveon Multi-Modality scanner.

Validation of CT-based attenuation correction for multi-pinhole PSF reconstruction for small-animal SPECT

We recently reported a numerical ray-tracing algorithm for calculating the point-spread function (PSF) used in 3-D ordered subsets expectation maximization (OSEM) reconstruction of single and multi-pinhole collimated single photon emission computed tomography (SPECT) images. In this work, we evaluated the performance of our PSF reconstruction method with and without X-ray CT-based attenuation correction (AC) and dual energy window scatter correction (SC). X-ray CT data was acquired to create the attenuation maps. SPECT data was acquired using 99mTc phantoms and 5-pinhole tungsten collimators with 1.0 mm diameter pinholes. With no corrections applied, an axial image slice of a 3 cm diameter cylinder uniformly filled with mTc showed a 13% dip near the center of the phantom. When AC and SC were applied, the cross-section through an axial slice showed a desirable flattened profile that dipped only 3%. We also scanned a mouse with 99mTc implantable sources that had negligible self-attenuation. The sources were first scanned in air for calibration. Our results show that the reconstructed SPECT images with no corrections underestimated the activity for each mTc implanted source by 12% on average, while the image with AC and SC underestimated the activity by only 3.3% on average. We repeated all of the experiments with 125I phantoms but did not apply SC to the 125I data. With no correction applied, an axial slice of a 3 cm diameter cylinder uniformly filled with 125I dipped 25 % near the center of the phantom. After applying AC, the 125I image profile no longer dipped but rather was overcorrected by 4.5%. Similarly, the reconstructed image of the 125I implants with no correction underestimated the activity of each source by 23% on average, while the 125I image with AC overestimated the activity in the sources by 4.6% on average. These results have shown that our PSF reconstruction method with CT-based attenuation correction improved the quantitative accuracy of SPECT images for representative 99mTc and 125I studies.

Generation of normalization maps for pixelated pinhole SPECT detectors by scanning a uniform cylinder phantom

In this work, a method of generating normalization maps by scanning a large uniform cylindrical object in standard tomography mode (with the collimator on) has been investigated. This method may have several advantages over point-source approaches: First, since the object is not attached to the collimator, the normalization map generated may be less sensitivity to the geometric changes than the point-source-atpinhole approach. Second, it represents the typical photon incident angles during imaging. Third, it can be applied to single-pinhole and multi-pinhole collimators. Combined with the point-source normalization at 360 mm distance, a normalization correction map (to correct for the 360 mm point-source normalization) can be generated for the specific isotope and collimator and thus applied to different scanners of the same type.

Reconstruction of multi-pinhole SPECT data with correction of attenuation, scatter and intrinsic detector resolution

Multi-pinhole SPECT collimators can provide sub-millimeter resolution and improved sensitivity over single-pinhole and parallel-beam collimators. Attenuation and scatter will degrade the quantitative accuracy of reconstruction for lower energy emitters like I-125 and therefore both effects should be accounted for during reconstruction. We implemented an OSEM MAP reconstruction which incorporated attenuation, scatter and detector intrinsic resolution for a multi-pinhole detector designed for whole-body mouse imaging. The ray- driven projector/backprojector implemented considerably reduced the calculation of attenuation factors and decreased reconstruction time compared to a voxel-driven approach. The multi-pinhole SPECT system simulated consists of 2 or 4 cameras, with a 5-pinhole collimator plate for each. The attenuation map would be obtained from a CT system mounted on the same gantry. Scatter is estimated from scatter windows using a triple energy window (TEW) method and applied during the iterative reconstruction. A quadratic smoothness prior is implemented to control noise. Simulations with the MOBY mouse phantom show that modeling of the pinhole sensitivity, attenuation and detector intrinsic resolution results in a more accurate reconstruction. Preliminary Monte Carlo simulations showed the importance of determining and correcting the attenuation and scatter for I-125 imaging. Further investigations will be performed towards accurate estimation of the point-spread-function or sensitivity model of the multi-pinhole collimator plate.

Automated least-squares calibration of the coregistration parameters for a micro PET-CT system

A previously developed method derives co-registration parameters from PET and CT images of a four-point-source calibration phantom by manually adjusting the offsets and orientation of the CT image to achieve alignment with the PET image in a graphic viewer. This manual process is tedious and can be inaccurate, especially when rotational offsets exist. An automated segmentation method has been developed, based on thresholding and application of constraints on the sizes of point sources in the images. After point sources are identified on PET and CT images, co-registration is performed using an analytic rigid-body registration algorithm which is based on singular value decomposition and minimization of the co-registration error. The co-registration parameters thus derived can then be applied to co-register other PET and CT images from the same system. Twenty PET-CT images of the calibration phantom at various locations and/or orientations were obtained on a Siemens Inveon® Multi-Modality scanner. We tested the use of from 1 to 10 data sets to derive the co-registration parameters, and found that the co-registration accuracy improves with increasing number of data sets until it stabilizes. Co-registration of PET-CT images with an accuracy of 0.33±0.11 mm has been achieved by this method on the Inveon Multi-Modality scanner.