Convergence of numerical time-averaging and stationary measures via Poisson equations

Numerical approximation of the long time behavior of a stochastic di.erential equation (SDE) is considered. Error estimates for time-averaging estimators are obtained and then used to show that the stationary behavior of the numerical method converges to that of the SDE. The error analysis is based on using an associated Poisson equation for the underlying SDE. The main advantages of this approach are its simplicity and universality. It works equally well for a range of explicit and implicit schemes, including those with simple simulation of random variables, and for hypoelliptic SDEs. To simplify the exposition, we consider only the case where the state space of the SDE is a torus, and we study only smooth test functions. However, we anticipate that the approach can be applied more widely. An analogy between our approach and Stein's method is indicated. Some practical implications of the results are discussed. Copyright © by SIAM. Unauthorized reproduction of this article is prohibited.

On-board Robotic Multi-pinhole SPECT System for Region-of-interest (ROI) Imaging

On-board image guidance, such as cone-beam CT (CBCT) and kV/MV 2D imaging, is essential in many radiation therapy procedures, such as intensity modulated radiotherapy (IMRT) and stereotactic body radiation therapy (SBRT). These imaging techniques provide predominantly anatomical information for treatment planning and target localization. Recently, studies have shown that treatment planning based on functional and molecular information about the tumor and surrounding tissue could potentially improve the effectiveness of radiation therapy. However, current on-board imaging systems are limited in their functional and molecular imaging capability. Single Photon Emission Computed Tomography (SPECT) is a candidate to achieve on-board functional and molecular imaging. Traditional SPECT systems typically take 20 minutes or more for a scan, which is too long for on-board imaging. A robotic multi-pinhole SPECT system was proposed in this dissertation to provide shorter imaging time by using a robotic arm to maneuver the multi-pinhole SPECT system around the patient in position for radiation therapy.

A 49-pinhole collimated SPECT detector and its shielding were designed and simulated in this work using the computer-aided design (CAD) software. The trajectories of robotic arm about the patient, treatment table and gantry in the radiation therapy room and several detector assemblies such as parallel holes, single pinhole and 49 pinholes collimated detector were investigated. The rail mounted system was designed to enable a full range of detector positions and orientations to various crucial treatment sites including head and torso, while avoiding collision with linear accelerator (LINAC), patient table and patient.

An alignment method was developed in this work to calibrate the on-board robotic SPECT to the LINAC coordinate frame and to the coordinate frames of other on-board imaging systems such as CBCT. This alignment method utilizes line sources and one pinhole projection of these line sources. The model consists of multiple alignment parameters which maps line sources in 3-dimensional (3D) space to their 2-dimensional (2D) projections on the SPECT detector. Computer-simulation studies and experimental evaluations were performed as a function of number of line sources, Radon transform accuracy, finite line-source width, intrinsic camera resolution, Poisson noise and acquisition geometry. In computer-simulation studies, when there was no error in determining angles (α) and offsets (ρ) of the measured projections, the six alignment parameters (3 translational and 3 rotational) were estimated perfectly using three line sources. When angles (α) and offsets (ρ) were provided by Radon transform, the estimation accuracy was reduced. The estimation error was associated with rounding errors of Radon transform, finite line-source width, Poisson noise, number of line sources, intrinsic camera resolution and detector acquisition geometry. The estimation accuracy was significantly improved by using 4 line sources rather than 3 and also by using thinner line-source projections (obtained by better intrinsic detector resolution). With 5 line sources, median errors were 0.2 mm for the detector translations, 0.7 mm for the detector radius of rotation, and less than 0.5° for detector rotation, tilt and twist. In experimental evaluations, average errors relative to a different, independent registration technique were about 1.8 mm for detector translations, 1.1 mm for the detector radius of rotation (ROR), 0.5° and 0.4° for detector rotation and tilt, respectively, and 1.2° for detector twist.

Simulation studies were performed to investigate the improvement of imaging sensitivity and accuracy of hot sphere localization for breast imaging of patients in prone position. A 3D XCAT phantom was simulated in the prone position with nine hot spheres of 10 mm diameter added in the left breast. A no-treatment-table case and two commercial prone breast boards, 7 and 24 cm thick, were simulated. Different pinhole focal lengths were assessed for root-mean-square-error (RMSE). The pinhole focal lengths resulting in the lowest RMSE values were 12 cm, 18 cm and 21 cm for no table, thin board, and thick board, respectively. In both no table and thin board cases, all 9 hot spheres were easily visualized above background with 4-minute scans utilizing the 49-pinhole SPECT system while seven of nine hot spheres were visible with the thick board. In comparison with parallel-hole system, our 49-pinhole system shows reduction in noise and bias under these simulation cases. These results correspond to smaller radii of rotation for no-table case and thinner prone board. Similarly, localization accuracy with the 49-pinhole system was significantly better than with the parallel-hole system for both the thin and thick prone boards. Median localization errors for the 49-pinhole system with the thin board were less than 3 mm for 5 of 9 hot spheres, and less than 6 mm for the other 4 hot spheres. Median localization errors of 49-pinhole system with the thick board were less than 4 mm for 5 of 9 hot spheres, and less than 8 mm for the other 4 hot spheres.

Besides prone breast imaging, respiratory-gated region-of-interest (ROI) imaging of lung tumor was also investigated. A simulation study was conducted on the potential of multi-pinhole, region-of-interest (ROI) SPECT to alleviate noise effects associated with respiratory-gated SPECT imaging of the thorax. Two 4D XCAT digital phantoms were constructed, with either a 10 mm or 20 mm diameter tumor added in the right lung. The maximum diaphragm motion was 2 cm (for 10 mm tumor) or 4 cm (for 20 mm tumor) in superior-inferior direction and 1.2 cm in anterior-posterior direction. Projections were simulated with a 4-minute acquisition time (40 seconds per each of 6 gates) using either the ROI SPECT system (49-pinhole) or reference single and dual conventional broad cross-section, parallel-hole collimated SPECT. The SPECT images were reconstructed using OSEM with up to 6 iterations. Images were evaluated as a function of gate by profiles, noise versus bias curves, and a numerical observer performing a forced-choice localization task. Even for the 20 mm tumor, the 49-pinhole imaging ROI was found sufficient to encompass fully usual clinical ranges of diaphragm motion. Averaged over the 6 gates, noise at iteration 6 of 49-pinhole ROI imaging (10.9 µCi/ml) was approximately comparable to noise at iteration 2 of the two dual and single parallel-hole, broad cross-section systems (12.4 µCi/ml and 13.8 µCi/ml, respectively). Corresponding biases were much lower for the 49-pinhole ROI system (3.8 µCi/ml), versus 6.2 µCi/ml and 6.5 µCi/ml for the dual and single parallel-hole systems, respectively. Median localization errors averaged over 6 gates, for the 10 mm and 20 mm tumors respectively, were 1.6 mm and 0.5 mm using the ROI imaging system and 6.6 mm and 2.3 mm using the dual parallel-hole, broad cross-section system. The results demonstrate substantially improved imaging via ROI methods. One important application may be gated imaging of patients in position for radiation therapy.

A robotic SPECT imaging system was constructed utilizing a gamma camera detector (Digirad 2020tc) and a robot (KUKA KR150-L110 robot). An imaging study was performed with a phantom (PET CT PhantomTM), which includes 5 spheres of 10, 13, 17, 22 and 28 mm in diameter. The phantom was placed on a flat-top couch. SPECT projections were acquired with a parallel-hole collimator and a single-pinhole collimator both without background in the phantom, and with background at 1/10th the sphere activity concentration. The imaging trajectories of parallel-hole and pinhole collimated detectors spanned 180 degrees and 228 degrees respectively. The pinhole detector viewed a 14.7 cm-diameter common volume which encompassed the 28 mm and 22 mm spheres. The common volume for parallel-hole was a 20.8-cm-diameter cylinder which encompassed all five spheres in the phantom. The maneuverability of the robotic system was tested by navigating the detector to trace the flat-top table while avoiding collision with the table and maintaining the closest possible proximity to the common volume. For image reconstruction, detector trajectories were described by radius-of-rotation and detector rotation angle θ. These reconstruction parameters were obtained from the robot base and tool coordinates. The robotic SPECT system was able to maneuver the parallel-hole and pinhole collimated SPECT detectors in close proximity to the phantom, minimizing impact of the flat-top couch on detector to center-of-rotation (COR) distance. In no background case, all five spheres were visible in the reconstructed parallel-hole and pinhole images. In with background case, three spheres of 17, 22 and 28 mm diameter were readily observed with the parallel-hole imaging, and the targeted spheres (22 and 28 mm diameter) were readily observed in the pinhole ROI imaging.

In conclusion, the proposed on-board robotic SPECT can be aligned to LINAC/CBCT with a single pinhole projection of the line-source phantom. Alignment parameters can be estimated using one pinhole projection of line sources. This alignment method may be important for multi-pinhole SPECT, where relative pinhole alignment may vary during rotation. For single pinhole and multi-pinhole SPECT imaging onboard radiation therapy machines, the method could provide alignment of SPECT coordinates with those of CBCT and the LINAC. In simulation studies of prone breast imaging and respiratory-gated lung imaging, the 49-pinhole detector showed better tumor contrast recovery and localization in a 4-minute scan compared to parallel-hole detector. On-board SPECT could be achieved by a robot maneuvering a SPECT detector about patients in position for radiation therapy on a flat-top couch. The robot inherent coordinate frames could be an effective means to estimate detector pose for use in SPECT image reconstruction.

Convergent differential regulation of parvalbumin in the brains of vocal learners.

Spoken language and learned song are complex communication behaviors found in only a few species, including humans and three groups of distantly related birds--songbirds, parrots, and hummingbirds. Despite their large phylogenetic distances, these vocal learners show convergent behaviors and associated brain pathways for vocal communication. However, it is not clear whether this behavioral and anatomical convergence is associated with molecular convergence. Here we used oligo microarrays to screen for genes differentially regulated in brain nuclei necessary for producing learned vocalizations relative to adjacent brain areas that control other behaviors in avian vocal learners versus vocal non-learners. A top candidate gene in our screen was a calcium-binding protein, parvalbumin (PV). In situ hybridization verification revealed that PV was expressed significantly higher throughout the song motor pathway, including brainstem vocal motor neurons relative to the surrounding brain regions of all distantly related avian vocal learners. This differential expression was specific to PV and vocal learners, as it was not found in avian vocal non-learners nor for control genes in learners and non-learners. Similar to the vocal learning birds, higher PV up-regulation was found in the brainstem tongue motor neurons used for speech production in humans relative to a non-human primate, macaques. These results suggest repeated convergent evolution of differential PV up-regulation in the brains of vocal learners separated by more than 65-300 million years from a common ancestor and that the specialized behaviors of learned song and speech may require extra calcium buffering and signaling.

PARTAKE survey of public knowledge and perceptions of clinical research in India.

BACKGROUND: A public that is an informed partner in clinical research is important for ethical, methodological, and operational reasons. There are indications that the public is unaware or misinformed, and not sufficiently engaged in clinical research but studies on the topic are lacking. PARTAKE - Public Awareness of Research for Therapeutic Advancements through Knowledge and Empowerment is a program aimed at increasing public awareness and partnership in clinical research. The PARTAKE Survey is a component of the program. OBJECTIVE: To study public knowledge and perceptions of clinical research. METHODS: A 40-item questionnaire combining multiple-choice and open-ended questions was administered to 175 English- or Hindi-speaking individuals in 8 public locations representing various socioeconomic strata in New Delhi, India. RESULTS: Interviewees were 18-84 old (mean: 39.6, SD ± 16.6), 23.6% female, 68.6% employed, 7.3% illiterate, 26.3% had heard of research, 2.9% had participated and 58.9% expressed willingness to participate in clinical research. The following perceptions were reported (% true/% false/% not aware): 'research benefits society' (94.1%/3.5%/2.3%), 'the government protects against unethical clinical research' (56.7%/26.3%/16.9%), 'research hospitals provide better care' (67.2%/8.7%/23.9%), 'confidentiality is adequately protected' (54.1%/12.3%/33.5%), 'participation in research is voluntary' (85.3%/5.8%/8.7%); 'participants treated like 'guinea pigs'' (20.7%/53.2%/26.0%), and 'compensation for participation is adequate' (24.7%/12.9%/62.3%). CONCLUSIONS: Results suggest the Indian public is aware of some key features of clinical research (e.g., purpose, value, voluntary nature of participation), and supports clinical research in general but is unaware of other key features (e.g., compensation, confidentiality, protection of human participants) and exhibits some distrust in the conduct and reporting of clinical trials. Larger, cross-cultural surveys are required to inform educational programs addressing these issues.

Genome-wide association study of perioperative myocardial infarction after coronary artery bypass surgery.

OBJECTIVES: Identification of patient subpopulations susceptible to develop myocardial infarction (MI) or, conversely, those displaying either intrinsic cardioprotective phenotypes or highly responsive to protective interventions remain high-priority knowledge gaps. We sought to identify novel common genetic variants associated with perioperative MI in patients undergoing coronary artery bypass grafting using genome-wide association methodology. SETTING: 107 secondary and tertiary cardiac surgery centres across the USA. PARTICIPANTS: We conducted a stage I genome-wide association study (GWAS) in 1433 ethnically diverse patients of both genders (112 cases/1321 controls) from the Genetics of Myocardial Adverse Outcomes and Graft Failure (GeneMAGIC) study, and a stage II analysis in an expanded population of 2055 patients (225 cases/1830 controls) combined from the GeneMAGIC and Duke Perioperative Genetics and Safety Outcomes (PEGASUS) studies. Patients undergoing primary non-emergent coronary bypass grafting were included. PRIMARY AND SECONDARY OUTCOME MEASURES: The primary outcome variable was perioperative MI, defined as creatine kinase MB isoenzyme (CK-MB) values ≥10× upper limit of normal during the first postoperative day, and not attributable to preoperative MI. Secondary outcomes included postoperative CK-MB as a quantitative trait, or a dichotomised phenotype based on extreme quartiles of the CK-MB distribution. RESULTS: Following quality control and adjustment for clinical covariates, we identified 521 single nucleotide polymorphisms in the stage I GWAS analysis. Among these, 8 common variants in 3 genes or intergenic regions met p<10(-5) in stage II. A secondary analysis using CK-MB as a quantitative trait (minimum p=1.26×10(-3) for rs609418), or a dichotomised phenotype based on extreme CK-MB values (minimum p=7.72×10(-6) for rs4834703) supported these findings. Pathway analysis revealed that genes harbouring top-scoring variants cluster in pathways of biological relevance to extracellular matrix remodelling, endoplasmic reticulum-to-Golgi transport and inflammation. CONCLUSIONS: Using a two-stage GWAS and pathway analysis, we identified and prioritised several potential susceptibility loci for perioperative MI.

A whole-cell and single-channel study of the voltage-dependent outward potassium current in avian hepatocytes.

Voltage-dependent membrane currents were studied in dissociated hepatocytes from chick, using the patch-clamp technique. All cells had voltage-dependent outward K+ currents; in 10% of the cells, a fast, transient, tetrodotoxin-sensitive Na+ current was identified. None of the cells had voltage-dependent inward Ca2+ currents. The K+ current activated at a membrane potential of about -10 mV, had a sigmoidal time course, and did not inactivate in 500 ms. The maximum outward conductance was 6.6 +/- 2.4 nS in 18 cells. The reversal potential, estimated from tail current measurements, shifted by 50 mV per 10-fold increase in the external K+ concentration. The current traces were fitted by n2 kinetics with voltage-dependent time constants. Omitting Ca2+ from the external bath or buffering the internal Ca2+ with EGTA did not alter the outward current, which shows that Ca2+-activated K+ currents were not present. 1-5 mM 4-aminopyridine, 0.5-2 mM BaCl2, and 0.1-1 mM CdCl2 reversibly inhibited the current. The block caused by Ba was voltage dependent. Single-channel currents were recorded in cell-attached and outside-out patches. The mean unitary conductance was 7 pS, and the channels displayed bursting kinetics. Thus, avian hepatocytes have a single type of K+ channel belonging to the delayed rectifier class of K+ channels.

Platelet Counts, Acute Kidney Injury, and Mortality after Coronary Artery Bypass Grafting Surgery.

BACKGROUND: Cardiac surgery requiring cardiopulmonary bypass is associated with platelet activation. Because platelets are increasingly recognized as important effectors of ischemia and end-organ inflammatory injury, the authors explored whether postoperative nadir platelet counts are associated with acute kidney injury (AKI) and mortality after coronary artery bypass grafting (CABG) surgery. METHODS: The authors evaluated 4,217 adult patients who underwent CABG surgery. Postoperative nadir platelet counts were defined as the lowest in-hospital values and were used as a continuous predictor of postoperative AKI and mortality. Nadir values in the lowest 10th percentile were also used as a categorical predictor. Multivariable logistic regression and Cox proportional hazard models examined the association between postoperative platelet counts, postoperative AKI, and mortality. RESULTS: The median postoperative nadir platelet count was 121 × 10/l. The incidence of postoperative AKI was 54%, including 9.5% (215 patients) and 3.4% (76 patients) who experienced stages II and III AKI, respectively. For every 30 × 10/l decrease in platelet counts, the risk for postoperative AKI increased by 14% (adjusted odds ratio, 1.14; 95% CI, 1.09 to 1.20; P < 0.0001). Patients with platelet counts in the lowest 10th percentile were three times more likely to progress to a higher severity of postoperative AKI (adjusted proportional odds ratio, 3.04; 95% CI, 2.26 to 4.07; P < 0.0001) and had associated increased risk for mortality immediately after surgery (adjusted hazard ratio, 5.46; 95% CI, 3.79 to 7.89; P < 0.0001). CONCLUSION: The authors found a significant association between postoperative nadir platelet counts and AKI and short-term mortality after CABG surgery.