A theory of hypoellipticity and unique ergodicity for semilinear stochastic PDEs

We present a theory of hypoellipticity and unique ergodicity for semilinear parabolic stochastic PDEs with "polynomial" nonlinearities and additive noise, considered as abstract evolution equations in some Hilbert space. It is shown that if Hörmander's bracket condition holds at every point of this Hilbert space, then a lower bound on the Malliavin covariance operatorμt can be obtained. Informally, this bound can be read as "Fix any finite-dimensional projection on a subspace of sufficiently regular functions. Then the eigenfunctions of μt with small eigenvalues have only a very small component in the image of Π." We also show how to use a priori bounds on the solutions to the equation to obtain good control on the dependency of the bounds on the Malliavin matrix on the initial condition. These bounds are sufficient in many cases to obtain the asymptotic strong Feller property introduced in [HM06]. One of the main novel technical tools is an almost sure bound from below on the size of "Wiener polynomials," where the coefficients are possibly non-adapted stochastic processes satisfying a Lips chitz condition. By exploiting the polynomial structure of the equations, this result can be used to replace Norris' lemma, which is unavailable in the present context. We conclude by showing that the two-dimensional stochastic Navier-Stokes equations and a large class of reaction-diffusion equations fit the framework of our theory.

Anti-hypotensive treatment and endothelin blockade synergistically antagonize exercise fatigue in rats under simulated high altitude.

Rapid ascent to high altitude causes illness and fatigue, and there is a demand for effective acute treatments to alleviate such effects. We hypothesized that increased oxygen delivery to the tissue using a combination of a hypertensive agent and an endothelin receptor A antagonist drugs would limit exercise-induced fatigue at simulated high altitude. Our data showed that the combination of 0.1 mg/kg ambrisentan with either 20 mg/kg ephedrine or 10 mg/kg methylphenidate significantly improved exercise duration in rats at simulated altitude of 4,267 m, whereas the individual compounds did not. In normoxic, anesthetized rats, ephedrine alone and in combination with ambrisentan increased heart rate, peripheral blood flow, carotid and pulmonary arterial pressures, breathing rate, and vastus lateralis muscle oxygenation, but under inspired hypoxia, only the combination treatment significantly enhanced muscle oxygenation. Our results suggest that sympathomimetic agents combined with endothelin-A receptor blockers offset altitude-induced fatigue in rats by synergistically increasing the delivery rate of oxygen to hypoxic muscle by concomitantly augmenting perfusion pressure and improving capillary conductance in the skeletal muscle. Our findings might therefore serve as a basis to develop an effective treatment to prevent high-altitude illness and fatigue in humans.

Primary care physician decision making regarding severe obesity treatment and bariatric surgery: a qualitative study.

BACKGROUND: Less than 1% of severely obese US adults undergo bariatric surgery annually. It is critical to understand the factors that contribute to its utilization. OBJECTIVES: To understand how primary care physicians (PCPs) make decisions regarding severe obesity treatment and bariatric surgery referral. SETTING: Focus groups with PCPs practicing in small, medium, and large cities in Wisconsin. METHODS: PCPs were asked to discuss prioritization of treatment for a severely obese patient with multiple co-morbidities and considerations regarding bariatric surgery referral. Focus group sessions were analyzed by using a directed approach to content analysis. A taxonomy of consensus codes was developed. Code summaries were created and representative quotes identified. RESULTS: Sixteen PCPs participated in 3 focus groups. Four treatment prioritization approaches were identified: (1) treat the disease that is easiest to address; (2) treat the disease that is perceived as the most dangerous; (3) let the patient set the agenda; and (4) address obesity first because it is the common denominator underlying other co-morbid conditions. Only the latter approach placed emphasis on obesity treatment. Five factors made PCPs hesitate to refer patients for bariatric surgery: (1) wanting to "do no harm"; (2) questioning the long-term effectiveness of bariatric surgery; (3) limited knowledge about bariatric surgery; (4) not wanting to recommend bariatric surgery too early; and (5) not knowing if insurance would cover bariatric surgery. CONCLUSION: Decision making by PCPs for severely obese patients seems to underprioritize obesity treatment and overestimate bariatric surgery risks. This could be addressed with PCP education and improvements in communication between PCPs and bariatric surgeons.

The Market for Apples: A Theory of Identity and Consumption

This paper presents an economic model of the effects of identity and social norms on consumption patterns. By incorporating qualitative studies in psychology and sociology, I propose a utility function that features two components – economic (functional) and identity elements. This setup is extended to analyze a market comprising a continuum of consumers, whose identity distribution along a spectrum of binary identities is described by a Beta distribution. I also introduce the notion of salience in the context of identity and consumption decisions. The key result of the model suggests that fundamental economic parameters, such as price elasticity and market demand, can be altered by identity elements. In addition, it predicts that firms in perfectly competitive markets may associate their products with certain types of identities, in order to reduce product substitutability and attain price-setting power.

Gender and racial/ethnic differences in addiction severity, HIV risk, and quality of life among adults in opioid detoxification: results from the National Drug Abuse Treatment Clinical Trials Network.

PURPOSE: Detoxification often serves as an initial contact for treatment and represents an opportunity for engaging patients in aftercare to prevent relapse. However, there is limited information concerning clinical profiles of individuals seeking detoxification, and the opportunity to engage patients in detoxification for aftercare often is missed. This study examined clinical profiles of a geographically diverse sample of opioid-dependent adults in detoxification to discern the treatment needs of a growing number of women and whites with opioid addiction and to inform interventions aimed at improving use of aftercare or rehabilitation. METHODS: The sample included 343 opioid-dependent patients enrolled in two national multi-site studies of the National Drug Abuse Treatment Clinical Trials Network (CTN001-002). Patients were recruited from 12 addiction treatment programs across the nation. Gender and racial/ethnic differences in addiction severity, human immunodeficiency virus (HIV) risk, and quality of life were examined. RESULTS: Women and whites were more likely than men and African Americans to have greater psychiatric and family/social relationship problems and report poorer health-related quality of life and functioning. Whites and Hispanics exhibited higher levels of total HIV risk scores and risky injection drug use scores than African Americans, and Hispanics showed a higher level of unprotected sexual behaviors than whites. African Americans were more likely than whites to use heroin and cocaine and to have more severe alcohol and employment problems. CONCLUSIONS: Women and whites show more psychopathology than men and African Americans. These results highlight the need to monitor an increased trend of opioid addiction among women and whites and to develop effective combined psychosocial and pharmacologic treatments to meet the diverse needs of the expanding opioid-abusing population. Elevated levels of HIV risk behaviors among Hispanics and whites also warrant more research to delineate mechanisms and to reduce their risky behaviors.

An integrated alcohol abuse and medical treatment model for patients with hepatitis C.

BACKGROUND: Patients with chronic hepatitis C virus (HCV) infection have high rates of alcohol consumption, which is associated with progression of fibrosis and lower response rates to HCV treatment. AIMS: This prospective cohort study examined the feasibility of a 24-week integrated alcohol and medical treatment to HCV-infected patients. METHODS: Patients were recruited from a hepatology clinic if they had an Alcohol Use Disorders Identification Test score >4 for women and >8 for men, suggesting hazardous alcohol consumption. The integrated model included patients receiving medical care and alcohol treatment within the same clinic. Alcohol treatment consisted of 6 months of group and individual therapy from an addictions specialist and consultation from a study team psychiatrist as needed. RESULTS: Sixty patients were initially enrolled, and 53 patients participated in treatment. The primary endpoint was the Addiction Severity Index (ASI) alcohol composite scores, which significantly decreased by 0.105 (41.7% reduction) between 0 and 3 months (P < 0.01) and by 0.128 (50.6% reduction) between 0 and 6 months (P < 0.01) after adjusting for covariates. Alcohol abstinence was reported by 40% of patients at 3 months and 44% at 6 months. Patients who did not become alcohol abstinent had reductions in their ASI alcohol composite scores from 0.298 at baseline to 0.219 (26.8% reduction) at 6 months (P = 0.08). CONCLUSION: This study demonstrated that an integrated model of alcohol treatment and medical care could be successfully implemented in a hepatology clinic with significant favorable impact on alcohol use and abstinence among patients with chronic HCV.

Vascular access, fluid resuscitation, and blood transfusion in pediatric trauma.

Trauma care in the general population has largely become protocol-driven, with an emphasis on fast and efficient treatment, good team communication at all levels of care including prehospital care, initial resuscitation, intensive care, and rehabilitation. Most available literature on trauma care has focused on adults, allowing the potential to apply concepts from adult care to pediatric care. But there remain issues that will always be specific to pediatric patients that may not translate from adults. Several new devices such as intraosseous (IO) needle systems and techniques such as ultrasonography to cannulate central and peripheral veins have become available for integration into our pre-existing trauma care system for children. This review will focus specifically on the latest techniques and evidence available for establishing intravenous access, rational approaches to fluid resuscitation, and blood product transfusion in the pediatric trauma patient.

Veterans health administration hepatitis B testing and treatment with anti-CD20 antibody administration.

AIM: To evaluate pretreatment hepatitis B virus (HBV) testing, vaccination, and antiviral treatment rates in Veterans Affairs patients receiving anti-CD20 Ab for quality improvement. METHODS: We performed a retrospective cohort study using a national repository of Veterans Health Administration (VHA) electronic health record data. We identified all patients receiving anti-CD20 Ab treatment (2002-2014). We ascertained patient demographics, laboratory results, HBV vaccination status (from vaccination records), pharmacy data, and vital status. The high risk period for HBV reactivation is during anti-CD20 Ab treatment and 12 mo follow up. Therefore, we analyzed those who were followed to death or for at least 12 mo after completing anti-CD20 Ab. Pretreatment serologic tests were used to categorize chronic HBV (hepatitis B surface antigen positive or HBsAg+), past HBV (HBsAg-, hepatitis B core antibody positive or HBcAb+), resolved HBV (HBsAg-, HBcAb+, hepatitis B surface antibody positive or HBsAb+), likely prior vaccination (isolated HBsAb+), HBV negative (HBsAg-, HBcAb-), or unknown. Acute hepatitis B was defined by the appearance of HBsAg+ in the high risk period in patients who were pretreatment HBV negative. We assessed HBV antiviral treatment and the incidence of hepatitis, liver failure, and death during the high risk period. Cumulative hepatitis, liver failure, and death after anti-CD20 Ab initiation were compared by HBV disease categories and differences compared using the χ(2) test. Mean time to hepatitis peak alanine aminotransferase, liver failure, and death relative to anti-CD20 Ab administration and follow-up were also compared by HBV disease group. RESULTS: Among 19304 VHA patients who received anti-CD20 Ab, 10224 (53%) had pretreatment HBsAg testing during the study period, with 49% and 43% tested for HBsAg and HBcAb, respectively within 6 mo pretreatment in 2014. Of those tested, 2% (167/10224) had chronic HBV, 4% (326/7903) past HBV, 5% (427/8110) resolved HBV, 8% (628/8110) likely prior HBV vaccination, and 76% (6022/7903) were HBV negative. In those with chronic HBV infection, ≤ 37% received HBV antiviral treatment during the high risk period while 21% to 23% of those with past or resolved HBV, respectively, received HBV antiviral treatment. During and 12 mo after anti-CD20 Ab, the rate of hepatitis was significantly greater in those HBV positive vs negative (P = 0.001). The mortality rate was 35%-40% in chronic or past hepatitis B and 26%-31% in hepatitis B negative. In those pretreatment HBV negative, 16 (0.3%) developed acute hepatitis B of 4947 tested during anti-CD20Ab treatment and follow-up. CONCLUSION: While HBV testing of Veterans has increased prior to anti-CD20 Ab, few HBV+ patients received HBV antivirals, suggesting electronic health record algorithms may enhance health outcomes.

Radiotherapy Treatment Assessment using DCE-MRI

Abstract

The goal of modern radiotherapy is to precisely deliver a prescribed radiation dose to delineated target volumes that contain a significant amount of tumor cells while sparing the surrounding healthy tissues/organs. Precise delineation of treatment and avoidance volumes is the key for the precision radiation therapy. In recent years, considerable clinical and research efforts have been devoted to integrate MRI into radiotherapy workflow motivated by the superior soft tissue contrast and functional imaging possibility. Dynamic contrast-enhanced MRI (DCE-MRI) is a noninvasive technique that measures properties of tissue microvasculature. Its sensitivity to radiation-induced vascular pharmacokinetic (PK) changes has been preliminary demonstrated. In spite of its great potential, two major challenges have limited DCE-MRI’s clinical application in radiotherapy assessment: the technical limitations of accurate DCE-MRI imaging implementation and the need of novel DCE-MRI data analysis methods for richer functional heterogeneity information.

This study aims at improving current DCE-MRI techniques and developing new DCE-MRI analysis methods for particular radiotherapy assessment. Thus, the study is naturally divided into two parts. The first part focuses on DCE-MRI temporal resolution as one of the key DCE-MRI technical factors, and some improvements regarding DCE-MRI temporal resolution are proposed; the second part explores the potential value of image heterogeneity analysis and multiple PK model combination for therapeutic response assessment, and several novel DCE-MRI data analysis methods are developed.

I. Improvement of DCE-MRI temporal resolution. First, the feasibility of improving DCE-MRI temporal resolution via image undersampling was studied. Specifically, a novel MR image iterative reconstruction algorithm was studied for DCE-MRI reconstruction. This algorithm was built on the recently developed compress sensing (CS) theory. By utilizing a limited k-space acquisition with shorter imaging time, images can be reconstructed in an iterative fashion under the regularization of a newly proposed total generalized variation (TGV) penalty term. In the retrospective study of brain radiosurgery patient DCE-MRI scans under IRB-approval, the clinically obtained image data was selected as reference data, and the simulated accelerated k-space acquisition was generated via undersampling the reference image full k-space with designed sampling grids. Two undersampling strategies were proposed: 1) a radial multi-ray grid with a special angular distribution was adopted to sample each slice of the full k-space; 2) a Cartesian random sampling grid series with spatiotemporal constraints from adjacent frames was adopted to sample the dynamic k-space series at a slice location. Two sets of PK parameters’ maps were generated from the undersampled data and from the fully-sampled data, respectively. Multiple quantitative measurements and statistical studies were performed to evaluate the accuracy of PK maps generated from the undersampled data in reference to the PK maps generated from the fully-sampled data. Results showed that at a simulated acceleration factor of four, PK maps could be faithfully calculated from the DCE images that were reconstructed using undersampled data, and no statistically significant differences were found between the regional PK mean values from undersampled and fully-sampled data sets. DCE-MRI acceleration using the investigated image reconstruction method has been suggested as feasible and promising.

Second, for high temporal resolution DCE-MRI, a new PK model fitting method was developed to solve PK parameters for better calculation accuracy and efficiency. This method is based on a derivative-based deformation of the commonly used Tofts PK model, which is presented as an integrative expression. This method also includes an advanced Kolmogorov-Zurbenko (KZ) filter to remove the potential noise effect in data and solve the PK parameter as a linear problem in matrix format. In the computer simulation study, PK parameters representing typical intracranial values were selected as references to simulated DCE-MRI data for different temporal resolution and different data noise level. Results showed that at both high temporal resolutions (<1s) and clinically feasible temporal resolution (~5s), this new method was able to calculate PK parameters more accurate than the current calculation methods at clinically relevant noise levels; at high temporal resolutions, the calculation efficiency of this new method was superior to current methods in an order of 102. In a retrospective of clinical brain DCE-MRI scans, the PK maps derived from the proposed method were comparable with the results from current methods. Based on these results, it can be concluded that this new method can be used for accurate and efficient PK model fitting for high temporal resolution DCE-MRI.

II. Development of DCE-MRI analysis methods for therapeutic response assessment. This part aims at methodology developments in two approaches. The first one is to develop model-free analysis method for DCE-MRI functional heterogeneity evaluation. This approach is inspired by the rationale that radiotherapy-induced functional change could be heterogeneous across the treatment area. The first effort was spent on a translational investigation of classic fractal dimension theory for DCE-MRI therapeutic response assessment. In a small-animal anti-angiogenesis drug therapy experiment, the randomly assigned treatment/control groups received multiple fraction treatments with one pre-treatment and multiple post-treatment high spatiotemporal DCE-MRI scans. In the post-treatment scan two weeks after the start, the investigated Rényi dimensions of the classic PK rate constant map demonstrated significant differences between the treatment and the control groups; when Rényi dimensions were adopted for treatment/control group classification, the achieved accuracy was higher than the accuracy from using conventional PK parameter statistics. Following this pilot work, two novel texture analysis methods were proposed. First, a new technique called Gray Level Local Power Matrix (GLLPM) was developed. It intends to solve the lack of temporal information and poor calculation efficiency of the commonly used Gray Level Co-Occurrence Matrix (GLCOM) techniques. In the same small animal experiment, the dynamic curves of Haralick texture features derived from the GLLPM had an overall better performance than the corresponding curves derived from current GLCOM techniques in treatment/control separation and classification. The second developed method is dynamic Fractal Signature Dissimilarity (FSD) analysis. Inspired by the classic fractal dimension theory, this method measures the dynamics of tumor heterogeneity during the contrast agent uptake in a quantitative fashion on DCE images. In the small animal experiment mentioned before, the selected parameters from dynamic FSD analysis showed significant differences between treatment/control groups as early as after 1 treatment fraction; in contrast, metrics from conventional PK analysis showed significant differences only after 3 treatment fractions. When using dynamic FSD parameters, the treatment/control group classification after 1st treatment fraction was improved than using conventional PK statistics. These results suggest the promising application of this novel method for capturing early therapeutic response.

The second approach of developing novel DCE-MRI methods is to combine PK information from multiple PK models. Currently, the classic Tofts model or its alternative version has been widely adopted for DCE-MRI analysis as a gold-standard approach for therapeutic response assessment. Previously, a shutter-speed (SS) model was proposed to incorporate transcytolemmal water exchange effect into contrast agent concentration quantification. In spite of richer biological assumption, its application in therapeutic response assessment is limited. It might be intriguing to combine the information from the SS model and from the classic Tofts model to explore potential new biological information for treatment assessment. The feasibility of this idea was investigated in the same small animal experiment. The SS model was compared against the Tofts model for therapeutic response assessment using PK parameter regional mean value comparison. Based on the modeled transcytolemmal water exchange rate, a biological subvolume was proposed and was automatically identified using histogram analysis. Within the biological subvolume, the PK rate constant derived from the SS model were proved to be superior to the one from Tofts model in treatment/control separation and classification. Furthermore, novel biomarkers were designed to integrate PK rate constants from these two models. When being evaluated in the biological subvolume, this biomarker was able to reflect significant treatment/control difference in both post-treatment evaluation. These results confirm the potential value of SS model as well as its combination with Tofts model for therapeutic response assessment.

In summary, this study addressed two problems of DCE-MRI application in radiotherapy assessment. In the first part, a method of accelerating DCE-MRI acquisition for better temporal resolution was investigated, and a novel PK model fitting algorithm was proposed for high temporal resolution DCE-MRI. In the second part, two model-free texture analysis methods and a multiple-model analysis method were developed for DCE-MRI therapeutic response assessment. The presented works could benefit the future DCE-MRI routine clinical application in radiotherapy assessment.