Impulsive Partial Hyperbolic Functional Differential Equations of Fractional Order with State-Dependent Delay

MSC 2010: 26A33, 34A37, 34K37, 34K40, 35R11

Efficient solution of two-sided nonlinear space-fractional diffusion equations using fast Poisson preconditioners

We develop a fast Poisson preconditioner for the efficient numerical solution of a class of two-sided nonlinear space fractional diffusion equations in one and two dimensions using the method of lines. Using the shifted Gr¨unwald finite difference formulas to approximate the two-sided(i.e. the left and right Riemann-Liouville) fractional derivatives, the resulting semi-discrete nonlinear systems have dense Jacobian matrices owing to the non-local property of fractional derivatives. We employ a modern initial value problem solver utilising backward differentiation formulas and Jacobian-free Newton-Krylov methods to solve these systems. For efficient performance of the Jacobianfree Newton-Krylov method it is essential to apply an effective preconditioner to accelerate the convergence of the linear iterative solver. The key contribution of our work is to generalise the fast Poisson preconditioner, widely used for integer-order diffusion equations, so that it applies to the two-sided space fractional diffusion equation. A number of numerical experiments are presented to demonstrate the effectiveness of the preconditioner and the overall solution strategy.

On the Riemann-Liouville Fractional q-Integral Operator Involving a Basic Analogue of Fox H-Function

2000 Mathematics Subject Classification: 33D60, 26A33, 33C60

On a Differential Equation with Left and Right Fractional Derivatives

Mathematics Subject Classification: 26A33; 70H03, 70H25, 70S05; 49S05

Mixed Fractional Integration Operators in Mixed Weighted Hölder Spaces

MSC 2010: 26A33

The impact of inter-fraction set-up errors on the probability of pulmonary and cardiac complication in left-sided breast cancer patients

Purpose This study evaluated the impact of patient set-up errors on the probability of pulmonary and cardiac complications in the irradiation of left-sided breast cancer. Methods and Materials Using the CMS XiO Version 4.6 (CMS Inc., St Louis, MO) radiotherapy planning system's NTCP algorithm and the Lyman -Kutcher-Burman (LKB) model, we calculated the DVH indices for the ipsilateral lung and heart and the resultant normal tissue complication probabilities (NTCP) for radiation-induced pneumonitis and excess cardiac mortality in 12 left-sided breast cancer patients. Results Isocenter shifts in the posterior direction had the greatest effect on the lung V20, heart V25, mean and maximum doses to the lung and the heart. Dose volume histograms (DVH) results show that the ipsilateral lung V20 tolerance was exceeded in 58% of the patients after 1cm posterior shifts. Similarly, the heart V25 tolerance was exceeded after 1cm antero-posterior and left-right isocentric shifts in 70% of the patients. The baseline NTCPs for radiation-induced pneumonitis ranged from 0.73% - 3.4% with a mean value of 1.7%. The maximum reported NTCP for radiation-induced pneumonitis was 5.8% (mean 2.6%) after 1cm posterior isocentric shift. The NTCP for excess cardiac mortality were 0 % in 100% of the patients (n=12) before and after setup error simulations. Conclusions Set-up errors in left sided breast cancer patients have a statistically significant impact on the Lung NTCPs and DVH indices. However, with a central lung distance of 3cm or less (CLD <3cm), and a maximum heart distance of 1.5cm or less (MHD<1.5cm), the treatment plans could tolerate set-up errors of up to 1cm without any change in the NTCP to the heart.

Unintended cardiac irradiation during left-sided breast cancer radiotherapy

Objective: Cardiac irradiation during left-sided breast radiotherapy may lead to
deleterious cardiac side effects. Using image guided radiotherapy, it is possible
to exclude the heart from treatment fields and monitor reproducibility of virtual simulation (VS) fields at treatment delivery using electronic portal imaging (EPI). Retrospectively, we evaluate the incidence of cardiac irradiation at VS and subsequent unintended cardiac irradiation during treatment.

Methods: Patients receiving left-sided radiotherapy to the breast or chest wall,
treated with a glancing photon field technique during a four-month period, were
included. VS images and EPIs during radiotherapy delivery were visually assessed.
The presence of any portion of the heart within the treatment field at VS or during treatment was recorded. Central lung distance and maximum heart distance were recorded.

Results: Of 128 patients, 45 (35.1%) had any portion of the heart within the
planned treatment field. Of these, inclusion of the heart was clinically unavoidable in 25 (55.6%). Of those with no heart included in the treatment fields at VS, 41 (49.4%) had presence of the heart as assessed on EPI during treatment.

Conclusion: Unintended cardiac irradiation during left-sided breast radiotherapy treatment occurs in a sizeable proportion of patients.

Advances in knowledge: Despite the use of three-dimensional computed tomography simulation and cardiac shielding, sizeable proportions of patients receiving left-sided breast cancer radiotherapy have unintended cardiac irradiation.

Volumetric modulated arc therapy and breath-hold in image-guided locoregional left-sided breast irradiation

PURPOSE: To investigate the effects of using volumetric modulated arc therapy (VMAT) and/or voluntary moderate deep inspiration breath-hold (vmDIBH) in the radiation therapy (RT) of left-sided breast cancer including the regional lymph nodes.

MATERIALS AND METHODS: For 13 patients, four treatment combinations were compared; 3D-conformal RT (i.e., forward IMRT) in free-breathing 3D-CRT(FB), 3D-CRT(vmDIBH), 2 partial arcs VMAT(FB), and VMAT(vmDIBH). Prescribed dose was 42.56 Gy in 16 fractions. For 10 additional patients, 3D-CRT and VMAT in vmDIBH only were also compared.

RESULTS: Dose conformity, PTV coverage, ipsilateral and total lung doses were significantly better for VMAT plans compared to 3D-CRT. Mean heart dose (D(mean,heart)) reduction in 3D-CRT(vmDIBH) was between 0.9 and 8.6 Gy, depending on initial D(mean,heart) (in 3D-CRT(FB) plans). VMAT(vmDIBH) reduced the D(mean,heart) further when D(mean,heart) was still >3.2 Gy in 3D-CRT(vmDIBH). Mean contralateral breast dose was higher for VMAT plans (2.7 Gy) compared to 3DCRT plans (0.7 Gy).

CONCLUSIONS: VMAT and 3D-CRT(vmDIBH) significantly reduced heart dose for patients treated with locoregional RT of left-sided breast cancer. When Dmean,heart exceeded 3.2 Gy in 3D-CRT(vmDIBH) plans, VMAT(vmDIBH) resulted in a cumulative heart dose reduction. VMAT also provided better target coverage and reduced ipsilateral lung dose, at the expense of a small increase in the dose to the contralateral breast.

A generalized Riemann- Stieltjes integral on time scales and discontinuous dynamical equations

This paper is concerned with a generalization of the Riemann- Stieltjes integral on time scales for deal with some aspects of discontinuous dynamic equations in which Riemann-Stieltjes integral does not works. © 2011 Academic Publications.

Worse outcomes in patients undergoing urgent surgery for left-sided diverticulitis admitted on weekends vs weekdays: a population-based study of 31 832 patients

Among patients undergoing urgent surgery for left-sided diverticulitis, those admitted on weekends vs weekdays have higher rates of Hartmann procedure and adverse outcomes.

Evaluation of Recurrence Risks for Left-Sided Cardiac Lesions

It is widely accepted that hypoplastic left heart syndrome (HLHS), aortic valve stenosis with or without bicuspid aortic valve (AS/BAV) and coarctation of the aorta (CoA) occur in families more commonly with each other than with any other congenital heart defect (CHD). Genetic counseling for CHDs is currently based on empiric risk estimates derived from data collected on all types of CHDs between 1968 and 1990. Additionally, for the specific group of defects described above, termed left-sided lesions, estimates are available for sibling recurrence. Utilizing family history data from 757 probands recruited between 1997 and 2007 from The Children’s Hospital of Philadelphia, this study reassessed the pre/recurrence risks for LSLs specifically. Sibling pre/recurrence risks for HLHS (5.5%, 95% CI: 3.1%-8.9%), CoA (4.0%, 95% CI: 2.1%-6.7%), and AS/BAV (6.0%, 95% CI: 3.3%-9.8%) were higher than currently quoted risks based on sibling data for individual LSLs. Additionally, the prevalence of BAV in 202, apparently unaffected, parents of 134 probands was assessed by echocardiography. BAV, which occurs at a frequency of 1% in the general population, was found to occur in approximately 10% of parents of LSL probands. Lastly, among affected first-degree relative pairs (i.e. siblings, parent-offspring), the majority (65%-70%) were both affected with a LSL. Defect specific concordance rates were highest for AS/BAV. Together, these findings suggest that over the past 20 years with changing diagnostic capabilities and environmental/maternal conditions (e.g. folic acid fortification, increased maternal diabetes and obesity) recurrence risks may have increased, as compared to current LSL specific risk estimates. Based on these risk estimate increases and prior studies, a protocol for screening first-degree relatives of LSL probands should be devised.

Fluoroscopic anatomy of left-sided heart structures for transcatheter interventions: insight from multislice computed tomography.

With the introduction of transcatheter structural heart therapies, cardiologists are increasingly aware of the importance of understanding anatomical details of left-sided heart structures. Understanding fluoroscopic cardiac anatomy can facilitate optimal positioning and deployment of prostheses during transcatheter valve repair/replacement, left atrial appendage occlusion, septal defect closure, and paravalvular leak closure. It is possible to use multislice computed tomography to determine optimal fluoroscopic viewing angles for such transcatheter therapies. The purpose of this paper is to describe how optimal fluoroscopic viewing angles of left-sided heart structures can be obtained using computed tomography. Two- and 3-chamber views are described and may become standard in the context of transcatheter structural heart interventions.