This paper investigates the simultaneous recovery for two time-dependent coefficients for heat equation under Neumann boundary condition. This problem is considered under extra conditions of nonlocal type. The main issue with this problem is the solution unstable to small contamination of noise in the input data. The Crank-Nicolson finite difference method is utilized to solve the direct problem whilst the inverse problem is viewed as nonlinear optimization problem. The later problem is solved numerically using optimization toolbox from MATLAB. We found that the numerical results are accurate and stable.
The aim of the study was to assess the predictive value of interim FDG-PET/CT (iPET) in patients with Hodgkin’s lymphoma (HL) treated with Adriamycin, bleomycin, vinblastine and dacarbazine (ABVD) chemotherapy. A total of 245 consecutive patients with de novo HL between 12/2013 and 12/2017 were evaluated retrospectively. All patients were treated with upfront ABVD, performed PET/CT scans at baseline, after 2 cycles (interim PET, iPET2) or 4 cycles (iPET4) and at the end of therapy, and followed up for at least 6 months after therapy. The response status on iPET was defined according to the standard five-point Deauville scores (DS) as follows: complete metabolic response (CMR, DS 1–3) and non-complete metabolic response (nCMR) (DS 4 and 5). End-of-treatment (EoT) response was assessed by FDG-PET/CT and if needed biopsy confirmation of PET-positive findings. The association between iPET and EoT response was investigated using logistic regression analysis. Survival analysis was performed using the Cox regression hazard model and Kaplan–Meier methods. Sixty-nine patients underwent iPET-2 and 176 iPET-4. No association was found between the timing of iPET and iPET response status (P-value = 0.71). Two hundred and one patients (82%) had iPET-CMR and 44 (18%) iPET -nCMR. iPET was strongly associated with EoT response status: 194/201 (96 .5%) of iPET-CMR had a complete response at the EoT while only 21/44 (47.7%) of patients with iPET-nCMR presented a complete response at EoT (P-value < 0.0001). The median follow-up was 32 months (range 6–81). Patients with iPET-CMR presented a better outcome with 91% 3 y event-free-survival (EFS) and 95% 3 y overall survival (OS) than those with iPET-nCMR (41 and 86%, respectively, P-value < 0.0001). In multivariable analyses, iPET retained an independent prognostic factor of EFS and OS (P-value < 0.0001 and P-value = 0.002, respectively). iPET is highly predictive of outcome of HL patients treated with ABVD and allows to tailor therapy to the individual patient.
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