RESUMO
The Gel'fand-Levitan equation, the Gopinath-Sondhi equation, and the Marchenko equation are developed for one-dimensional inverse scattering problems. Recently, a version of the Marchenko equation based on wavefield decomposition has been introduced for focusing waves in multi dimensions. However, wavefield decomposition is a limitation when waves propagate horizontally at the focusing level. Here, the Marchenko equation for focusing without wavefield decomposition is derived, and by iteratively solving the Marchenko equation, the Green's function for an arbitrary location in the medium is retrieved from the scattered waves recorded on a closed receiver array and an estimate of the direct-wave without wavefield decomposition.
RESUMO
AIMS: To determine the pulmonary effects of locoregional irradiation on clinical and sub-clinical radiographic and functional end points in women with breast cancer, and whether the course of these end points is affected by laterality. MATERIALS AND METHODS: Twenty patients (10 irradiated on the left side and 10 irradiated on the right side) were prospectively evaluated for changes in pulmonary function tests, Tc-99m DTPA (diethylenetriamine pentaacetic acid) lung clearance scintigraphy and high-resolution computed tomography (HRCT) at 6, 16 and 52 weeks after radiotherapy. Tc-99m DTPA clearance, expressed as the biological half-time, T(1/2), was computed from the time-activity curves for 10 min for each lung. The irradiated lung volume was calculated for each patient. RESULTS: The mean irradiated lung volume was 6.4% +/- 2 (range 3-11%) for the entire population. In the whole study population, two (10%) patients, who were irradiated on the left side, had mild symptomatic radiation pneumonitis in the follow-up period. There was a statistically significant gradual reduction in all pulmonary function test values during the follow-up period. For patients irradiated on the left side, Tc-99m DTPA clearance T(1/2) values were statistically significantly decreased during the follow-up period (P = 0.03), but the decrease was not statistically significant for patients irradiated on the right side (P = 0.62). Tc-99m DTPA clearance T(1/2) values were statistically significantly decreased in the irradiated lung compared with the opposite lung, and no improvement was seen at week 52 after radiotherapy. The number of patients with changes on HRCT scans increased after radiotherapy, reaching a maximum at 16 weeks, when 80% of patients had changes. There was subsequent partial recovery 52 weeks after radiotherapy. CONCLUSION: Locoregional irradiation for breast cancer may cause sub-clinical irreversible impairment of radiological and functional pulmonary parameters. The increase in clearance rate of Tc-99m DTPA may be more prominent for patients with left-sided breast cancer.