Higher conservation laws for coherent optical pulse propagation in an inhomogeneously broadened medium.
The description of coherent optical pulse propagation in terms of coupled Maxwell and Schroedinger- Bloch equations in slowly varying envelope approximation possesses conservation laws in addition to those of field energy and field momentum. Comparison with preliminary numerical results has shown that these higher conservation laws can be used to predict the amplitude of each of the 2pi pulses into which an intense coherent pulse may decompose as it propagates through an attenuator. In the present paper a comparison with more extensive numerical results is carried out. It is shown that over a wide range of variation of the parameters involved the conservation laws yield results in agreement with those obtained through numerical computation.
Systems of non-linear, partial differential equations for coherent optical pulse propagation in an inhomogeneously broadened medium and associated conservation laws
Abstract The undamped Schrodinger-Bloch equations governing coherent optical pulse propagation in a medium consisting of non-degenerate two-level systems are used to derive a system of two non-linear, partial differential equations which generalize the well-known single partial differential equation by means of which pulse propagation in a homogeneously broadened medium is described. A systematic and rigorous method is presented whereby conservation laws of various orders associated with this system may be derived.
A quality control model that uses PTV-rectal distances to predict the lowest achievable rectum dose, improves IMRT planning for patients with prostate cancer.
BACKGROUND AND PURPOSE
To predict the lowest achievable rectum D35 for quality assurance of IMRT plans of prostate cancer patients.


MATERIALS AND METHODS
For each of 24 patients from a database of 47 previously treated patients, the anatomy was compared to the anatomies of the other 46 to predict the minimal achievable rectum D35. The 24 patients were then replanned to obtain maximally reduced rectum D35. Next, the newly derived plans were added to the database to replace the original clinical plans, and new predictions of the lowest achievable rectum D35 were made.


RESULTS
After replanning, the rectum D35 reduced by 9.3 Gy±6.1 (average±1 SD; p<0.001) compared to the original plan. The first predictions of the rectum D35 were 4.8 Gy±4.2 (average±1 SD; p<0.001) too high when evaluated with the new plans. After updating the database, the replanned and newly predicted rectum D35 agreed within 0.1 Gy±2.8 (average±1 SD; p=0.89). The doses to the bladder, anus and femoral heads did not increase compared to the original plans.


CONCLUSIONS
For individual prostate patients, the lowest achievable rectum D35 in IMRT planning can be accurately predicted from dose distributions of previously treated patients by quantitative comparison of patient anatomies. These predictions can be used to quantitatively assess the quality of IMRT plans.