Brachytherapy treatment planning method and apparatus

A method for planning the placement of seeds for the brachytherapy treatment of diseased tissue using a treatment planning model formulated as a mixed integer program, the method comprising the steps of:

• representing a placement or non-placement of a seed in each point of a predetermined three dimensional placement grid of potential seed locations with a binary indicator variable;
• representing a tumor and surrounding tissue as a predetermined three dimensional tissue grid having a plurality of tissue points;
• associating an upper bound and a lower bound for an amount of radiation received with each point in the tissue grid;
• calculating an objective value representing whether the radiation received by the tissue points as a result of a placement of seeds adheres to the upper and lower bounds;
• and
• selecting a placement of seeds based upon the objective value, wherein the selecting step is performed by selecting a placement of seeds for which the objective value is optimized by maximizing a sum of rewards associated with achieving the upper and lower bounds.

A method for planning the placement of seeds for the brachytherapy treatment of diseased tissue using a treatment planning model formulated as a mixed integer program, the method comprising the steps of:

• representing a placement or non-placement of a seed in each point of a predetermined three dimensional placement grid of potential seed locations with a binary indicator variable;
• representing a tumor and surrounding tissue as a predetermined three dimensional tissue grid having a plurality of tissue points;
• associating an upper bound and a lower bound for an amount of radiation received with each point in the tissue grid;
• calculating an objective value representing whether the radiation received by the tissue points as a result of a placement of seeds adheres to the upper and lower bounds;
• and
• selecting a placement of seeds based upon the objective value, wherein the selecting step is performed by selecting a placement of seeds for which the objective value is optimized by minimizing a sum of penalties associated with deviating from the upper and lower bounds.

A method for planning the placement of seeds for the brachytherapy treatment of diseased tissue using a treatment planning model formulated as a mixed integer program, the method comprising the steps of:

• representing a placement or non-placement of a seed in each point of a predetermined three dimensional placement grid of potential seed locations with a binary indicator variable;
• representing a tumor and surrounding tissue as a predetermined three dimensional tissue grid having a plurality of tissue points;
• associating an upper bound and a lower bound for an amount of radiation received with each point in the tissue grid;
• calculating an objective value representing whether the radiation received by the tissue points as a result of a placement of seeds adheres to the upper and lower bounds;
• and
• selecting a placement of seeds based upon the objective value, wherein the distances between neighboring points in the tissue grid is smaller than the distance between neighboring points in the placement grid.

A method for planning the placement of seeds for the brachytherapy treatment of diseased tissue using a treatment planning model formulated as a mixed integer program, the method comprising the steps of:

• representing a placement or non-placement of a seed in each point of a predetermined three dimensional placement grid of potential seed locations with a binary indicator variable;
• representing a tumor and surrounding tissue as a predetermined three dimensional tissue grid having a plurality of tissue points;
• associating an upper bound and a lower bound for an amount of radiation received with each point in the tissue grid;
• calculating an objective value representing whether the radiation received by the tissue points as a result of a placement of seeds adheres to the upper and lower bounds;
• and
• selecting a placement of seeds based upon the objective value, wherein the distances between neighboring points in the tissue grid is larger than the distance between neighboring points in the placement grid.

A computer system for planning the placement of seeds for the brachytherapy treatment of a tumor, the computer system comprising:

• a processor, and
• a memory connected to the processor,
• wherein the processor is configured to perform the steps of:
• representing a placement or non-placement of a seed in each point of a predetermined three dimensional placement grid of potential seed locations with a binary indicator variable;
• representing a tumor and surrounding tissue as a predetermined three dimensional tissue grid;
• associating an upper bound and a lower bound for an amount of radiation received with each point in the tissue grid;
• calculating an objective value representing a measure of how well the radiation received by the tissue points as a result of a placement of seeds adheres to the upper and lower bounds;
• and
• selecting a placement of seeds based upon the objective value, wherein the selecting step is performed using a branch-and-bound method.

A computer readable medium having stored thereon sequences of instructions for causing a processor to perform the steps of:

• representing a placement or non-placement of a seed in each point of a predetermined three dimensional placement grid of potential seed locations with a binary indicator variable;
• representing a tumor and surrounding tissue as a predetermined three dimensional tissue grid;
• associating an upper bound and a lower bound for an amount of radiation received with each point in the tissue grid;
• calculating an objective value representing a measure of how well the radiation received by the tissue points as a result of a placement of seeds adheres to the upper and lower bounds;
• and
• selecting a placement of seeds based upon the objective value, wherein selecting is performed using a branch-and-bound method.

A method for treating diseased tissue using a treatment planning model formulated as a mixed integer program comprising the steps of:

• representing a placement or non-placement of a seed in each point of a predetermined three dimensional placement grid of potential seed locations with a binary indicator variable;
• representing a tumor and surrounding tissue as a predetermined three dimensional tissue grid;
• associating an upper bound and a lower bound for an amount of radiation received with each point in the tissue grid;
• calculating an objective value representing whether the radiation received by the tissue points as a result of a placement of seeds adheres to the upper and lower bounds;
• and
• selecting a placement of seeds based upon the objective value, wherein selecting is performed using a branch-and-bound method.

A method for treating diseased tissue using a treatment planning model formulated as a mixed integer program comprising the steps of:

• representing a placement or non-placement of a seed in each point of a predetermined three dimensional placement grid of potential seed locations with a binary indicator variable;
• representing a tumor and surrounding tissue as a predetermined three dimensional tissue grid;
• associating an upper bound and a lower bound for an amount of radiation received with each point in the tissue grid;
• calculating an objective value representing whether the radiation received by the tissue points as a result of a placement of seeds adheres to the upper and lower bounds;
• and
• selecting a placement of seeds based upon the objective value, wherein selecting is performed by selecting a placement of seeds for which the objective value is optimized by maximizing a sum of rewards associated with achieving the upper and lower bounds.

A method for treating diseased tissue using a treatment planning model formulated as a mixed integer program comprising the steps of:

• representing a placement or non-placement of a seed in each point of a predetermined three dimensional placement grid of potential seed locations with a binary indicator variable;
• representing a tumor and surrounding tissue as a predetermined three dimensional tissue grid;
• associating an upper bound and a lower bound for an amount of radiation received with each point in the tissue grid;
• calculating an objective value representing whether the radiation received by the tissue points as a result of a placement of seeds adheres to the upper and lower bounds;
• and
• selecting a placement of seeds based upon the objective value, wherein selecting is performed by selecting a placement of seeds for which the objective value is optimized by minimizing a sum of penalties associated with deviating from the upper and lower bounds.