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CONSEQUENCES OF A QUANTITATIVE FREE BREATHING MOTION MODEL
S 166
IGRT: B REATHING ADAPTED R ADIOTHERAPY
two plans. Doses to organs at risk such as heart, left anterior descending (LAD) coronary artery and ipsilateral lung were assessed. Results: Compared to FB, the DIBH-plans obtained lower dose to the heart and lung, with the same coverage of PTV. The average mean heart dose was significantly reduced from 7.6 Gy to 3.5 Gy and the number of patients with <0.5% heart volume receiving more than 25 Gy was increased from 3/18 to 13/18. For the LAD coronary artery the result was 37.9 Gy to 14.2 Gy and 4/18 to 13/18. The average ipsilateral lung volume receiving more than 20 Gy was significantly reduced from 12.3% to 10.4%. Conclusions: Breathing adapted radiotherapy with DIBH reduces cardiac and pulmonary doses for tangentially treated left sided breast patients without compromising the target coverage. 446 poster (Physics Track) CONSEQUENCES OF A QUANTITATIVE FREE BREATHING MOTION MODEL D. Low1 , T. Zhao1 , P. Parikh1 , W. Lu1 , S. Mutic1 , J. Hubenschmidt1 , C. Noel1 , D. Yang1 , J. Bradley1 1 WASHINGTON U NIVERSITY, Radiation Oncology, Saint Louis, USA
Purpose: To examine the consequences of a quantitative free breathing motion model developed for radiation therapy applications. Materials: We have developed a free breathing motion model that relates the position of tissues within the lungs (including lung tumors) to externally monitorable surrogates; tidal volume v and airflow f. The tidal volume surrogate relates the positions to the inhalation state of the lungs. Hysteresis motion, found in many parts of the lungs, is assumed to be caused by pressure imbalances during the inhalation and exhalation process. These pressure imbalances are assumed to be proportional to the vacuum used create breathing and therefore proportional to airflow. The form of the equation that relates position to volume and airflow is linear, namely the position of a piece of tissue is X and is related to its position at 0 volume and 0 airflow (exhalation) X0 by X = X0 + αv + β f, where α and β are vector fields that identify the motion characteristics of the tissue lying at X0 at v =f=0. While the model is linear in volume and flow, it is not linear in time. The complex motion found in human breathing is possible because α and β are not necessarily parallel, airflow is the time derivative of tidal volume, and the tidal volume exhibits a wave-like periodicity in time. We took the motion equation and applied the continuity equation, modifying the independent variable from time to tidal volume. In other words, we examined the continuity as a function of tidal volume. The resulting equation related was examined using Gauss’ law, which relates the volume integral of the divergence of a vector field to the surface integral of that vector field. Physical interpretations of the results were evaluated. Results: The motion equation shows the behavior of each point within the lungs as a function of tidal volume and airflow. The continuity equation: div(ρ V ) = -dρ/dv, where ρ is the tissue density, V is the velocity field and the standard definition of velocity dX /dt has been replaced by dX/dv was applied. The independence in the motion model between the tidal volume and airflow removed two of the terms in the velocity and the remaining term div(ρ α) was split using the product rule. The two terms include div(α) and the gradient of the density. A coordinate transformation was made to track the local tissues, which left only one term. The equation was div(α) -1/ρ dρ/dv. The right side of the equation was the relative local change in tissue density as a function of tidal volume and was assumed to change with response to radiation and disease state. The term on the left was the divergence of α which related local motion to tidal volume as though the patient had breathed infinitely slowly. The motion data were acquired during free breathing when hysteresis confounds and complicates lung tissue motion. Therefore, an analysis of div(α) might provide insight to fundamental dynamic tissue behavior during free breathing. An example of the α distribution for a lung cancer patient scanned 5 weeks apart during therapy is shown in the Figure. A change in α is clearly evident and the boundary of that change is coincident with the radiation beams.Gauss’ law was applied to the divergence equation, which relates the volume integral of the divergence of a vector field to the surface integral of that vector field. In this case, the vector field was α, the motion as a function of tidal volume. The surface integral of that motion integrated over the entire lung surface was equal to the lung expansion per tidal volume, which was simply the expansion in volume of the lungs as a function of tidal volume. Because the air temperature and humidity within the lungs is greater than room air, the density of air in the lungs is 1.11 times less than room air, so the lungs will inflate 1.11 times more than the tidal volume. Therefore the volume integral of div(α) = 1.11! This model can be directly and quantitatively validated for each clinical case.
Conclusions: The relationship between the relative tissue density change and the measured motion parameters will allow a quantitative and verifiable determination of fundamental lung tissue function as expressed by local tissue density changes as a function of inhaled tidal volume. The correlation between dose and changes in α have been seen in numerous patients receiving the scanning protocol. 447 poster (Physics Track) DEVELOPMENT OF A MOTION REPLICATION TOOL L. Dunn1 , L. McDermott1 , R. Franich1 , T. Kron2 , P. Johnston1 1 RMIT U NIVERSITY, Applied Physics, Melbourne, Australia 2 P ETER M ACCALLUM C ANCER I NSTITUTE, Physical Sciences, East Melbourne, Australia 3 ARPANSA, Environmental and Radiation Health, Melbourne, Australia
Purpose: In gated radiotherapy, the lung tumour position is often correlated with an external respiratory signal. A common method is using an infra-red (IR) tracking camera which tracks IR reflective markers on the patient’s chest. The aim of this work was to design and test a motion platform capable of replicating patient chest wall motion. A tool is presented that can be used to evaluate the performance and accuracy of technologies and methods such as gating, 4D-CT/PET and 4D dynamic tracking using multi-leaf collimators. The Real-Time Position Management system (RPM, Varian) is used to evaluate the accuracy of the motion platform and of the RPM. Materials: A lift-table was designed consisting of a stepper motor and two plates connected via brass guide rails and Teflon bushes. The stepper motor controls a screw which raises and lowers the platform based on the direction of rotation of the motor. Using custom designed MATLAB software (The MathWorks Inc.) various motion profiles can be sent to the platform. The following were tested: 1) regular, idealised, sinusoidal profiles, 2) ’breath-hold’ profiles, whereby after successive breaths, the patient is instructed to hold their breath at deep inspiration / expiration, and 3) actual patient traces, recorded with the Varian RPM system and later replicated. Results: There was statistically significant correlation between six pairs of recorded and replicated patient traces, (maximum p-value = 0.0045). Values for the mean differences between maxima and minima of the data for the six patients also agreed well, with an average difference between maxima of 0.034 cm, and minima of 0.0102 cm. The mean difference between the recorded and replicated standard deviations was 0.01 cm and the mean difference in the mean anterior-posterior position was 0.02 cm, indicating a sub-mm average degree of replication accuracy. Residual errors for the six patients fluctuated between 0 and 0.2 cm
IGRT: B REATHING ADAPTED R ADIOTHERAPY
two plans. Doses to organs at risk such as heart, left anterior descending (LAD) coronary artery and ipsilateral lung were assessed. Results: Compared to FB, the DIBH-plans obtained lower dose to the heart and lung, with the same coverage of PTV. The average mean heart dose was significantly reduced from 7.6 Gy to 3.5 Gy and the number of patients with <0.5% heart volume receiving more than 25 Gy was increased from 3/18 to 13/18. For the LAD coronary artery the result was 37.9 Gy to 14.2 Gy and 4/18 to 13/18. The average ipsilateral lung volume receiving more than 20 Gy was significantly reduced from 12.3% to 10.4%. Conclusions: Breathing adapted radiotherapy with DIBH reduces cardiac and pulmonary doses for tangentially treated left sided breast patients without compromising the target coverage. 446 poster (Physics Track) CONSEQUENCES OF A QUANTITATIVE FREE BREATHING MOTION MODEL D. Low1 , T. Zhao1 , P. Parikh1 , W. Lu1 , S. Mutic1 , J. Hubenschmidt1 , C. Noel1 , D. Yang1 , J. Bradley1 1 WASHINGTON U NIVERSITY, Radiation Oncology, Saint Louis, USA
Purpose: To examine the consequences of a quantitative free breathing motion model developed for radiation therapy applications. Materials: We have developed a free breathing motion model that relates the position of tissues within the lungs (including lung tumors) to externally monitorable surrogates; tidal volume v and airflow f. The tidal volume surrogate relates the positions to the inhalation state of the lungs. Hysteresis motion, found in many parts of the lungs, is assumed to be caused by pressure imbalances during the inhalation and exhalation process. These pressure imbalances are assumed to be proportional to the vacuum used create breathing and therefore proportional to airflow. The form of the equation that relates position to volume and airflow is linear, namely the position of a piece of tissue is X and is related to its position at 0 volume and 0 airflow (exhalation) X0 by X = X0 + αv + β f, where α and β are vector fields that identify the motion characteristics of the tissue lying at X0 at v =f=0. While the model is linear in volume and flow, it is not linear in time. The complex motion found in human breathing is possible because α and β are not necessarily parallel, airflow is the time derivative of tidal volume, and the tidal volume exhibits a wave-like periodicity in time. We took the motion equation and applied the continuity equation, modifying the independent variable from time to tidal volume. In other words, we examined the continuity as a function of tidal volume. The resulting equation related was examined using Gauss’ law, which relates the volume integral of the divergence of a vector field to the surface integral of that vector field. Physical interpretations of the results were evaluated. Results: The motion equation shows the behavior of each point within the lungs as a function of tidal volume and airflow. The continuity equation: div(ρ V ) = -dρ/dv, where ρ is the tissue density, V is the velocity field and the standard definition of velocity dX /dt has been replaced by dX/dv was applied. The independence in the motion model between the tidal volume and airflow removed two of the terms in the velocity and the remaining term div(ρ α) was split using the product rule. The two terms include div(α) and the gradient of the density. A coordinate transformation was made to track the local tissues, which left only one term. The equation was div(α) -1/ρ dρ/dv. The right side of the equation was the relative local change in tissue density as a function of tidal volume and was assumed to change with response to radiation and disease state. The term on the left was the divergence of α which related local motion to tidal volume as though the patient had breathed infinitely slowly. The motion data were acquired during free breathing when hysteresis confounds and complicates lung tissue motion. Therefore, an analysis of div(α) might provide insight to fundamental dynamic tissue behavior during free breathing. An example of the α distribution for a lung cancer patient scanned 5 weeks apart during therapy is shown in the Figure. A change in α is clearly evident and the boundary of that change is coincident with the radiation beams.Gauss’ law was applied to the divergence equation, which relates the volume integral of the divergence of a vector field to the surface integral of that vector field. In this case, the vector field was α, the motion as a function of tidal volume. The surface integral of that motion integrated over the entire lung surface was equal to the lung expansion per tidal volume, which was simply the expansion in volume of the lungs as a function of tidal volume. Because the air temperature and humidity within the lungs is greater than room air, the density of air in the lungs is 1.11 times less than room air, so the lungs will inflate 1.11 times more than the tidal volume. Therefore the volume integral of div(α) = 1.11! This model can be directly and quantitatively validated for each clinical case.
Conclusions: The relationship between the relative tissue density change and the measured motion parameters will allow a quantitative and verifiable determination of fundamental lung tissue function as expressed by local tissue density changes as a function of inhaled tidal volume. The correlation between dose and changes in α have been seen in numerous patients receiving the scanning protocol. 447 poster (Physics Track) DEVELOPMENT OF A MOTION REPLICATION TOOL L. Dunn1 , L. McDermott1 , R. Franich1 , T. Kron2 , P. Johnston1 1 RMIT U NIVERSITY, Applied Physics, Melbourne, Australia 2 P ETER M ACCALLUM C ANCER I NSTITUTE, Physical Sciences, East Melbourne, Australia 3 ARPANSA, Environmental and Radiation Health, Melbourne, Australia
Purpose: In gated radiotherapy, the lung tumour position is often correlated with an external respiratory signal. A common method is using an infra-red (IR) tracking camera which tracks IR reflective markers on the patient’s chest. The aim of this work was to design and test a motion platform capable of replicating patient chest wall motion. A tool is presented that can be used to evaluate the performance and accuracy of technologies and methods such as gating, 4D-CT/PET and 4D dynamic tracking using multi-leaf collimators. The Real-Time Position Management system (RPM, Varian) is used to evaluate the accuracy of the motion platform and of the RPM. Materials: A lift-table was designed consisting of a stepper motor and two plates connected via brass guide rails and Teflon bushes. The stepper motor controls a screw which raises and lowers the platform based on the direction of rotation of the motor. Using custom designed MATLAB software (The MathWorks Inc.) various motion profiles can be sent to the platform. The following were tested: 1) regular, idealised, sinusoidal profiles, 2) ’breath-hold’ profiles, whereby after successive breaths, the patient is instructed to hold their breath at deep inspiration / expiration, and 3) actual patient traces, recorded with the Varian RPM system and later replicated. Results: There was statistically significant correlation between six pairs of recorded and replicated patient traces, (maximum p-value = 0.0045). Values for the mean differences between maxima and minima of the data for the six patients also agreed well, with an average difference between maxima of 0.034 cm, and minima of 0.0102 cm. The mean difference between the recorded and replicated standard deviations was 0.01 cm and the mean difference in the mean anterior-posterior position was 0.02 cm, indicating a sub-mm average degree of replication accuracy. Residual errors for the six patients fluctuated between 0 and 0.2 cm