Sarah E. Geneser

Application of Stochastic Finite Element Methods to Study the Sensitivity of ECG Forward Modeling to Organ Conductivity

Because numerical simulation parameters may significantly influence the accuracy of the results, evaluating the sensitivity of simulation results to variations in parameters is essential. Although the field of sensitivity analysis is well developed, systematic application of such methods to complex biological models is limited due to the associated high computational costs and the substantial technical challenges for implementation. In the specific case of the forward problem in electrocardiography, the lack of robust, feasible, and comprehensive sensitivity analysis has left many aspects of the problem unresolved and subject to empirical and intuitive evaluation rather than sound, quantitative investigation. In this study, we have developed a systematic, stochastic approach to the analysis of sensitivity of the forward problem of electrocardiography to the parameter of inhomogeneous tissue conductivity. We apply this approach to a two-dimensional, inhomogeneous, geometric model of a slice through the human thorax. We assigned probability density functions for various organ conductivities and applied stochastic finite elements based on the generalized polynomial chaos-stochastic Galerkin (gPC-SG) method to obtain the standard deviation of the resulting stochastic torso potentials. This method utilizes a spectral representation of the stochastic process to obtain numerically accurate stochastic solutions in a fraction of the time required when employing classic Monte Carlo methods. We have shown that a systematic study of sensitivity is not only easily feasible with the gPC-SG approach but can also provide valuable insight into characteristics of the specific simulation.

Quantifying variability in radiation dose due to respiratory-induced tumor motion

State of the art radiation treatment methods such as hypo-fractionated stereotactic body radiation therapy (SBRT) can successfully destroy tumor cells and avoid damaging healthy tissue by delivering high-level radiation dose that precisely conforms to the tumor shape. Though these methods work well for stationary tumors, SBRT dose delivery is particularly susceptible to organ motion, and few techniques capable of resolving and compensating for respiratory-induced organ motion have reached clinical practice. The current treatment pipeline cannot accurately predict nor account for respiratory-induced motion in the abdomen that may result in significant displacement of target lesions during the breathing cycle. Sensitivity of dose deposition to respiratory-induced organ motion represents a significant challenge and may account for observed discrepancies between predictive treatment plan indicators and clinical patient outcomes. Improved treatment-planning and delivery of SBRT requires an accurate prediction of dose deposition uncertainties resulting from respiratory motion. To accomplish this goal, we developed a framework that models both organ displacement in response to respiration and the underlying random variations in patient-specific breathing patterns. Our organ deformation model is a four-dimensional maximum a posteriori (MAP) estimation of tissue deformation as a function of chest wall amplitudes computed from clinically obtained respiratory-correlated computed tomography (RCCT) images. We characterize patient-specific respiration as the probability density function (PDF) of chest wall amplitudes and model patient breathing patterns as a random process. We then combine the patient-specific organ motion and stochastic breathing models to calculate the resulting variability in radiation dose accumulation. This process allows us to predict uncertainties in dose delivery in the presence of organ motion and identify tissues at risk of receiving insufficient or harmful levels of radiation.

Sensitivity Analysis of Cardiac Electrophysiological Models Using Polynomial Chaos

Mathematical models of biophysical phenomena have proven useful in the reconstruction of experimental data and prediction of biological behavior. By quantifying the sensitivity of a model to certain parameters, one can place an appropriate amount of emphasis in the accuracy with which those parameters are determined. In addition, investigation of stochastic parameters can lead to a greater understanding of the behavior captured by the model. This can lead to possible model reductions, or point out shortcomings to be addressed. We present polynomial chaos as a computationally efficient alternative to Monte Carlo for assessing the impact of stochastically distributed parameters on the model predictions of several cardiac electrophysiological models

Incorporating Patient Breathing Variability into a Stochastic Model of Dose Deposition for Stereotactic Body Radiation Therapy

Hypo-fractionated stereotactic body radiation therapy (SBRT) employs precisely-conforming high-level radiation dose delivery to improve tumor control probabilities and sparing of healthy tissue. However, the delivery precision and conformity of SBRT renders dose accumulation particularly susceptible to organ motion, and respiratory-induced motion in the abdomen may result in significant displacement of lesion targets during the breathing cycle. Given the maturity of the technology, sensitivity of dose deposition to respiratory-induced organ motion represents a significant factor in observed discrepancies between predictive treatment plan indicators and clinical patient outcome statistics and one of the major outstanding unsolved problems in SBRT. Techniques intended to compensate for respiratory-induced organ motion have been investigated, but very few have yet reached clinical practice. To improve SBRT, it is necessary to overcome the challenge that uncertainties in dose deposition due to organ motion present. This requires incorporating an accurate prediction of the effects of the random nature of the respiratory process on SBRT dose deposition for improved treatment planning and delivery of SBRT. We introduce a means of characterizing the underlying day-to-day variability of patient breathing and calculate the resulting stochasticity in dose accumulation.

The Influence of Stochastic Organ Conductivity in 2D ECG Forward Modeling: A Stochastic Finite Element Study

Quantification of the sensitivity of the electro-cardiographic forward problem to various parameters can effectively direct the generalization of patient specific models without significant loss in accuracy. To this purpose we applied polynomial chaos based stochastic finite elements to assess the effect of variations in the distributions of tissue conductivity in a two-dimensional torso geometry generated from MRI scans and epicardial boundary conditions specified by intra-operatively recorded heart potentials. The polynomial chaos methodology allows sensitivity analysis of this type to be done in a fraction of the time required for a Monte Carlo analysis

SU‐E‐T‐399: Improving Gated Delivery Efficiency Using Brief Breath Holds at Both Inhale and Exhale

PURPOSE Respiration-gated intensity modulated radiation therapy (IMRT) and volumetric modulated radiation therapy (VMAT) deliver the treatment beam at a single phase to reduce dose uncertainties resulting from respiratory-induced organ motion. In some cases, gating can significantly prolong treatment times, leading to increased patient discomfort, treatment duration, and dose uncertainty due to patient postural shifts. To decrease treatment duration without increasing dose uncertainty, we propose dual-gating in conjunction with with alternating coached five to ten second breath holds at inhale and exhale. In this study, we examine the feasibility of maintaining reproducible inhale and exhale RPM marker positions in a healthy volunteer and compare the expected dual-gated delivery speedup over the free breathing case. MATERIALS/METHODS Varian Real-Time Position Management (RPM) respiratory signals from a volunteer were recorded during free breathing and during alternating ten second inspiration and exhalation breath hold coaching. The signals were then processed to examine the volunteers ability to consistently reproduce RPM marker position during subsequent breath holds. Conventionally-gated and dual-gated treatment times were simulated for a given treatment plan under both normal and alternating breath hold conditions and compared. RESULTS Dual-gated delivery under free breathing increases the duty cycle from 30.3% to 58.3% as compared with gating at exhale only. Alternated breath hold coaching further improves the duty cycle to 85.1%. Treatment delivery requiring 29.05 minutes to complete under normal exhale gating conditions is reduced to 16.58 minutes for dual-gating during free breathing and only 5.88 minutes with dual-gated alternated breath holds. RPM marker reproducibility was within 8% over the course of the delivery time. CONCLUSION While additional improvements and testing are necessary, dual-gated treatment delivery during alternated breath hold coaching is a feasible method for increasing duty cycle and thus improving treatment efficiency for tumors undergoing respiratory-motion.

SU-E-T-482: Measuring Planned and Delivered Dose Discrepancies of Gated IMRT

Purpose: Respiration‐gated radiation therapy restricts delivery to a window around a specific phase or amplitude of the external breathing trace. In planning, the computed doses assume no motion within the gating window and ignores the residual motion within the gating window. We deliverIMRT to a torso phantom while (1) stationary and (2) undergoing 2 cm superior‐inferior motion, measure the resulting dose distributions using gafchromic film, and compare the delivered and the planned doses. Methods: A respiration‐gated treatment planned in Eclipse was delivered to a Quasar torso phantom on a 1D motion stage under two situations; non‐gated delivery to the stationary phantom and gated delivery while the phantom underwent sinusoidal translation. The resulting dose depositions were measured using gafchromic film, scanned, and quantified. The delivereddose distributions were compared to one another and the planned distribution and the dosimetric dependence caused by residual motion within the gating window was analyzed.Results: The static delivereddose matched the planned gated dose within 5%. The largest dose discrepancies occur primarily in the regions where high dose derivative (quick dose falloff) are perpendicular to the direction of movement. With up to 0.6 cm translation during the gating window, the static delivered and gated delivereddoses showed differences as high as 0.4 Gy or 20% of the PTV prescribed dose. Much of the significant under‐dosing occurs within the PTV, while the overdosed areas of 0.2 Gy and higher occur outside of the PTV in the ipsilateral lung. Conclusions: Residual motion may lead to large dosimetric discrepancies from the gated treatment plan generated on the static patient model corresponding to the gating phase, and an effective way to mitigate this should be developed in the future for accurate gated planning and dosedelivery.

SU‐GG‐I‐08: Impact of Phase Shift Between Respiratory Surrogate and Internal Target On Retrospectively Reconstructed, 4D CT Images

Purpose: We quantified the impact of various phase shifts between an external surrogate motion and internal target motion on the 4D modeling of target motion using a 4D dynamic phantom. Method and Materials: The CIRS Dynamic Thorax phantom Model 008 (CIRS, Norfolk, VA) is capable of separating the target and surrogate motions via two independent motors. Phase shift impact on 4D images was studied for two types of breathing signals: a standard sinusoidal signal and a real patient breathing signal. The phantom was imaged on a LightSpeed RT CT 16 slice scanner (GE Health Care, Waukesha, WI) at 0.5s per revolution, 2.5 × 0.6 × 0.6 mm voxel size at 120 kV. The real‐time position management (RPM) system (Varian Oncology Systems, Palo Alto, CA) was used to measure the respiratory signal and GE AW 4D software v4.4 was used to generate 10 reconstructedCT phases. The 10 CT phases were then auto‐segmented by ITK‐SNAP program and evaluated for both target volume and shape. Result: The internal target volume (ITV) varied by 1% for the standard sinusoidal signal at different phase shifts, but varied by 10% for the real patient signal, with the change being larger for greater phase shifts. Because the internal target is a 3 cm diameter sphere, we used a “sphericity” metric to evaluate the degree of target shape distortion. For the case of 45° phase shift, the target shape remained essentially spherical (5% variation) throughout the 10 phases for the sinusoidal signal, but the shape changed significantly (28% variation) from phase to phase for the real patient signal. Conclusion: Our results suggest that phase shift variations between surrogate and target present a greater challenge to the 4D binning process in the case of irregular real patient breathing signal than for a standard sinusoidal signal.

TU‐C‐213CD‐02: Improving Respiration‐Gated IMRT Delivery Efficiency by Dual‐Gating at Inhale and Exhale: Treatment Planning Formalism

Purpose: Dual‐gating is a novel method proposed to enhance the delivery efficiency of respiratory‐gated IMRT by delivering the beam at both inhale and exhale. Here, we develop a treatment planning framework for dual‐gated IMRT (DG‐IMRT) without compromising tumor coverage or normal tissue sparing. We produce a DG‐IMRT plan for a lungtumor case with ∼1.5 cm motion and compare to a conventional IMRT plan gated at exhale. Methods: Implementation of DG‐IMRT requires individual inhale and exhale fluences during each of the gating windows. Rather than optimizing the inhale and exhale plans separately, the inverse treatment planning problem is formulated to optimize over both plans simultaneously, producing inhale and exhale fluences that achieve the ideal total dose. To achieve dose accumulation of the inhale and exhale doses, deformable image registration is used to register the inhale dose to the exhale geometry. The treatment planning framework is evaluated on a lung patient case with ∼1.5 cm tumor motion. Results: Comparison of the dual‐gated and single‐gated plans demonstrate that dual gating enables improved PTV dose homogeneity, with a 2.7 Gy increase in minimum dose to the PTV, and a 4.6Gy decrease in maximum dose to the PTV. The DG‐IMRT plan also exhibits lower maximum doses to the ispilateral lung, but slightly higher maximum doses to the contralateral lung,heart, and spinal cord. Conclusions: The treatment planning results demonstrate that the proposed framework can produce IMRT plans equivalent to or better than conventional IMRT plans gated at exhale. In the presence of free breathing, dual‐gating can improve respiration‐delivery efficiency by up to a factor of two and perhaps even greater when combined with coaching to encourage brief breath‐holds at inhale and exhale. This work was supported by the National Cancer Institute (T32 CA09695 ‐ Glazer) and the National Institutes of Health (1RO1 CA 133474 ‐ Xing).

SU‐E‐J‐83: Improving Respiration‐Gated IMRT Delivery Efficiency by Dual‐Gating at Inhale and Exhale: Evaluation of Planning on Eclipse and the Need for Accurate Image Registration

PURPOSE Dual-gated intensity modulated radiation therapy (DG-IMRT) is a novel delivery method for speeding respiratory-gated IMRT delivery in which dose is delivered during both inhale and exhale windows. To determine the feasibility of designing DG-IMRT plans using current clinical treatment planning systems, we design and evaluate a lung patient plan using Eclipse. METHODS Tumor target volumes were contoured on inhale and exhale CTs for a lung cancer patient with ∼1mm motion. Separate 5-field IMRT plans were optimized in Eclipse for the inhale PTV on the inhale CT and for the exhale PTV on the exhale CT. The inhale plan dose was mapped to the exhale geometry using several deformable medical image registration methods, and the two doses were summed to produce the DG-IMRT dose. The accumulated dual-gated dose for the best performing registration is presented. RESULTS Though the dual-gated inhale and exhale plans meet clinical requirements, the accumulated dual-gated dose performs quite poorly. Examination of the deformations indicates that only about two-thirds of the voxels within the inhale PTV map to voxels within the exhale PTV, indicating an unacceptably low level of physiological accuracy. CONCLUSION It is possible to design dual-gated plans in Eclipse, but there is currently no accurate means of evaluated the summed dose. Furthermore, our results underscore the need for image registration methods that accurately model underlying tissue deformations before they can be used for dose accumulation in the presence of organ motion. This work was supported by the National Cancer Institute (T32 CA09695 - Glazer) and the National Institutes of Health (1RO1 CA 133474 - Xing).