Purpose: Predicting complex patterns of respiration can benefit the management of the respiratory motion for radiation therapy of lung cancer. The purpose of the present work was to develop a patient-specific, physiologically relevant respiratory motion model which is capable of predicting lung tumor motion over a complete normal breathing cycle. Methods: Currently employed techniques for generating the lung geometry from four-dimensional computed tomography data tend to lose details of mesh topology due to excessive surface smoothening. Some of the existing models apply displacement boundary conditions instead of the intrapleural pressure as the actual motive force for respiration, while others ignore the nonlinearity of lung tissues or the mechanics of pleural sliding. An intermediate nonuniform rational basis spline surface representation is used to avoid multiple geometric smoothing procedures used in the computational mesh preparation. Measured chest pressure-volume relationships are used to simulate pressure loading on the surface of the model for a given lung volume, as in actual breathing. A hyperelastic model, developed from experimental observations, has been used to model the lung tissue material. Pleural sliding on the inside of the ribcage has also been considered. Results:The finite-element model has been validated using landmarks from four patient CT data sets over 34 breathing phases. The average differences of end-inspiration in position between the landmarks and those predicted by the model are observed to be 0.450Ϯ 0.330 cm for Patient P1, 0.387Ϯ 0.169 cm for Patient P2, 0.319Ϯ 0.186 cm for Patient P3, and 0.204Ϯ 0.102 cm for Patient P4 in the magnitude of error vector, respectively. The average errors of prediction at landmarks over multiple breathing phases in superior-inferior direction are less than 3 mm. Conclusions:The prediction capability of pressure-volume curve driven nonlinear finite-element model is consistent over the entire breathing cycle. The biomechanical parameters in the model are physiologically measurable, so that the results can be extended to other patients and additional neighboring organs affected by respiratory motion.

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Abstract. Prediction of respiratory motion has the potential to substantially improve cancer radiation therapy. A nonlinear finite element (FE) model of respiratory motion during full breathing cycle has been developed based on patient specific pressure-volume relationship and 4D Computed Tomography (CT) data. For geometric modeling of lungs and ribcage we have constructed intermediate CAD surface which avoids multiple geometric smoothing procedures. For physiologically relevant respiratory motion modeling we have used pressure-volume (PV) relationship to apply pressure loading on the surface of the model. A hyperelastic soft tissue model, developed from experimental observations, has been used. Additionally, pleural sliding has been considered which results in accurate deformations in the superior-inferior (SI) direction. The finite element model has been validated using 51 landmarks from the CT data. The average differences in position is seen to be 0.07 cm (SD = 0.20 cm), 0.07 cm (0.15 cm), and 0.22 cm (0.18 cm) in the left-right, anterior-posterior, and superior-inferior directions, respectively.

In the motor industry, the number of spot welded points is closely related to overall cost of the vehicle assembly. A design based on experience is probable to lead redundant spot welded joints. Welded joints are critical in the structural performance, so it is hard to reduce the number. A measurable design index on the design of spot weld configuration is proposed in this study. We optimized the spot welding location and number in the lower control arm of the vehicle and automobile body, as far as the structure retained the structural stiffness. In order to ensure the requirements, we use a sizing optimization of each spot weld stiffness for the global structural rigidity. The survival index is defined the summation of resulted design variables, which is equal to the number of survival in the series of sizing optimizations. With this design index, one can optimally measure the importance of each spot weld joint and remove the redundant spot welds from the structure design.

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