Predictive modeling of lung motion over the entire respiratory cycle using measured pressure-volume data, 4DCT images, and finite-element analysis

Abstract

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 0.450 +/- 0.330 cm for Patient P1, 0.387 +/- 0.169 cm for Patient P2, 0.319 +/- 0.186 cm for Patient P3, and 0.204 +/- 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.

Figure 1

A flow diagram of the modeling scheme showing the steps to convert 4DCT images to FE models with boundary conditions.

Figure 2

Geometry and tumor location of all four patients (P1–P4).

Figure 3

Sequence of steps in converting 4DCT image data into a FE mesh through an intermediate NURBS representation in P2.

Figure 4

FE models including a thoracic cavity, a tumor (gross target volume for radiation treatment purposes), and lungs for P2.

Figure 5

Pressure-volume relationship from the parameterized P-V curve (Ref. 52) (TV=500 ml and transpulmonary pressure=10 cm H₂O).

Figure 6

Comparison of relaxing (Laplacian smoothing) vs proposed NURBS surface reconstruction procedure in P2 showing changes in mesh volume and elements that are close to or violating the quality indices.

Figure 7

Landmark positions of P2; bifurcation of vessels and airway were determined by radiologists (a) locating landmarks at anatomical points of bifurcations and at the center of the tumor (tumor, arrow; LR-AP, sectional view on top; AP-SI, sectional view on bottom left; LR-SI, sectional view on bottom right); (b) 48 points of landmarks; and (c) five points of landmarks close to the tumor.

Figure 8

Prediction errors at landmarks between EE and EI for each patient: (a) P1, (b) P2, (c) P3, and (d) P4.

Figure 9

Inferior-superior motion of landmark at tumor centroid for proposed model and 4DCT over multiple breathing phases: (a) P1, (b) P2, (c) P3, and (d) P4.