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Research Papers

Modeling the Nonlinear Motion of the Rat Central Airways

[+] Author and Article Information
G. Ibrahim

Department of Engineering,
University of Leicester,
University Road,
Leicester LE1 7RH, UK
e-mail: gi12@leicester.ac.uk

A. Rona

Department of Engineering,
University of Leicester,
University Road,
Leicester LE1 7RH, UK
e-mail: ar45@leicester.ac.uk

S. V. Hainsworth

Department of Engineering,
University of Leicester,
University Road,
Leicester LE1 7RH, UK
e-mail: svh2@leicester.ac.uk

Manuscript received September 19, 2014; final manuscript received November 6, 2015; published online December 8, 2015. Assoc. Editor: Naomi Chesler.

J Biomech Eng 138(1), 011007 (Dec 08, 2015) (13 pages) Paper No: BIO-14-1468; doi: 10.1115/1.4032051 History: Received September 19, 2014; Revised November 06, 2015

Advances in volumetric medical imaging techniques allowed the subject-specific modeling of the bronchial flow through the first few generations of the central airways using computational fluid dynamics (CFD). However, a reliable CFD prediction of the bronchial flow requires modeling of the inhomogeneous deformation of the central airways during breathing. This paper addresses this issue by introducing two models of the central airways motion. The first model utilizes a node-to-node mapping between the discretized geometries of the central airways generated from a number of successive computed tomography (CT) images acquired dynamically (without breath hold) over the breathing cycle of two Sprague-Dawley rats. The second model uses a node-to-node mapping between only two discretized airway geometries generated from the CT images acquired at end-exhale and at end-inhale along with the ventilator measurement of the lung volume change. The advantage of this second model is that it uses just one pair of CT images, which more readily complies with the radiation dosage restrictions for humans. Three-dimensional computer aided design geometries of the central airways generated from the dynamic-CT images were used as benchmarks to validate the output from the two models at sampled time-points over the breathing cycle. The central airway geometries deformed by the first model showed good agreement to the benchmark geometries within a tolerance of 4%. The central airway geometry deformed by the second model better approximated the benchmark geometries than previous approaches that used a linear or harmonic motion model.

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Figures

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Fig. 1

The airway mesh deformation framework

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Fig. 2

Normalized waveform of the volume change measured by the ventilator unit for (a) Rat_1 and (b) Rat_2. The black dots denote the CT image acquisition time points.

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Fig. 3

(a) A sample slice of the dynamic-CT image of Rat_1 before (left) and after filtering (right). (b) An example of the 3D reconstructed airway geometries (G0) of Rat_1 (left) and Rat_2 (right).

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Fig. 4

The blocking strategy illustrated on a sample branch. The magnification illustrates the slight manual modification applied to a vertex location.

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Fig. 5

Code flowchart to resequence the nodal positions at β as δ

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Fig. 6

The dynamic-CT based deforming mesh at different inflation levels over the breathing cycle. (a) Rat_1 and (b) Rat_2.

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Fig. 7

(a) Locations of the landmarks on a sample geometry of Rat_1. (b) Calculated trajectory of a sample landmark (Pt), where  t is the deformation time. (c) Distribution of the calculated perpendicular distance (d) of each landmark to its associated straight trajectory between end-exhale and end-inhale. d is normalized by the average linear node displacement ℓ between the mesh at end-exhale M0, and the mesh at end-inhale M5.

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Fig. 8

Normalized ensemble-averaged displacement of projected landmarks (dots) superimposed on a normalized actual waveform of Rat_1 and linear volume change approximation (lines). Error bars represent the standard deviation.

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Fig. 9

Residuals from fitting (a) the normalized lung volume change waveform from Fig. 2 and (b) a straight line to the normalized displacements of the landmarks. The residuals are normalized by the average linear node displacement ℓ between the mesh at end-exhale M0 and the mesh at end-inhale M5.

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Fig. 10

The two-CT based deforming mesh at different inflation levels over the breathing cycle. (a) Rat_1 and (b) Rat_2.

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Fig. 11

Maximum computed Hausdorff distance of the deformed mesh of (a) Rat_1 at t4 and (b) Rat_2 at t8. The results are normalized by the average linear node displacement ℓ between the end-exhale mesh M0 and the end-inhale mesh M5. The sign is defined as positive in the deformation direction between end-exhale and end-inhale.

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Fig. 12

Distance between the surface nodes of the deformed CFD mesh of Rat_1 to their corresponding position on the wall of the reference mesh at selected time-point during (a) inspiration and (b) expiration. The mesh was deformed using (1) the two-CT based deforming model, (2) linear deformation, and (3) harmonic deformation The results are normalized by the average linear node displacement ℓ between the end-exhale mesh M0 and the end-inhale mesh M5. The positive and the negative values represent, respectively, the over-estimation and the under-estimation of the nodes anatomical positions in the node displacement direction from M0 to M5.

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Fig. 13

Distance between the surface node of the deformed CFD mesh of Rat_2 to their corresponding position on the wall of the reference mesh at selected time-point during (a) inspiration and (b) expiration. The mesh was deformed using (1) the two-CT based deforming model, (2) linear deformation, and (3) harmonic deformation The results are normalized by the average linear node displacement ℓ between the end-exhale mesh M0 and the end-inhale mesh M5. The positive and the negative values represent, respectively, the over-estimation and the under-estimation of the nodes anatomical positions in the node displacement direction from M0 to M5.

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