Model-based Registration of Deaeration Deformation for in vivo
Animal Lungs

Kotaro Kobayashi*, Megumi Nakao*, Junko Tokuno**, Toyofumi F. Chen-Yoshikawa**,Hiroshi Date **, Tetsuya Matsuda**

Dept. of System Science, Graduate School of Informatics, Kyoto University,**

Dept. of Thoracic Surgery, Kyoto University Hospital

PurposeRecent advances in imaging techniques have enabled visualization of minute lung nodules in earlystage cancer, and thoracoscopic surgery is often performed as treatment. Although lung nodules areexamined using preoperative CT images, the positions of the nodules change during surgery becauseof deaeration. Although many models have been reported on modeling hepatectomy [1] andpulmonary respiratory deformation, computation models for deaeration deformation have not beendeveloped.
A past study reported results for the large surface deformation of deflated lungs [2]. This study
focuses on the analysis of whole displacement including internal structures. However, CT intensity
shifts during deaeration deformation because the amount of air in a lung in inflated and deflated states
differs substantially. Although there are many studies on image-based registration which tends toincrease registration error, the CT intensity shift should be addressed to ensure deformation analysis
is precise. To address large surface deformation and intensity shift, we propose a model-basedalgorithm focusing on the surface and centerline data of the bronchus, an internal structure. Intensity
shift causes the bronchial regions extracted in the inflated and deflated states to differ so that it isdifficult to correspond the local points between the states using bronchus-only based registration. To
overcome this difficulty, we propose an algorithm that can register both the lung surface and the entire
internal structure of deaeration deformation.

MethodIn our framework, a tetrahedral mesh of the surface and centerline model are used to represent thewhole lung structure. Triangulated surfaces of the upper and lower lobes are first reconstructed fromtheir volumetric labels. In this method, the inflated shape is registered to the deflated shape. The
registration algorithm consists of the following four steps.
STEP 1 Tetrahedral meshes are generated using the nodes of the inflated surface and centerline
consisting of the end-points and bifurcations. For each tetrahedron region, the barycentric
coordinates of the existing centerline data in the region are registered.

STEP 2
Surface data are registered using the method in [2] and the tetrahedron region is deformed. The
inflated centerline data is moved to avoid changing the barycentric coordinates registered in STEP 1.
STEP 3
The tetrahedron region is deformed by moving the inner points to minimize an evaluation function.
The centerline data are moved as in STEP 2.
STEP 4Return to STEP 3 until the evaluation value converges.
A larger region is extracted from inflated state data than deflated state data because thenumber of bifurcations is greater in an inflated state. Hence, the evaluation function
measures the distance from each node of the deflated centerline data to that of theinflated data. Additionally, from visual observations of the deaeration deformation, we
assume that the shape of the bronchus does not locally deform much during deaeration
deformation. Hence, to achieve a spatially smooth deformation, additional constraints
are placed on the angle of the centerline data and the rate of increase in the tetrahedral
region. The evaluation function is defined as follows.
(1)
Here, 𝑛𝑛 /𝑚𝑚 is the number of vertices of the inflated / deflated centerline data, 𝑑𝑑𝑖𝑖 is the shortest

distance from each vertex of the deflated centerline data to a vertex of the inflated centerline data, 𝒏𝒏𝑖𝑖
is a vector from each vertex of inflated centerline data to an adjacent vertex, 𝒏𝒏0𝑖𝑖 is 𝒏𝒏𝑖𝑖 modified by
STEP 3, 𝑙𝑙 is the number of tetrahedron regions, 𝑅𝑅𝑘𝑘 is the rate of increase in volume of the 𝑘𝑘 th

tetrahedron region from STEP 3, 𝑅𝑅𝑘𝑘mean is the average rate of increase in volume of the regions
adjacent to the 𝑘𝑘 th tetrahedral region from STEP 3, and 𝑤𝑤 and 𝑣𝑣 are weighting parameters.

ResultExperiments were conducted to confirm the accuracy of registration using the proposed algorithm.
Three-dimensional (3D) labeled data of the upper / lower lobes and bronchial regions of left lung offive in vivo Beagle dogs were extracted from a 3D CT image using Synapse VINCENT
manufactured by Fuji Film Co. Ltd. to obtain surface data. There are 250 vertices for all surfaces and500 tetrahedral elements. Centerline data of bronchi were converted from label data using theVascular Modeling Toolkit. These processes are automatically done in the software. We used fivedata sets, referred to as case i, (i = {1,2,3,4,5}). The inflated centerline data has 1440 – 1692
vertices, and the deflated centerline data has 1040 – 1094 vertices. There are 120 – 160 (inflated)and 67 − 124 (deflated) end-points and bifurcations in the data. We used 0.01 for both w and v in

equation (1) after examination of several values.
Figure 1 shows the inflated and deflated shapes of cases 2 and 5 obtained using our algorithm. Here,both the point-to-point correspondence among centerline data and spatially smooth deformation
were achieved, even though extracted regions differed between the two states. To evaluate
registration error, we selected less than six reference points for each case that correspond visuallywith the centerline data and compared the coordination obtained from registration and manualpointing. The average target registration error of the five cases before surface registration was 6.0mm, that after STEP 2 was 5.0 mm, and that after centerline data registration was 2.1 mm.
Conclusion
We proposed an algorithm that registers both surface and centerline data for deaeration deformation.
This algorithm overcomes the difficulties caused by large surface deformation and intensity shift.
The experiment demonstrated that its average registration error is 2.1 mm, which is a clinically
acceptable level. Our future work includes analyzing the displacement of the bronchus and modelingdeaeration deformation statistically.
Reference[1] Nakao. M, and Minato. K, (2010), "Physics-based Interactive Volume Manipulation for Sharing
Surgical Process, "IEEE Trans. on Information Technology in Biomedicine, Vol.14, No. 3, pp. 809816.
[2] Kobayashi. K, Nakao. M, Tokuno. J, Yoshikawa. T. C, Matsuda. T, (2018), "Analysis ofDeaeration Deformation in Ex Vivo Animal Lung by Laplacian-Based Surface Registration", 40th
Annual International Conference of the IEEE Engineering in Medicine and Biology Society, Poster
July.
Fig. 1 Registration results before surface registration (left) and after centerline dataregistration (right): (a) case 2, (b) case 5