Personalized heterogeneous deformable model for fast volumetric registration
 Weixin Si†^{1, 2},
 Xiangyun Liao†^{2},
 Qiong Wang^{2}Email authorView ORCID ID profile and
 Pheng Ann Heng†^{1, 2}
DOI: 10.1186/s1293801703213
© The Author(s) 2017
Received: 12 October 2016
Accepted: 10 February 2017
Published: 20 February 2017
Abstract
Background
Biomechanical deformable volumetric registration can help improve safety of surgical interventions by ensuring the operations are extremely precise. However, this technique has been limited by the accuracy and the computational efficiency of patientspecific modeling.
Methods
This study presents a tissue–tissue coupling strategy based on penalty method to model the heterogeneous behavior of deformable body, and estimate the personalized tissue–tissue coupling parameters in a datadriven way. Moreover, considering that the computational efficiency of biomechanical model is highly dependent on the mechanical resolution, a practical coarsetofine scheme is proposed to increase runtime efficiency. Particularly, a detail enrichment database is established in an offline fashion to represent the mapping relationship between the deformation results of highresolution hexahedral mesh extracted from the raw medical data and a newly constructed lowresolution hexahedral mesh. At runtime, the mechanical behavior of human organ under interactions is simulated with this lowresolution hexahedral mesh, then the microstructures are synthesized in virtue of the detail enrichment database.
Results
The proposed method is validated by volumetric registration in an abdominal phantom compression experiments. Our personalized heterogeneous deformable model can well describe the coupling effects between different tissues of the phantom. Compared with highresolution heterogeneous deformable model, the lowresolution deformable model with our detail enrichment database can achieve 9.4× faster, and the average target registration error is 3.42 mm, which demonstrates that the proposed method shows better volumetric registration performance than stateoftheart.
Conclusions
Our framework can well balance the precision and efficiency, and has great potential to be adopted in the practical augmented reality imageguided robotic systems.
Keywords
Biomechanical deformable volumetric registration Tissue–tissue coupling Datadriven parameters estimation Coarsetofine schemeBackground
Surgical procedures are traditionally supported with preoperative images, such as the computed tomography (CT) images and magnetic resonance (MR) images. The image quality can be very good, while when it comes to the surgical procedures, the link between images and patient is lost. In this regard, it can be intuitively displayed as an overlay of preoperative images onto the patient’s body, which creates an augmented reality environment that enables surgeons to visualize the structures of interest [1]. Imaging looks inside the patient’s body, exposing the patient’s anatomy beyond what is visible on the surface.
A variety of methods have been developed to provide intraoperative image registration, which can be mainly classified into rigid and nonrigid registration. Rigid registration is generally applied when the target anatomy fulfills the criterion of rigidity and spatial distortions are not introduced in the image acquisition process [2]. It is a relatively quick and straightforward process that uses a rigid motion model with rotation and translation parameters of the target objects where tissue deformation can be ignored. Unfortunately, purely rigid transformation is not sufficient to describe the mechanical behaviors of human organ for most of the surgeries. To this end, this technique cannot produce an optimal alignment when human organ undergoes deformations caused by external forces (such as surgical tools) or natural motions (such as respiration). In such cases, nonrigid registration is required when the imaged anatomy nonrigidly deforms between acquisitions, which can provide a relatively accurate alignment for cases of nonrigid deformations. Readers can refer to [3] for a thorough and comprehensive introduction of nonrigid registration.
Moreover, nonrigid registration can be broadly classified as either surface registration or volumetric registration. Both of these two approaches have advantages and weaknesses. Surface registration methods [4–10] have been shown to accurately align the highly complex morphological details on the surface of the human organ. Although these methods can offer the possibility to achieve visually coherent surface registration, they are limited to surface overlay without considering heterogeneous internal structures, such as vessels and tumors. In this regard, it is crucial to consider volumetric registration [11, 12]. Generally, volumetric registration methods can provide a correspondence field across the entire human organ, including common target regions (such as tumors and vessels) that are not in the domain of the surfacebased alignment procedures.
Biomechanical model has proven to be a promising way for nonrigid volumetric registration [11, 13–20], which can accurately estimate the motion of indepth volumetric structures. The finite element method (FEM) is the most widely used physicsbased approach for developing deformable model, which can accurately describe the mechanical behaviors of human organ as continuous medium. Many researchers have reported certain success in achieving accurate volumetric registration based on FEM model. However, conventional FEM is so complicated that makes solution procedure timeconsuming, which limits its application in clinical practice [21]. In this paper, we employ the total Lagrangian explicit dynamics (TLED) FEM to model the mechanical response of human organ under interactions. This is because TLED FEM is an efficient numerical algorithm that is based on the FEM while using the total Lagrangian formulation, where stresses and strains are measured with respect to the original configuration which allows for precomputing of most spatial derivatives before the commencement of the timestepping procedure [22]. Besides, TLED FEM is capable of handling both geometric and material nonlinearities, which is beneficial to perform the large deformation analysis induced by tool–tissue interactions. In addition, the accuracy of the FEM relies heavily on the quality of geometric models meshes, while the geometric models of human organs are often complicated and irregular for representing the morphological details of the organs. Here we directly extract the uniform hexahedral mesh from the segmented medical images, which can greatly reduce the complexity of volumetric geometric mesh reconstruction and provide the highquality mesh for biomechanical modeling.

Personalized heterogeneous deformable model. Our deformable model is based on a uniform and highresolution hexahedral mesh directly extracted from the MR images, which is beneficial for the accuracy of TLED FEM analysis. A novel and effective tissue–tissue coupling strategy based on penalty method is proposed to model the indepth anatomical structure of deformable body, and the personalized tissue–tissue coupling parameters are estimated in a datadriven way.

Coarsetofine scheme. We propose a coarsetofine scheme to reduce the computational complexity of heterogeneous deformable model for fast volumetric registration. In more detail, we perform the TLED FEM on lowresolution hexahedral mesh first and then synthesize the microstructures using a detail enrichment database constructed by the highresolution heterogeneous deformable model.
Methods
Materials
Hexahedral mesh construction
In this paper, we focus on the cases when lesions (such as tumors) are present inside the parenchyma, these can be taken into account also from the mechanical point of view as they usually introduce significant heterogeneity. This heterogeneity can be straightforwardly included in the model through volumetric mesh. In this regard, hexahedral mesh or tetrahedral mesh [11–13] are often employed rather than triangular mesh. Note that traditional volumetric registration methods are based on reconstructed tetrahedral mesh, while the reconstruction process may cause loss of precision. Considering that the segmented MR images are pixel level representation of the scanned phantom, we can avoid this limitation by directly constructing the hexahedral mesh. More importantly, we concentrate on improving the efficiency of volumetric registration, however, the tetrahedral mesh is usually irregular and contains distorted elements when deforms [25, 26], which requires remeshing and results in huge computational cost and makes the simulation timeconsuming [27, 28]. While the hexahedral mesh is known to be efficient in terms of stability and computational cost [25, 26], and hexahedral mesh presents better accuracy and efficiency than tetrahedral mesh in solid mechanics and structural engineering problems [29].
It is worth noting that there are truly jaggy structures in our method around the hexahedral boundary no matter what kind of resolution it uses, and this will degrades the performance of our method in a certain degree. However, this is a kind of inevitable precision loss in the process of geometric mesh generation, even for the commonly adopted triangular mesh or tetrahedral mesh, since converting the raw medical images to surface/volumetric mesh leads to the loss of precision. Theoretically, the higher resolution the hexahedral mesh is, the more accurate registration method is. In this regard, we adopt a relative high resolution \(74 \times 18 \times 54\) to reduce the precision loss induced by jaggy structures as much as possible. Meanwhile, the coarsetofine scheme proposed in this paper guarantees our registration efficiency is not influenced by the highresolution hexahedral mesh.
Personalized heterogeneous deformable model
Highresolution heterogeneous deformable model
Taking liver tissue containing a tumor as an example, the hexahedron containing both part of tumor and soft tissue is called boundary hexahedron. Here the shared vertices of liver hexahedral and tumor hexahedral meshes forms the internal surfaces and these vertices are called internal surface vertices. By representing the internal surface vertices using their neighboring hexahedral vertices, the coupling forces can be transmitted to the neighboring hexahedra vertices whose displacements can also be reflected on the internal surface vertices.
Data driven parameters estimation
To precisely model volumetric deformation, we have to obtain the tissue–tissue coupling parameters for our heterogeneous deformable model. It is unrealistic to find universal coefficients \(k_{c,st}\) and \(k_{c,sv}\) which fit all the patients and circumstances [33]. There is an important variation of values when it comes to the parameters estimation of our deformable model. The parameters should be selected according to the personalized application.
Dynamics
Coarsetofine scheme
However, there is a difference between highresolution and lowresolution hexahedral meshes. For the highresolution hexahedral mesh, the parenchyma and lesion are separated from each other by the internal boundary as shown as the two splitted vertices and imaginary line, which have no direct connection with the parenchyma or lesion hexahedral mesh. The force transmission between parenchyma and lesion is realized by the internal boundary vertices using MLS method. For the lowresolution hexahedral mesh, the parenchyma hexahedral and lesion hexahedral meshes are connected directly and force transmission between them is also direct. For each material’s hexahedral mesh, we assign different Young’s modulus for them, each hexahedron’s tissue type is determined by the largest number of pixel inside that hexahedron. To achieve accurate volumetric registration with lowresolution hexahedral mesh, we store the mapping relationship between vertices on highresolution hexahedral mesh and corresponding lowresolution hexahedral mesh using MLS method on different compression conditions (respectively 50 different displacements and 20 different orientations at each of the 5 compression positions) to build a detail enrichment database.
Experiments
We conducts several experiments to validate our method mainly from two perspectives: accuracy and efficiency. Young’s modulus for parenchyma, vessel and tumor used in the phantom are respectively \(2\times 10^5\), \(10^6\) pa and \(5\times 10^6 pa\) pa, and the Poisson’s ratio for them are 0.49. All experiments are conducted on a PC equipped with Intel Xeon CPU E31230 V2 (3.30GHz) CPU, 4G RAM and NVIDIA GeForce GTX 650 Ti.

Compare the overall registration accuracy and performance of our method with the registrations using highresolution heterogeneous deformable model and Han et al. [13], which is also a nonrigid registration method based on the TLED FEM while without considering the tissue heterogeneity.

Compare the surface and internal registration results of our method with the above two registration methods respectively, demonstrating the accuracy of heterogeneity representation of our method.
Meanwhile, we evaluate the registration accuracy of 11 surface landmarks and 14 internal landmarks on the phantom model respectively, as shown in Fig. 13b. For highresolution heterogeneous deformable model, the average TRE of surface landmarks and internal landmarks are respectively 2.45 and 2.04 mm. While for our method, the average TRE of surface landmarks and internal landmarks are 3.46 and 3.38 mm, respectively. Using Han’s method, the average TRE of surface landmarks and internal landmarks are 6.39 and 8.81 mm, respectively. Experimental results indicate our method can well describe the heterogeneity of human organ, and achieve better registration accuracy than Han’s method [13].
In addition, we achieve 27.2 fps of volumetric registration by our method with the average computation time 36.76 ms, this frame rate can fulfill the requirement of realtime tracking system. It is also worth noting that at the expense of accuracy for about 1 mm, our method can speed up \(9.4\times\) than the highresolution heterogeneous deformable model, as well as about \(9.4\times\) faster than Han’s method which is applied on the highresolution deformable model. The experimental results demonstrate that our method can well balance the computational efficiency and accuracy.
Discussion and conclusion
In this paper, an efficient personalized heterogeneous deformable model is presented for volumetric registration. Our method includes three core components: a heterogeneous deformable model, a personalized tissue–tissue coupling strategy and a coarsetofine scheme. In more detail, we propose the highresolution heterogeneous deformable model for a uniform and highresolution hexahedral mesh and model the mechanical behavior of heterogeneous anatomical structure with TLED FEM and penalty method. Besides, we present a data driven parameters estimation method for the highresolution heterogeneous deformable model to obtain the tissue–tissue coupling parameters of our method in vivo for FE analysis. In addition, we put forward a coarsetofine scheme to achieve fast volumetric registration, which is to first perform the volumetric deformation on the lowresolution hexahedral mesh and then synthesize the microstructures according to the detail enrichment database. We have tested the highresolution heterogeneous deformable model and our method with the real compression of phantom in five experiments. The experimental results indicate our method can achieve fast and accurate registration results, which are essential for clinical applications.
Biomechanical deformable model is an effective way to reliably predict deformation for volumetric registration and many researchers have demonstrated good nonrigid registration that meets the accuracy requirements of specific surgery. AlMayah et al. [17] proposed a 3D FEM based biomechanical model for image registration of head and neck cancer treatment, they applied the linear elastic material properties to their method and adopted linear geometry. Oktay et al. [16] proposed a linear FEM deformation based registration method for preoperative and intraoperative 3D image fusion for laparoscopy surgery. Though the linear FE analysis is an approximation that makes the analysis of the structure more tractable, the assumptions of linearity are often not adequate for real tissues which often undergoes nonlinear behaviour. Compared with the work of [16, 17], our TLED FEM analysis adopts nonlinear elastic material properties which can provide more accurate biomechanical analysis. Hopp et al. [15] presented a nonlinear biomechanical FEM analysis based registration method for Xray mammograms with DCEMRI volumes. The mean TRE was 13.2 mm that was within the clinically relevant range. However, the deformable body was modelled as homogeneous soft tissue which could not describe the deformation distribution inside the soft tissue. Thus their method is not suitable for the registration of organs with internal heterogeneous structures such as tumors or vessels. To address the heterogeneous issue, Haouchine et al. [11] used a deformable volumetric biomechanical model accounting for heterogeneity and anisotropy in hepatic surgery guidance with the best tumor registration accuracy of 2.5 mm. Samavati et al. [18] proposed a biomechanical model with heterogenous material property for deformable prostate image registration with average registration accuracy of 4.8 mm, also they have presented a hybrid biomechanical intensity based deformable image registration method for lung 4DCT [19] and achieved average registration accuracy of 2.9 mm. Han et al. [13] proposed a patientspecific biomechanical modeling framework for heterogeneous breasts based on nonlinear FEM solver, which achieved relative accurate volumetric breasts registration with the best registration accuracy of \(3.18\pm 1.69\) mm by anisotropic heterogeneous model. They assigned different material properties for different tissues to construct the heterogeneous structures. Different from the above heterogenous models, our method constructs the heterogeneous deformable on a uniform and highresolution hexahedral mesh directly extracted from the MR images for investigating the motion of liver’s vessels and tumors, and the different types of tissues are coupled by a penalty method. The proposed highresolution heterogeneous deformable model achieves average registration accuracy of 2.22 mm on a fine resolution grid of \(74\times 18\times 54\). Our method achieves average registration accuracy of 3.42 mm on a lowresolution grid of \(24\times 18\times 18\) with detail enrichment database, while the method of Han et al. [13] achieves TRE of 7.74 mm.
In spite of high registration accuracy achieved by our heterogeneous model, the efficiency due to the tremendous computation has limited the applications of many work [11, 13, 18, 19], whose registration process is timeconsuming. However, the efficiency is an essential issue in the imageguided surgery for the reason that even in a few seconds the registration target would deform or shift a lot which could lead to the failure of the registration. It is crucial to develop a fast biomechanical model based registration methods which incorporate the advantages of high accuracy and efficient computation. To achieve fast volumetric registration, we propose a practical coarsetofine scheme and establish a detail enrichment database at the preprocessing stage. At runtime, we simulate the mechanical behavior of the lowresolution hexahedral mesh and synthesize the microstructures in virtue of detail enrichment database. With the expense of accuracy for about 1mm, our method can speed up \(9.4\times\) than the highresolution heterogeneous deformable model.
There are certain limitations of our method. In clinical practice, the personalized Young’s modulus is unknown while it is very essential for the construction of personalized deformation model. We plan to obtain the patientspecific Young’s modulus by ultrasound elastography in vivo [34]. Besides, the accuracy of the lowresolution deformable model is not as accurate as the highresolution one, so that we plan to incorporate the generalized moving least squares (GMLS) [35] into our coarsetofine scheme to improve its accuracy. In addition, we intend to improve the setup of boundary conditions for the temporal registration phase, which is an important and challenging problem. Besides, we will also adopt our method to align the preoperative volumetric liver MR images to intraoperative ultrasound image and obtain quantitative errors on real data.
Notes
Abbreviations
 CT:

computed tomography
 MR:

magnetic resonance
 MRI:

magnetic resonance imaging
 FEM:

finite element method
 TLED:

total Lagrangian explicit dynamics
 MLS:

moving least squares
 GMLS:

generalized moving least squares
 TRE:

target registration error
 DCEMRI:

dynamic contrastenhanced magnetic resonance imaging
 4DCT:

4dimension computed tomography
Declarations
Authors’ contributions
WS, XYL, QW and PAH participated in literature search, data analysis, manuscript writing and editing. WXS and XYL contributed equally to this work. All authors read and approved the final manuscript.
Acknowledgments
This paper is supported by Hong Kong Research Grants Council General Research Fund (Project Nos. CUHK 14202514 and CUHK 14203115), National Natural Science Foundation of China (Nos. 61233012, 61305097 and 81601576) and Guangdong province science and technology plan project (No. 2016A020220013).
Competing interests
The authors declare that they have no competing interests.
Declarations
Please contact author for data requests.
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.
Authors’ Affiliations
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