An Insight Toolkit (ITK) processing framework for simultaneous segmentation of multiple objects using 
active contours without edges is presented in this paper. These techniques are also popularly referred to 
as multiphase methods. Earlier, we had an implemented the Chan and Vese [1] algorithm that uses level- 
sets to accomplish region segmentation in images with poor or no gradient information. The current 
work extends that submission to use multiple level sets that evolve concurrently. The basic idea is to 
partion the image into several sets of piecewise constant intensity regions. This work is in contrast to 
the level-set methods currently available in ITK which necessarily require gradient information and also 
necessarily segment a single object-of-interest. Similar to those methods, the methods presented in this 
paper are also made efﬁcient using a sparse implementation strategy that solves the contour evolution 
PDE at the level-set boundary. This work does not introduce any new ﬁlter but extends the earlier 
submitted to ﬁlters to process multiple objects. We include 2D/3D example code, parameter settings and 
show the results generated on a 2D cardiac image.

level set segmentation using coupled active surfaces

 Junctions of tubular structures (vasculature, trachea, neuron, etc) in medical images are critical for the topology of these structures. Identification of them is helpful in many applications. For example, quantification of geometric vascular features, registration of trachea movement due to respiration, tracing of neuron path. However, manual extraction of junctions can be tedious, time-consuming, and subject to operator bias. In this paper, we propose a novel method to detect them automatically and describe how to implement it in ITK framework. The input is a 2D/3D binary image that can be obtained from any segmentation techniques. The output will be positions of junctions and their sizes. There are only two parameters which need to be set by the user. We provide here the implementation as a ITK class: itk::JunctionDetectionFilter.
Please cite the following paper if you are interested in our work.
G. Xiong, C. Chen, J. Chen, Y. Xie, and L. Xing, Tracking the Motion Trajectories of Junction Structures in 4D CT Images of the Lung, Vol. 57, No. 15, pp. 4905-4930, Physics in Medicine and Biology, 2012.

Automatic Junction Detection for Tubular Structures

Mathematical modeling and computer simulation have proved tremendously
successful in engineering. One of the greatest challenges for mechanists is
to extend the success of computational mechanics to fields outside
traditional engineering, in particular to biology, biomedical sciences, and
medicine. The proposed workshop will provide an opportunity for
computational biomechanics specialists to present and exchange opinions on
the opportunities of applying their techniques to computer-integrated
medicine. For example, continuum mechanics models provide a rational basis
for analyzing biomedical images by constraining the solution to biologically
reasonable motions and processes. Biomechanical modeling can also provide
clinically important information about the physical status of the underlying
biology, integrating information across molecular, tissue, organ, and
organism scales. The main goal of this workshop is to showcase the clinical
and scientific utility of computational biomechanics in computer-integrated
medicine.

The authors of the best papers presented at the Computational Biomechanics
for Medicine workshop will be requested to submit an extended version of
their papers to the special section of the Medical Image Analysis journal.

Computational Biomechanics for Medicine III: a MICCAI 2008 satellite

We propose a new nonlinear image registration model which is based on nonlinear elastic regularization and unbiased registration. The nonlinear elastic and the unbiased regularization terms are simplified using the change of variables by introducing an unknown that approximates the Jacobian matrix of the displacement field. This reduces the minimization to involve linear differential equations. In contrast to recently proposed unbiased fluid registration method, the new model is written in a unified variational form and is minimized using gradient descent. As a result, the new unbiased nonlinear elasticity model is computationally more efficient and easier to implement than the unbiased fluid registration. The unbiased large-deformation nonlinear elasticity method was tested using volumetric serial magnetic resonance images and shown to have some advantages for medical imaging applications.

Nonlinear Elastic Registration with Unbiased Regularization in Three Dimensions

Nonlinear finite element methods are described in which cyclic organ motion is implied from 4D scan data. The equations of motion corresponding to an explicit integration of the total Lagrangian formulation are reversed, such that the sequence of node forces which produces known changes in displacement is recovered. The forces are resolved from the global coordinate system into systems local to each element, and at every simulation time step are expressed as weighted sums of edge vectors. In the presence of large deformations and rotations, this facilitates the combination of external forces, such as tool-tissue interactions, and also positional constraints. Applications in the areas of surgery simulation and minimally invasive robotic interventions are discussed, and the methods are illustrated using CT images of a pneumatically-operated beating heart phantom.

Inverse Nonlinear Finite Element Methods for Surgery Simulation and Image Guidance

In this paper, we propose a Mix-resolution Bone-related Statistical Deformable Model (mBr-SDM) to improve the predicting accuracy of orthognathic surgery, particularly for the main deformation region. Mix-resolution Br-SDM consists of two separate Br-SDM of different resolutions: a high-resolution Br-SDM which is trained with more samples to capture the detail deforming variations in the main deforming regions of interest, together with a low-resolution Br-SDM which is trained with a smaller number of samples to capture the major variations of the remaining facial points. The experiments have shown that the mix-resolution Br-SDM is able to significantly reduce the predicting error compared with the corresponding Finite Element Model, while giving a low computational cost which is characteristic of the SDM approach.

A Mix-resolution Bone-related Statistical Deformable Model (mBr-SDM) for Soft Tissue Prediction in Orthognathic Surgery Planning

In this paper we propose the usage of a very efficient contact implementation for modeling the brain-skull interaction. This contact algorithm is specially design for our Dynamic Relaxation solution method for solving soft-tissue registration problems. It makes possible the use of complex biomechanical models which include different nonlin-ear materials, large deformations and contacts for image registration. The computational examples prove the accuracy and the computational efficiency of our methods. For a model having more than 50000 degrees of freedom, a complete simulation can be done in less than a minute.

Realistic And Efficient Brain-Skull Interaction Model For Brain Shift Computation

We present a framework for statistical finite element analysis allowing performing statistical statements of biomechanical performance of peri-articular implants across a given population. In this paper, we focus on the design of orthopaedic implants that fit a maximum percentage of the target population, both in terms of geometry and biomechanical stability. CT scans of the bone under consideration are registered non-rigidly to obtain correspondences in position between them. A statistical model of shape is computed by means of principal component analysis. A method to automatically propagate standardize fractures on the statistically-based bone population has been developed as well as tools to optimize implant position to best-fit the bone surface. Afterwards, finite element analysis is performed to analyse the biomechanical performance of the bone/implant construct. The mechanical behaviour of different PCA bone instances is compared for tibia representing the Asian and Caucasian populations.

Assessment of Peri-Articular Implant Fitting Based on Statistical Finite Element Modeling

Primary stability of osseointegrated implants is necessary for short and long-term success of the treatment. This paper presents a method to help clinicians preoperatively assess this primary implant stability. The method combines a planning software with a in-house finite element solver. Once the clinician has chosen a position for the implant on the planning tool, a finite element analysis is automatically started and calculates the mechanical stability of the implant at this position. The process is designed to be as simple and fast as possible for an efficient clinical use. Mechanical testing material was used to validate the stability measured by the software. The novel tool presented here leads the way to a new generation of intelligent computer-assisted tools able to give a priori indication on the life span of the implant.

Predicting implant stability: in vitro validation in artificial bone

Meaningful physical models are important for studying cardiac physiology, such as quantitative assessments of pathology via changes in model parameters, and recovering information from medical images. In order to achieve realistic deformation studies, an anatomically accurate cardiac model under the prolate spheroidal coordinate system has been proposed, which comprises the pole-zero constitutive law characterized by 18 material parameters. Nevertheless, the large number of parameters and the complicated mathematics under the curvilinear coordinate system make it difficult to implement and computationally expensive. In consequence, we propose a cardiac model under the cartesian coordinate system comprising the Costa law, which is tailored for medical image analysis. The Costa law is characterized by a strain energy function with only seven material parameters, but has been reported as the best among the five tested well-known models in a comparative study, including the pole-zero law. In our framework, the penalty method for material incompressibility is used to avoid introduction of extra variables. Furthermore, we introduce a simple but novel boundary condition for enforcing cardiac specific boundary displacements under the cartesian coordinate system. With the active stresses provided by cardiac electromechanical models, and also the blood pressures acting as the natural boundary conditions on the endocardial surfaces, the physiologically plausible active deformation of the heart can be simulated. Experiments have been done on a cubical object to verify the correctness of the implementation, and also on a canine heart architecture to show the physiological plausibility of the cardiac model.