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The distribution model described above is intended to depict the locations of muscles on the basis of the centerline and landmarks. However, the muscle-specific shape is not included in the distribution model. We describe a technique for

S. Hanaoka et al.

168

Distribution model of the skeletal muscle

Fig. 3.9 Distribution model of the skeletal muscle

statistically modeling the outer shape of the muscle, expressed as a mathematical function. We describe the modeling of the psoas major muscle, which has a characteristic shape. SSM requires muscle area data by semiautomatic or manual extraction of the target muscle.

The psoas major muscle is spindle shaped. It is assumed that the cross section of the outer shape can be represented by a quadratic function that is symmetric to the centerline. Based on this assumption, a muscle area is extracted from the training data to determine the distance to the outer shape from each centerline. The approximate curve of the quadratic function is fitted to the distribution of the distance values along the centerlines. The curve generated can be the quadratic function whose vertex is located at the midpoint of the centerline. Here it should be noted that two parameters are present in the quadratic function, gradient alpha and intercept beta. We define the value that represents the muscle-specific shape as gradient alpha. The fitting parameter which accommodates individual differences in muscle mass is defined as intercept beta. The gradients resulting from the approximate curve fitting are saved as the shape parameters. Fitting parameters are determined from the test data in the recognition process described later.

  • 3 Understanding Medical Images Based on Computational Anatomy Models
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We used SSMs to recognize the deeply situated psoas major muscle and the superficially situated rectus abdominis muscle. If the modeling can be applied to a characteristic shape, it is not limited to superficial or deep locations.

Recognition The choice of recognition method depends on the model. First, using only the distribution model. In this pattern, it is necessary in identifying the skeletal muscle by using a grayscale value inside and outside of the boundary. Second, using an SSM. The SSM-based method needs, for calculating the fitting parameters, intercept beta, which is a parameter of remaining that has not been determined in the model building process. These parameters are calculated automatically on the test data by generating the centerlines. For example, in psoas major muscle recognition, where the cross section of the midpoint position of the centerline is thickest, the maximum diameter of the muscle is determined from the test data and defines intercept beta. Finally, it fits the model function to the landmarks and performs the recognition of the muscle using the grayscale value from the CT image.

Ordinarily, each model is only intended to indicate a representative area or boundary of the muscle region. Therefore, in the recognition process, as well as in other organ recognitions, a precise extraction process is needed.

Figure 3.10 shows the recognition results of the rectus abdominis muscle and psoas major muscle using the SSM.

Recognition of Lower Limb Muscles In the above sections, recognition methods for relatively isolated single muscles were described. In the lower limb muscles, multiple muscles are densely and closely interrelated and adjacent to each other. Therefore, the above described methods may not be useful for the lower limb, and segmentation methods suitable for densely interrelated muscles need to be developed.

Recognition results of the rectus abdominis muscle and psoas major muscle

Fig. 3.10 Recognition results of the rectus abdominis muscle and psoas major muscle

Lower limb muscle segmentation was mainly motivated by biomechanics research. To overcome the limitations of conventional musculoskeletal biomechanical simulations using line segments as muscle models, precise geometries of muscles are needed to be reconstructed. Early works used manual [39] or interactive segmentation [106, 107] to reconstruct musculoskeletal anatomy models from MR data to perform patient-specific simulations. More recently, attention to lower limb muscle segmentation has been paid for diagnostic purposes, and automated segmentation methods have been investigated. Random walks [34] and multi-atlas segmentation [95, 301] data were used in order to deal with incomplete boundaries among the muscle regions. MR data were usually considered to be suitable [34, 39, 106, 107, 301], but CT data have also been also utilized [95]. Figure 3.11 shows typical results of automated segmentation of the hip and thigh muscles from CT data [95]. In this method, the bone regions (the pelvis and femur) of the segmentation target CT data were nonrigidly registered to the atlas data of the training dataset for spatial normalization, and then the muscle regions were segmented. The muscle regions were also used for spatial normalization in the next stage of the method, and some muscles were further segmented and used for further normalization.

Conclusion We described automatic recognition methods based on CA, a general technique of skeletal muscle recognition in non-contrast CT images using anatomic features. We present the recognition of landmarks, construction of anatomical centerlines, and anatomical shape model generation. The SSM describes the outer shape of the muscle, and the distribution model indicates the existence area of the muscle.

Typical segmentation result of the bones and muscles in the pelvis and thigh from CT data

Fig. 3.11 Typical segmentation result of the bones and muscles in the pelvis and thigh from CT data. (a) Input CT data, (b) segmentation of the pelvis and femurs, (c) segmentation of muscle tissues, (d) segmentation of individual muscles

Automatic recognition of skeletal muscle based on a CA model is robust. When separation from other organs is difficult, the shape model provides a useful initial region. However, this requires careful selection of the appropriate modeling function for outer shape determination and also requires accurate extraction.

 
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