An update on computational anthropomorphic anatomical models

Introduction

Human anatomical models have been developed to represent the spatial distribution of different tissues in the body (human anatomy).^1,2 These models were mainly constructed to provide a non-invasive and inexpensive way to test various diagnostic imaging and interventional/therapeutic procedures, ³ such as dosimetric calculations for ionizing/non-ionizing radiation exposure, optimizing medical imaging facilities, and personalized medicine. An important category of anatomical models is physical phantoms composed of solid materials with properties equivalent to human tissues, e.g. homogenized cylindrical water phantoms used for the calibration of radiation detectors and diagnostic imaging systems.^4,5 However, these phantoms are usually expensive while reflecting a crude approximation of the human body. In addition, using physical phantoms for the calibration of advanced systems can be very costly and time-consuming. As a result, computational phantoms representing a mathematical model of the human anatomy in a digital format were developed originally for applications in radiation protection and medical imaging optimization. Recently, the ultimate objective of constructing human computational models as the ancestor of the digital twins (i.e. computational objects employed in medicine or other fields as surrogate or replica of the human body to certain process, e.g. to ionizing radiation) is the personalization of medical procedures within the paradigm of precision medicine. ⁶ Starting in the 1960s, the development of the computational models evolved through many generations, and in the 1980s, further efforts were made in this domain. In this regard, the Visible Human Project led to the creation of the first complete anatomical model for dose calculation purposes. ⁷ The first generation of computational phantoms suffered from a variety of limitations, including lack of anatomical realism, the non-inclusion of tissue characteristics, calculation speed, as well as their incompatibility with available analytical or Monte Carlo simulation codes. More importantly, these computational phantoms have not been designed for subject-specific modeling and ignored inter-subject anatomical variability. ⁸

Advances in high-performance computing stimulated the development and usage in research of realistic computational anthropomorphic models. To date, more than 200 computational phantoms have been reported in the literature. ² Examples of widely used anatomical models are the NURBS-based XCAT phantom series ⁹ and the Virtual Population based on triangle mesh.^10,11 Advances in medical imaging modalities and computational algorithms allow fast construction of personalized computational models through automated segmentation techniques and enable the incorporation of physiological motion into anatomical models.

The fundamentals of computational models design

Multiple factors should be considered during the construction of a realistic anthropomorphic anatomical model. ¹² These include anatomy (tissues, organs, and regions), tissue properties, computational efficiency, as well as compatibility with analytical or Monte Carlo simulation codes.

As a result, the first step in anthropomorphic anatomical model construction consists of defining geometrical surfaces and tissue properties. This can be done either by using constructive solid geometry (CSG) or boundary representation (BREP) approaches.^13,14 In CSG, objects are created using primitives, such as cylinders, ellipsoids, spheres, … etc. A number of examples can be found in the literature that fall under this category ranging from whole organ representation ⁸ to voxel-based representations. ¹⁵ Although whole organ representation approaches have the advantage that they are computationally efficient and compatible with existing Monte Carlo radiation transport simulation codes, they suffer from the lack of anatomical realism. Conversely, voxel-based representation has the advantage of reflecting anatomical realism that can be integrated into simulation codes. ¹⁵ However, the geometric fidelity is dependent on voxel size, and the simulations are computationally inefficient, especially for organ shapes readjustment. In BREP modeling, tissues can be characterized using boundary surfaces, such as non-uniform rational B-splines (NURBS) or polygon mesh surfaces. As in the case of voxel-based CSG, the data can be extracted from CT images by contouring organ surfaces followed by modeling to end up with smooth and continuous boundaries. The BREP representation better reflects anatomical realism compared to CSG, given that it can model complex anatomical features using an extended set of operation tools.

Although BREP models provide improved realism compared to previous modeling techniques, the corresponding models are still static. Therefore, a number of additional parameters have to be included to mimic the reality. There are many reasons behind this as summarized by Neufeld et al. ¹² : -

Slow changes in anatomy during treatment in radiotherapy,

From mathematical to voxel-based to boundary representation models

Computational human phantoms have been developed to realistically model patients’ anatomy and physiology, considering the geometry and structures of organs/tissues, material composition, temporal changes, such as respiratory/cardiac motions, fluid dynamics such as blood flow or contrast perfusion, … etc. ²⁴ Computational phantoms have been extended from simple water-filled slabs and spheres to anthropomorphic models with a realistic representation of the anatomy and material composition. Computational models are typically classified into three main categories: (a) stylized phantoms, (b) voxel phantoms, and (c) boundary representation phantoms (Figure 1).

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Figure 1.

The evolution of computational phantoms from simple macro-bodies to detailed personalized models. Adapted with permission from. ²⁵

The first generation of computational phantoms was constructed for radiation protection purposes in the 1960s. It was primarily composed of simple macrobodies, easily described based on quadratic equations, such as cuboids, cylinders, spheres, ellipsoids, … etc. ²⁶ The first anthropomorphic stylized phantom developed by Fisher and Snyder comprised only three regions (skeleton, lungs, and remainder tissues). ²⁷ Nine years later, they built an improved version of their phantom composed of main organs defined by simple geometric primitives. ²⁸ Along with the technical developments of stylized phantoms, diversities in the target population according to age (from newborn to adult), gender (male/ female), and pregnancy gestation (fetus models)^29–31 were modeled. For a long time, mathematical models served as the de facto standard in radiation protection and dose management. Many upgraded versions of these phantoms have been constructed, such as Adam and Eva, ³² precise head and brain models, ³³ bone and marrow,^34,35 gastrointestinal tract, ³⁶ … etc. Furthermore, to cover anatomical diversities of patient/worker populations, a library of stylized phantoms with different statures has been devised. ³⁷ 4D stylized phantoms representing organ motion were developed based on surface equations, such as superquadratics ³⁸ and non-uniform rational B-splines (NURBS). ³⁹ Mathematical models have the advantages of easy manipulation of shape and size adjustment or motion simulation. ⁴⁰ However, this design lacks anatomical realism as the model represents only a crude approximation of organs’ shape and position. In addition, the definition of heterogenous tissue composition in macrobodies is not possible.

Through the advent of tomographic medical imaging modalities, such as CT and MRI, the visualization of the human anatomy in three-dimensions was made feasible. Medical images consist of small elements called pixels in 2D and voxels in 3D representing tissue information. To construct a 3D computational phantom, a label is assigned to each voxel according to the anatomical region (i.e. liver, brain, bone, … etc.) and tissue characteristics (material composition and density) obtained from medical images (i.e. CT or MRI). The segmentation of organs and tissues from medical images is traditionally performed manually, a labor-intensive and time-consuming process. Although voxel phantoms provided significant anatomical realism compared to stylized models, they suffer from limitations attributed to the finite voxel resolution of structural images (in the order of millimeters) and the inherent nature of voxel element geometry (uneven steps). In fact, tomographic images are not capable of representing fine structures in micrometer dimensions, such as the skin, eye lens, and epithelial tissue in the digestive tract. As a result, the anatomical fidelity of the developed model depends on voxel size, and most existing voxel models involve some level of assumptions about the anatomical structures. Furthermore, CT images that are mostly used as reference structural images do not generally represent soft-tissue contrast and typically cover only part of the body (not total-body images).

A number of reference anthropomorphic voxel phantoms have been developed mostly based on CT images. These reference models were first developed for the adult male model and later extended to the adult female, pediatric, and pregnant phantoms. In the late 1980s, Zankl et al. constructed voxel computational models using CT images of healthy patients that eventually ended up in 12-phantoms family representing different ages, gender, and size.^41–43 In 1994, a head-torso voxel model, referred to as the VoxelMan was developed from CT images to support imaging physics research in nuclear medicine. ⁴⁴ In 2000, the VIP-Man phantom was developed by Xu et al. as the first model constructed based on color photographic images of a cadaver. ⁴⁵ In 2002, the dose Calculation task group of the International Commission on Radiological Protection (ICRP) Committee launched a project focusing on the development of a set of standard voxel phantoms to be released to the public as the ICRP reference phantoms (adult male and female). ⁴⁶ Bolch et al. created a series of pediatric reference phantoms from newborn to 15-year-old teenager. ⁴⁷ As the most recent developed pediatric family phantoms, ICRP publication 143 describes the development of a series of 10 computational models composed of male and female newborn, 1 year, 5 years, 10 years, and 15 years old phantoms. ⁴⁸

Computational models based on boundary representation techniques were introduced as a new computational model generation taking advantage of both mathematical and voxel-based models. BREP phantoms are able to represent realistic anatomy of the human body while benefiting from the advantages of mathematical phantoms in modeling the deformations. Surface-based models, such as non-uniform rational B-splines and polygon mesh models, are subcategories of BREP modeling. These advanced surface models are capable of realistically representing the anatomical structures while enabling the simulation of anatomical deformation (posture and involuntary organ motion) by providing a rich set of mathematical operation tools. In surface-based designs, the transformations can be simply applied to the surfaces or vertex points to morph the object.

In the BREP or hybrid approach, voxel data are combined with stylized modeling techniques to design a computational phantom that benefits the advantages of both voxel models in representing the anatomical realism and stylized phantoms in providing the flexibility for anatomical variations. ⁴⁹ A series of reference phantoms (adult and pediatric) in hybrid format has been developed by the University of Florida.^50–52 A series of hybrid pregnant female phantoms at the end of three gestational periods has been developed by Xu et al., ⁵³ whereas a family of Iranian BREP phantoms (adult male/female and pregnant reference phantoms) has been developed at Ferdowsi University of Mashhad^54–56 as illustrated in Figure 2. The Virtual Family, a series of surface-based computational phantoms, has been developed based on high-resolution MR images.^10,11 A polygon surface phantom at Hanyang University in Korea extended from the reference voxel model of VKH-Man was also designed. ⁵⁷ Recently, mesh-type ICRP reference adult phantoms, which account for surface-based counterparts of the voxel-type ICRP reference phantoms, have also been developed.^58,59

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Figure 2.

The reference BREP Iranian computational phantoms. Left panel: Male/female adult reference computational phantoms. Right-top panel: The segmented structural/anatomical details and, Right-bottom panel: The reference pregnant phantom with fetus model at three gestation periods. Courtesy of Dr Miri and Dr Rafat, Ferdowsi University of Mashhad.

Extensions of reference phantoms

Libraries of computational human phantoms

Reference phantoms are constructed according to the anatomical characteristics of a single subject considering anthropomorphic data of the average population, therefore lacking inter-subject anatomical variability. The diversity of anthropometric parameters between individuals raises the demand for building patient-specific computational phantoms. Although personalized phantoms are deemed to represent the ideal digital twins, there are some limitations associated with the construction of individualized phantoms. This includes the lack of high-resolution tomographic images for specific patients and the time-consuming procedures for organ/tissue segmentation. In this regard, habitus-specific phantom series created based upon the deformation of a reference phantom assembling different anatomical variables for population-based assessments have been introduced. Deformation algorithms have been typically developed based on morphing the tissues considering hyper-elastic soft-tissue and stiff joints. Some interactive tools enabling topological morphing and interpolation of tissues, such as tissue growth (analogous to thermal expansion), to construct a habitus-variable computational population from a reference model have been developed. A number of studies reported on size-adjustable phantoms representing the variability of anatomical and anthropomorphic parameters, such as body size, organ volume/shape, … etc. Johnson et al. ⁷⁰ extended the UF hybrid adult phantoms to 25 habitus-specific computational phantoms. Na et al. ¹⁹ reported on the construction of a library of adult phantoms (weight-specific) extended from the RPI reference models using an automated deformation algorithm implemented on polygon mesh surfaces. In addition, a number of obese phantoms and a set of age-dependent Chinese computational models in mesh format have been developed based on the RPI reference phantoms to examine the effect of obesity on CT dosimetry.^71,72 Broggio et al. ⁷³ constructed 25 adult phantoms to cover the diversity of heights and weights in the adult male population. Lloyd et al. ⁷⁴ developed a non-rigid deformation algorithm to extend the population of the Virtual Family phantoms using biomechanical finite element methods. Geyer et al. ⁷⁵ extended the UF phantom family to height/weight-specific phantoms. A Korean library of voxel phantoms has been developed to represent different body shapes and sizes. ⁷⁶ More recently, Akhavanallaf et al. ⁶⁵ developed an automated algorithm to construct a comprehensive library of phantoms extended from voxel-based ICRP reference phantoms. Choi et al. ⁷⁷ extended a body-size dependent family of adult phantoms based on mesh-type ICRP reference phantoms. Hoseinian et al.^78–80 created a comprehensive series of BREP whole-body phantoms covering statistical diversities of the Iranian population (Figure 3). Beside the development of total-body phantom families, Erickson et al. ⁸¹ established a database of realistic virtual breast models based on breast computed tomography images.

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Figure 3.

Series of adult computational phantoms (males and females) developed based on CT images of healthy Iranian population. The distribution of anthropomorphic indices, height and weight (top panel), along with the structural details of the developed computational models (left-bottom panel) are shown. As an example, the anatomical deviations of the thyroid gland in this population is illustrated (right-bottom panel). Courtesy of Dr Miri and Dr Rafat, Ferdowsi University of Iran.

Advances in computational models

Recent advances in computational phantoms design focused on two main aspects: first, realistic representation of patient-specific anatomy; and second, upgrade of reference phantoms by adding small (micrometer-scale) or complex anatomical structures. The anatomical fidelity of the developed computational phantoms depends strongly on the voxel resolution of the reference tomographic images. Current imaging technologies are not capable of representing complex or fine structures, such as bone marrow, eye lens, alimentary tract structures, … etc., in micrometer-scale. In this context, Yeom et al. from Hanyang University developed mesh type ICRP phantoms extended from the reference ICRP voxel models through preserving the original anatomical structures. Complex structures of the gastrointestinal system have been improved and the fine structures of the alimentary and respiratory tracts and lung airways were added (Figure 4).^82,83 In a recent study, mesh-type skeletal systems for pediatric population and detailed eye models for children and adolescents of the ICRP reference phantoms were developed in a fine-structure.^84,85 Abadi et al. ⁸⁶ elaborated on the lung architecture of the XCAT series by modeling the airways and pulmonary vasculature. MIDA is a detailed head and neck model (over 160 structures) constructed from a series of high-resolution multimodal MR sequences. ⁸⁷ In parallel, advanced functionalized anatomical models have been developed. ¹²

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Figure 4.

Adult male and female mesh-type ICRP reference computational phantoms. Micron-scale radiosensitive regions of major organs and tissues are visualized on the left and right sides of the phantoms. Reprinted with permission from. ⁸⁸

Toward the 4th-generation patient-specific digital twins, semi-automatic segmentation techniques based on texture patterns or manual delineation along with deformable registration algorithms have been traditionally employed. In state-of-the-art approaches, this process was labor-intensive and time-consuming which limited the construction of patient-specific computational models. ⁸⁹ Recently Carter et al. proposed to use deformable registration techniques to create individualized phantoms to better support patient-specific dosimetry. ⁹⁰ Thanks to recent advances in artificial intelligence algorithms, fully automated segmentation of medical images became feasible. In this field, machine learning and deep learning techniques proved to serve as useful techniques to generate patient-specific phantoms. Deep learning algorithms demonstrated their capabilities in image segmentation^91–95 and image registration^91,96 that can be integrated into the workflow for the construction of patient-specific computational phantoms for diagnostic and radiotherapy risk assessment purposes.^97,98 In 2019, Xie et al. ⁹⁹ constructed patient-specific pregnant phantoms by means of deep learning anchor organ segmentation and used them as input for Monte Carlo organ dose calculations. As illustrated in Figure 5, the generated patient-specific phantoms were utilized to estimate fetal exposure from abdominal CT examinations.

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Figure 5.

Illustration of the deep learning pipeline used to automatically generate pregnant computational phantoms.

Peng et al. ⁹² used deep learning techniques to automatically segment CT images and combined it with accelerated Monte Carlo simulations to calculate patient-specific radiation dose to make the implementation of the proposed approach in clinical setting feasible. They claimed that the proposed patient-specific phantom constructed based on automatic segmentation is prone to much less error compared with the selection of a computational phantom from available libraries. Recently Fu et al. ⁹¹ developed a unified pipeline to create personalized computational models from radiological images. The proposed pipeline is composed of three main steps: first, some anchor organs were segmented from CT images using deep learning algorithms; second, the best-matching reference phantom was selected from a template phantom library using parametrized template matching approach; and third, a deformable registration between CT images merged with anchor organ masks and the selected reference phantom was carried out. They registered patient images to one of the phantoms selected from the XCAT library (Figure 6).

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Figure 6.

The pipeline for automated construction of personalized computational phantoms. Reprinted with permission from. ⁹¹