Deformable torso phantoms of Chinese adults for personalized anatomy modelling

Abstract

In recent years, there has been increasing demand for personalized anatomy modelling for medical and industrial applications, such as ergonomics device development, clinical radiological exposure simulation, biomechanics analysis, and 3D animation character design. In this study, we constructed deformable torso phantoms that can be deformed to match the personal anatomy of Chinese male and female adults. The phantoms were created based on a training set of 79 trunk computed tomography (CT) images (41 males and 38 females) from normal Chinese subjects. Major torso organs were segmented from the CT images, and the statistical shape model (SSM) approach was used to learn the inter‐subject anatomical variations. To match the personal anatomy, the phantoms were registered to individual body surface scans or medical images using the active shape model method. The constructed SSM demonstrated anatomical variations in body height, fat quantity, respiratory status, organ geometry, male muscle size, and female breast size. The masses of the deformed phantom organs were consistent with Chinese population organ mass ranges. To validate the performance of personal anatomy modelling, the phantoms were registered to the body surface scan and CT images. The registration accuracy measured from 22 test CT images showed a median Dice coefficient over 0.85, a median volume recovery coefficient (RC _vlm) between 0.85 and 1.1, and a median averaged surface distance (ASD) < 1.5 mm. We hope these phantoms can serve as computational tools for personalized anatomy modelling for the research community.

Introduction

Digital human phantoms are widely used in anatomy‐based medical simulations, anatomy education, and industrial design. As analysed in several reviews (Zaidi & Xu, 2007; Zaidi & Tsui, 2009; Xu, 2014), a new direction of digital human phantom research is to model individual human anatomy, which is the basic requirement of person‐specific applications, such as clinical radiological dose calculation (Alziar & Bonniaud, 2009; Divoli et al. 2009; Marcatili et al. 2015; Momennezhad et al. 2016), electromagnetic exposure evaluation (Conil et al. 2008; Wu et al. 2011; Li et al. 2017), patient‐specific biomechanics simulation (Bijar et al. 2016; Miller, 2016; Wittek et al. 2016), anatomy education (Blum et al. 2012), and animation character design (Ali‐Hamadi et al. 2013). Hereafter we will first briefly review the history of digital human phantoms and the state‐of‐the‐art of personal anatomy modelling and then propose our idea of deformable human phantoms that can match individual human anatomy based on statistical learning from a large training set of real‐subject computed tomography (CT) images.

The earliest digital human phantoms were the ‘stylized phantoms’ composed of simple geometric primitives of spheres, cylinders, and slabs (ICRP, 1959). Later, more anatomically realistic phantoms were constructed by segmenting medical images [CT or magnetic resonance (MR)] of the reference human subjects (Gibbs et al. 1984; Williams et al. 1986). Beginning in the 1990s, visible human project (VHP) datasets were generated in several countries (Ackerman, 1998; Zhang et al. 2004; Park et al. 2006) using cryosectioning images of human cadavers, leading to the creation of a series of highly detailed phantoms, including the VIP‐man, voxel‐man, Chinese adult anatomical models, and the VHK‐man (Schiemann et al. 2000; Xu et al. 2000; Sang et al. 2008; Wu et al. 2011). In the 21st century, more phantoms were constructed using boundary representation (BREP), e.g. non‐uniform rational B‐spline surface (NURBS) or polygonal meshes. Due to the convenience of modelling shape deformation, BREP was used to adjust the organ shape and size of existing phantoms to match the reference anthropometry values (e.g. body weight, height, and organ volumes), resulting in the ‘reference human phantoms’ of average anthropometry parameters, such as the RPI‐AM/AF phantoms (Zhang et al. 2009), FASH/MASH phantoms (Cassola et al. 2010; Kramer et al. 2010), and the PSRK‐man for Koreans (Kim et al. 2011).

Later, to meet the requirements of population‐orientated simulation, anatomical phantoms representing different percentiles of height, weight, and body mass index (BMI) were created from multi‐subject medical images or by adapting the anatomy of existing reference human phantoms. The Foundation for Research on Information Technologies in Society (IT'IS) in Zurich, Switzerland used MR images of volunteers to create a ‘virtual family’ (Christ et al. 2010) and ‘virtual population’ library (Gosselin et al. 2014) of different genders, ages, heights, and weights. The RPI‐AM/AF phantoms were adjusted to create phantoms of different BMIs (Ding et al. 2012) and different breast cup sizes (Hegenbart et al. 2008). Farah et al. (2010) from IRSN of France also constructed 34 female torso phantoms of different chest girths and breast cup sizes. The FASH/MASH phantoms were deformed to create adult and paediatric phantoms matching different percentiles of heights and weights (Cassola et al. 2011). The 4D XCAT phantoms (Stabin et al. 2012) were also adapted to create phantoms of adults, children, and pregnant females according to reference organ mass values (ICRP, 2002). The University of Florida (UF) group created a library of UF family phantoms (Geyer et al. 2014) by segmenting CT and MR images of adults, children, and newborns, followed by the adjustment of organ meshes to match the reference organ masses. Segars et al. (2013) morphed the 4D XCAT phantoms to match CT datasets of 58 adults and 10 children (Li et al. 2008; Segars & Tsui, 2009). Broggio et al. (2011) from IRSN of France selected 25 representative body surface scans from the CAESAR database (Robinette et al. 2002) and fit the internal organs into each body surface by adjusting the organ sizes according to the literature equations.

As reflected from the above history, a trend in digital human phantom development is to model increasingly specific anatomical subtypes, ultimately for the individual person. To realize individualized anatomy modelling, some studies have constructed deformable phantoms to match individual human anatomy. The concept of the deformable phantom was proposed during the early development of BREP phantoms. A well‐known example is the 4D NURBS‐based cardiac‐torso (NCAT) phantom developed by Segars et al. (2001). By deforming the NUBS surface of torso anatomy, this phantom models respiration motion and heart beating and also emulates inter‐subject variations in body height, chest measurements, diaphragm position, heart size, position, and orientation. Based on a similar strategy, Segars et al. (2010) later developed the 4D extended cardiac‐torso (XCAT) phantom of the entire body, including more structures and finer timing resolution of cardiac/respiratory motions than the NCAT phantoms. Na et al. (2010) at the Rensselaer Polytechnic Institute (RPI) developed deformable adult human phantoms that can adapt the body height, weight, and organ volumes. Their adaptation of phantom anatomy was realized by adjusting the organ meshes of the RPI‐AM/AF phantoms (Zhang et al. 2009) to match the anthropometry values of different population percentiles.

For personalized anatomy modelling, a limitation of the existing deformable phantoms is that they model inter‐subject variations at a relatively coarse level (e.g. body weight, height, and fat quantity). Although the 4D NCAT and XCAT phantoms enable the adjustment of organ size, position, and orientation, they do not model the realistic shape variations between different individuals. Therefore, it is desirable to create deformable phantoms by learning realistic anatomical variations from a large training set of real‐subject medical images.

The objective of this study was to construct digital human phantoms that can be deformed to match the anatomy of different individuals. To learn realistic inter‐subject anatomical variations, we used the statistical shape modelling (SSM) technique, which has been successfully used for anatomical variation modelling (Heimann & Meinzer, 2009) of human organs (Mofrad et al. 2010) and small animals (Wang et al. 2012, 2015). The training images used in this study include 79 health‐screening positron emission tomography/computed tomography (PET/CT) images from four central hospitals in China. Because the health‐screening images mainly cover the torso region, this study constructs torso phantoms for male and female adults, which are named the DCHT‐M and DCHT‐F (Deformable Chinese Torso Male and Female, respectively) phantoms. To match the deformable torso phantoms with individuals, we used the active shape model (ASM) approach (Heimann & Meinzer, 2009), which was commonly adopted to register SSM with patient data. In this study, individual body surface scan and torso CT image were used as the targets of phantom matching, obtaining the estimation of individual subject trunk anatomy.

Methods

The workflow of phantom construction is illustrated in Fig. 1. The male and female phantoms were constructed using the same workflow.

Figure 1.

The workflow of phantom construction. (A) The low‐dose torso CT images of the training subjects. (B) Surface rendering of the segmented type I organs. (C) The template mesh of the reference human model and the torso region cut from the template. (D) Type I and II organs rendered in different colours. (E) Type I organs registered to the training subjects. (F) Type II organs mapped via the registered type I organs. (G) The constructed phantom.

Data collection

Because it is difficult to recruit a large number of healthy volunteers for CT or MR acquisition, we collected medical images already stored in the hospital database. In past decades, thousands of Chinese people have received PET/CT scans for early cancer screening (Tong, 2016), although most of them were diagnosed as asymptomatic. The PET/CT scans of asymptomatic subjects within the ages of 20–80 and weights of 40–120 kg were collected as the training images of this study. We used only the CT images for phantom construction, leaving the PET images for future metabolism modelling research. Figure 1A shows typical low‐dose CT images of the health‐screening PET/CT scans. We collected 79 PET/CT images of normal Chinese adults from four central hospitals in the northeast, southeast, and central areas of China. Table 1 lists the number of collected images for different genders and ages. All the images cover the body region from the neck to the upper thigh, including the entire pelvis. The CT pixel sizes ranged from 0.59 to 1.37 mm, and the inter‐slice spacing was between 1.25 and 3.00 mm. The CT scanner settings were 100–140 kV for tube potential and 28–298 mA for tube current.

Table 1.

The number of collected images for different genders and ages

Ages	Number of images (total/male/female)
20–29	1/1/0
30–39	16/10/6
40–49	21/9/12
50–59	19/10/9
60–69	19/10/9
70–79	3/1/2
All	79/41/38

Ethics statement

This study was performed under the ethical approval from Dalian University of Technology Ethics Committees. No patient identification information has been used in this research or presented in this paper.

Organ segmentation

Due to the low X‐ray dose used for typical PET/CT acquisition, the CT image contrast only facilitates the segmentation of bones and major trunk organs. All the organ structures were segmented using semi‐automatic methods, followed by the proofreading of a radiologist with over 10 years of working experience.

The whole body, skeleton, and lungs were segmented using the thresholding method, followed by manual correction using the mitk software (Wolf et al. 2005). The segmentation results were further polished by morphological closing and hole‐filling procedures. Based on the whole skeleton segmentation, each individual bone was separated using the interactive graph cuts method (Boykov & Jolly, 2000). The limb bones were excluded, as they are not fully covered by the CT scan. Internal soft organs, including the pericardium, liver, spleen, kidneys, pancreas, aorta, inferior vena cava, and torso cavity, were semi‐automatically segmented using the contour interpolation tool of mitk software. The segmentation of skeletal muscles and subcutaneous fat were constrained between the surfaces of the torso cavity and the skin using thresholding with a manually adjusted threshold for each subject. All the segmented organs were converted into triangular surface meshes (Fig. 1B) using the marching cubes algorithm (Lorensen & Cline, 1987).

Template mesh registration

Due to the imperfect image contrast of low‐dose CT, not all the organs can be segmented from the CT images. We refer to the segmented organs as ‘type I organs’ and the unsegmented organs as ‘type II organs’. To compensate for the missing type II organs, a 3D template model of complete human anatomy (Fig. 1C) was registered to each training subject. The template models for the male and female were purchased from the TurboSquid web store (Turbosquid, 2017), from which the torso structures of both genders were cut out (Fig. 1C). Table 2 lists all the anatomical structures contained in the torso region. The meshes of type I template organs (Fig. 1D) were registered to the segmented organs using the robust point matching (RPM) method (Chui & Rangarajan, 2003). Afterwards, the meshes of type II template organs were mapped to the individual subjects via thin‐plate‐spline (TPS) interpolation method. The control points (P _C) of the TPS interpolation were selected as the type I organ vertices within 10 mm to the type II organ surfaces. After the template registration, the motion vectors of the control points (V _C) were calculated as the difference between their registered positions (${\tilde{P}}_{\mathrm{C}}$) and the original positions (i.e. $V_{\mathrm{C}}={\tilde{P}}_{\mathrm{C}}-P_{\mathrm{C}}$). From V _C, we interpolated the motion vectors (V _II) for all the type II organ vertices (P _II), using the TPS interpolation method (Bookstein, 1996), and then obtained the mapped positions of the type II organ vertices as ${\tilde{P}}_{\mathrm{II}}=P_{\mathrm{II}}+V_{\mathrm{II}}$.

Table 2.

List of organ structures included in the phantom (type I organs are marked with bold and italic font)

Organ system	Included structures/organs
Musculoskeletal	Skin, skeletal muscles, psoas major, diaphragm; Individual bones (24 vertebrae, 12 ribs, clavicles, scapulae, sternum, pelvis, sacrum, intervertebral disc)
Cardiovascular	Heart (pericardium, left and right ventricles, left and right atriums, mitral valve, tricuspid, cardiac vein, coronary artery) Main aorta, vena cava
Respiratory	Lungs, trachea, bronchus
Digestive	Liver, hepatic ligaments, gallbladder, bile duct, esophagus, stomach, pancreas, large and small intestines
Immune	Spleen, Thymus
Renal/Urinary	Kidneys and adrenal, ureter prostate, bladder
Reproductive	Urethra Male: testis, penis, seminiferous duct Female: uterus, ovary, fallopian tube, mammary gland, vagina
Adipose	Subcutaneous fat, abdominal fat

For the registration of type I organs, the RPM method sometimes generates unsatisfactory results for complex‐shaped organs (e.g. the vertebrae). We developed a marker‐based version of the RPM method for these difficult cases. A user interface was programmed for manually specifying an arbitrary number of landmark pairs on the two meshes to be registered. Each landmark is duplicated n _d times and added to the point cloud being registered. In this way, the RPM method simultaneously matches the mesh vertices and the landmarks. The parameter n _d serves as a weighting factor for the landmarks. It should be large enough to guide correct registration and small enough to tolerate potential user bias. An empirical value of n _d = 10 was used in this study, which yielded visually correct registration and an averaged surface distance (i.e. the average distance between the closest vertices of the two meshes) below 0.1 mm. To ensure the proper registration of individual vertebrae, six landmarks were specified for each vertebra at the vertebra body centre, the two superior articular facets, the two transverse costal facets, and the tip of the spinous process. Figure 1E demonstrates the typical template registration results of type I organs. Figure 1F shows the mapped type II organs together with the registered type I organs.

Construction of the statistical shape model

As a result of the template mesh registration, each vertex of the template mesh were mapped to the corresponding anatomical locations of different training subjects. The registered template meshes were used to represent the organ shapes of individual training subjects, so that different subjects have the same number of mesh vertices. The inter‐subject anatomical variations were modelled as the changes in corresponding mesh vertex coordinates between the training subjects. The statistical shape model (SSM) method was used to construct the deformable phantoms (Fig. 1F). Prior to the construction of the SSMs, the generalized Procrustes analysis (GPA) (Bookstein, 1996) should be applied to remove the inter‐subject differences of translation, rotation, and scaling, such that only the shape difference remains. Unlike the conventional GPA method, we did not remove the scaling differences because body size variation is an important feature of human anatomy.

After the GPA step, the 3D vertex coordinates of all the registered template organs were concatenated to form the shape vector of each training subject. Let ${\mathrm{X}}_i=\left(x_{i,1},y_{i,1},z_{i,1},x_{i,2},y_{i,2},z_{i,2},\dots ,x_{i,N},y_{i,N},z_{i,N}\right)$ be the shape vector of the ith training subject, where (x _i,j , y _i,j , z _i,j) denotes the 3D coordinate of the jth vertex of the subject i. N is the total vertex number of all the organs in the template mesh, which is 363 916 and 43 539 for the male and female phantoms, respectively. Because both the vertex number N and the order of vertices in the shape vector were inherited from the original template mesh, every training subject had the same number of elements (i.e. 3N) and the same order of vertex arrangement in the shape vector.

Principal component analysis (PCA) was applied to construct the SSM based on the shape vectors. First, mean shape vector $\overline{\mathbf{X}}$ of all the training subjects was calculated, and the shape vector of each training subject was centralized by subtracting $\overline{\mathbf{X}}$ from X _i, i.e. $\widetilde{{\mathrm{X}}_{\mathrm{i}}}={\mathrm{X}}_{\mathrm{i}}-\overline{\mathrm{X}}$, where ${\tilde{X}}_i$ was the centralized shape vector. Let $\mathbf{Q}=[{\tilde{X}}_1,{\tilde{X}}_2\dots ,{\tilde{X}}_k]$ be the matrix containing the shape vectors of k training subjects and each subject corresponds to one column of Q. The size of Q was 3N × k, where k ≪ 3N, as the number of training subjects was much less than the number of template mesh vertices. The value of k was 41 and 38 for the male and female phantoms, respectively. Conventionally, PCA performs eigendecomposition of the covariance matrix QQ ^T, but in our study the size of QQ ^T (3N × 3N) was too large for a direct eigendecomposition. Instead, we performed eigendecomposition of Q ^T Q (size k × k) and then left‐multiplied Q by the resultant eigenvectors to obtain the same eigenvectors as direct eigendecomposition of QQ ^T.

The resulting eigenvectors {${\mathrm{\varnothing }}_i$} represent the modes of shape variation, and the eigenvalues {λ_i} are the corresponding variances of different modes. In this paper, we will frequently use the term ‘mode’ to represent the eigenvectors and use ‘mode i’ to represent ${\mathrm{\varnothing }}_i$. The shape variation modes are ordered by their variances (i.e. λ₁ ≥ λ₂ ··· ≥ λ_n) such that mode 1 corresponds to the largest variance, mode 2 corresponds to the second largest variance, and so on. The variance percentage ratio of mode i is computed as $100\%\times {\lambda }_i/({\sum }_{j=1}^n{\lambda }_j)$.

The SSM was represented as the mean shape vector plus the linear combinations of different shape variation modes (Heimann & Meinzer, 2009):

$$\mathbf{X}=\overline{\mathbf{X}}+\sum _{i=1}^n{a}_i{\mathrm{\varnothing }}_i,$$

where X is a shape instance generated by the SSM represented as a shape vector (x ₁, y ₁, z ₁, x ₂, y ₂, z ₂, …, x _k, y _k, z _k)^T containing the 3D coordinates of k mesh vertices, $\overline{\mathbf{X}}$ is the mean shape vector of all training subjects, {${\mathrm{\varnothing }}_i$} is the shape variation modes obtained via PCA based on the shape vectors of all training subjects, and {a _i} is the shape coefficient serving as the weight of the variation modes. Different values of {a _i} will result in different instances of torso anatomy.

Because the phantom shape is controlled by the real‐valued coefficients {a _i}, it is possible to generate infinite numbers of shape instances of the population by adjusting the coefficient values. When the coefficient values are adjusted continuously, one can observe continuous deformation of the phantom. This is why the phantoms are called ‘deformable’. The phantom deformation can be achieved in real‐time, as the computation is trivial for modern personal desktop computers.

Personalized anatomy modelling

By adjusting the SSM shape coefficients {a _i}, the phantom can be registered to the medial image (e.g. CT and MR) or body surface scan data of an individual person. The registered phantom provides the model of entire torso anatomy which is useful for personalized medical treatment, electromagnetic simulation, ergonomics device design, animation character creation, etc. To realize phantom registration, we used the point set registration approach to match the phantom vertices with the point set of an individual person. For the surface scan data, the individual point set was acquired by scanning the external body surface using a 3D surface scanner. For the medical images, the individual point set included the surface points of the high‐contrast organs, which were segmented using the semi‐automated method described in the Organ segmentation section. The marching cubes algorithm (Lorensen & Cline, 1987) was used to extract the organ surface points from the segmented regions.

The phantom registration included two steps: an initial rigid alignment of the SSM mean shape and a subsequent deformable registration of the SSM. The iterative closest point registration (ICP) strategy (Besl & McKay, 1992) was used in both steps. In each iteration of ICP, the closest target points to the phantom vertices were searched, and a spatial transform T was computed to bring the phantom vertices closer to the searched target points. For the initial alignment, T was a rigid transform composed of 3D translation and rotation. For the deformable registration, T included not only the rigid components but also an isotropic scaling factor and a nonlinear shape deformation controlled by the SSM shape coefficients {a _i}. The optimal values of the rigid components, the scaling factor, and the shape coefficients {a _i} were computed using the ASM approach (Heimann & Meinzer, 2009).

Results

We conducted two types of experiments: a free deformation test and a personalized anatomy modelling test. The free deformation test deformed the phantoms by freely adjusting each shape coefficient {a _i} to observe the anatomical meaning of each variation mode (i.e. each eigenvector of the SSM). The masses of the freely deformed phantom organs were compared with the reference organ masses of the Chinese population to verify whether the deforming organs remain in a plausible mass range. The personalized anatomy modelling test registered the phantoms with individual Chinese subjects to quantify the accuracy of personal anatomy modelling.

Free deformation test

To observe the anatomical variation of each mode, we separately adjusted each shape coefficient a _i while keeping the other coefficients at zero. The value of each a _i was adjusted in the range of $[-3\sqrt{{\mathrm{\lambda }}_i},3\sqrt{{\mathrm{\lambda }}_i}]$, which is the plausible deformation range commonly used in the literature.

Figure 2 shows the anatomical variations corresponding to the two largest variation modes of both genders. The two largest modes were related to global‐scale changes of body height (Fig. 2A) and fat quantity (Fig. 2B). The body height changes corresponded to 34.3 and 31.0% of the total variation for males and females, respectively. The fat quantity changes corresponded to 15.0 and 13.3% of the total variation for males and females, respectively. Notably, mode 2 (i.e. eigenvector ${\mathrm{\varnothing }}_2$) revealed different fat accumulation patterns for different genders. The male phantom showed a change in abdomen girth, especially from the lateral view. In contrast, the female phantom showed a change in subcutaneous fat thickness. This finding coincides with the phenomenon that men are prone to store visceral fat, while women tend to accumulate subcutaneous fat (Lovejoy & Sainsbury, 2009; O'Sullivan, 2009). This gender‐specific fat accumulation pattern was not modelled by previous human phantoms.

Figure 2.

Variation modes related to the changes of (A) body height and (B) fat amount. For each mode, the deformed phantoms corresponding to different ai values are rendered. In the top row, the phantoms are rendered with semi‐transparent skin and muscles to illustrate internal organs; In the bottom row, the phantoms are rendered with opaque skin to demonstrate outer body shape. The variance percentage ratio of each mode is marked besides the mode name.

Figure 3 demonstrates the variation modes for internal organs. As the phantoms of both genders have similar variation patterns, we only show the results of the male phantom. Figure 3A demonstrates the internal organ deformation related to the respiratory process, including the change in lung volume, the rotation of ribs, and the motion of abdominal organs. These variations are reflected from mode 3 of DCHT‐M and mode 4 of DCHT‐F, corresponding to 7.7 and 6.5% of the total variation for each gender, respectively. We can see that the thoracic and abdominal organs all move in accordance with each other. During the inhalation process, the bottom of the lungs expands behind the back of the liver. Meanwhile, the liver and kidneys are pushed downwards. At first glance, it seems unreasonable that the SSM can learn respiratory motions, as all the training subjects were holding their breath during the CT acquisition. However, because different subjects were holding their breath at different levels, the SSM learned the variation in breath‐holding levels, resulting in a deformation pattern similar to respiratory motion.

Figure 3.

Variation modes of (A) respiratory motion and (B) abdominal organ geometry.

Figure 3B shows the variations in abdominal organ positions, orientations, and shapes. These variations are found in mode 7 of DCHT‐M and mode 4 of DCHT‐F, corresponding to 3.2 and 6.5% of the total variation in the male and female phantoms, respectively. It can be observed that when the left kidney moves downwards, the spleen also moves in the same direction. Similarly, when the liver becomes smaller, the right kidney moves upwards to stay close to the bottom of the liver. Such synchronized motions and deformations between adjacent abdominal organs are essential for precise modelling of personal abdominal anatomy.

Figure 4 displays the gender‐specific variations, including the changes in male muscle size and female breast size, which are 1.8 and 4.2% of the total variation for the male and female phantoms, respectively. Mode 10 of the male phantom reveals the muscle size variation (Fig. 4A). We can observe the increase in the latissimus dorsi and pectoralis major as a ₁₀ decreases from $3\sqrt{{\mathrm{\lambda }}_{10}}\text{to}-3\sqrt{{\mathrm{\lambda }}_{10}}$. For the female phantom, the variation in breast size is presented by mode 6 (Fig. 4B). Notably, the growth in breast size and increments of the waist girth are correlated. This is a natural phenomenon, as female subjects tend to grow both breast size and subcutaneous fat in order to rear children. It should be mentioned that the size changes in male muscle and female breast are not very visually significant because the training set does not include particularly muscular males or big‐breasted females.

Figure 4.

Gender‐specific variation of (A) male muscle size and (B) female breast size.

Summarizing the above observations, SSM successfully learned several principal modes reflecting realistic inter‐subject anatomical variations. There are still some modes without an obvious anatomical explanation. SSM is a mathematical method; without taking account of anatomical knowledge, it cannot guarantee that every mode has actual anatomical meaning. Nevertheless, for the purpose of personalized anatomical modelling, all modes contribute to the phantom registration whether or not they have apparent anatomical meaning.

To evaluate how well the organ masses of the DCHT‐M/F phantoms agree with large population statistics, we compared the organ masses of the DCHT‐M/F phantoms with the statistics of Chinese organ masses in the IAEA 1998 publication (Kawamura et al. 1998), which is based on over 20 000 Chinese subjects (age > 20 years) collected from 1950 to 1990. The z‐score was used to measure the deviation of the phantom from the population mean value:

$$z=(x-\mathrm{\mu }/\mathrm{\sigma })$$

where x is the organ mass of the phantom, μ is the mean of the population, and σ is the standard deviation of the population. To estimate the phantom organ mass, we multiplied the phantom organ volume by the reference organ densities in the literature (ICRP, 2009). Because the organ volumes change with the value of a _i, we varied a _i of each mode within the range $[-3\sqrt{{\mathrm{\lambda }}_i},3\sqrt{{\mathrm{\lambda }}_i}]$ (i = 1,2,3) and computed the corresponding z‐score ranges. The results are plotted in Fig. 5. We plotted only the first three variation modes, which accounted for 50.0 and 57.3% of the total variation for males and females, respectively. The other modes have much narrower z‐score ranges than the first three modes and therefore are not plotted in order to retain figure clarity.

Figure 5.

The z ‐scores comparing the phantom organ masses with the reference values from a large population survey (IAEA 1998). Different variation modes of the phantoms are plotted with different colours. The circles mark the z‐scores of a _i  = 0 (i.e. the mean shape of the phantom). The error bars mark the z‐score ranges for a _i∈$[-3\sqrt{{\mathrm{\lambda }}_i},3\sqrt{{\mathrm{\lambda }}_i}]$. The z‐score levels of 1.96 and −1.96 (which correspond to P‐value 0.05) are plotted as horizontal lines.

In this test, a normal distribution of population statistics was assumed. Therefore, if the z‐score value falls out of the range [−1.96, 1.96], the probability that the phantom organ mass belongs to the population distribution is <5% (P < 0.05). As shown in Fig. 5, the mean shapes (a _i = 0) of all of the soft organs and bone parts had z‐scores within the range of −1.96 to 1.96 (i.e. P > 0.05), and more than half of them fell between −1 and 1 (corresponding to P > 0.32). When the shape coefficients varied between $[-3\sqrt{{\mathrm{\lambda }}_i},3\sqrt{{\mathrm{\lambda }}_i}]$, the z‐score ranges of most organs remained within −1.96 to 1.96. These results imply a reasonable agreement between the phantom organ masses and the population statistics data. It can also be observed that the phantoms slightly overestimated the masses of the kidneys, sternum, and sacrum, and underestimated the masses of the heart, pancreas, and clavicles. One possible reason for this difference is that the phantom training set is much smaller than the large population samples, and potential bias may exist in our small sample set. If more training data are used, less bias can be expected.

Personalized anatomy modelling test

We tested the ability of the phantoms to model individual anatomy by deforming them to match personal body surface scans or torso CT images of different individual subjects. Figure 6A illustrates the phantom registration results with the surface point clouds of a male and a female subject. The male surface data were acquired for one of the authors (aged 25 years) using a hand‐held 3D surface scanner to simulate the application of animation character design from the real‐subject surface scan. The female surface data were created using the human zbuilder software (Human‐zBuilder, 2017) to mimic an old woman in an intra‐operative surgery situation. As shown in Fig. 6A, despite the interference of the shirt on the male surface and the loose skin of the female surface, the registered phantoms were properly matched to both subjects, giving an estimation of internal organ structures. Because the surface scan data do not include internal organs, it is impossible to quantify the accuracy of organ estimation. The surface data registration experiment only proves the feasibility of internal organ estimation based on outer body shape. Quantitative assessment of internal organ accuracy is given by the following CT‐based registration experiment.

Figure 6.

Personalized anatomy modelling results. (A) Phantom registration with body surface scan. (B) Phantom registration with CT images. The results are displayed as organ contours overlaid onto representative sagittal and coronal slices of the target CT images. The top and bottom rows show the results for male and female subjects, respectively. The left and right columns show thin and fat subjects, respectively. (C) Box plots of organ registration accuracy of the 22 test CT images as measured by Dice, RC _vlm and ASD, respectively.

For the CT‐based experiment, the phantoms were registered to 22 CT images of healthy subjects not included in the training images, including 13 males (ages between 31 and 88 years and body weights between 51 and 93 kg) and nine females (ages between 35 and 77 years and body weights between 41 and 60 kg). The acquisition protocol of the test CT images is the same as that described in section Data collection above. To provide ground truth organ regions, major trunk organs (including skin, whole skeleton, lungs, whole heart, liver, spleen, and kidneys) were segmented from the torso CT images by a human expert, and the surface meshes of these organs were extracted using the marching cubes method. The purpose of this experiment was to evaluate the performance of the phantoms for modelling complete torso anatomy given the boundaries of a few high‐contrast organs.

Figure 6B shows the registration results for four representative test subjects of different genders and body fat quantities. The registered phantoms are displayed as coloured contours overlaid on the target CT images. Different coronal and sagittal sections of the torso are displayed to give complete observation of the registration results. For most major organs, the registered phantoms were well‐matched, with minor inconsistency of the organ edges. For quantitative evaluation of the CT‐registration results, the registration accuracy was measured via three metrics: the Dice coefficient (Dice), recovery coefficient of organ volume (RC_vlm), and averaged surface distance (ASD):

$$\text{Dice}=2\frac{\left|{\mathrm{R}}_{\mathrm{P}}\cap {\mathrm{R}}_{\mathrm{T}}\right|}{\left|{\mathrm{R}}_{\mathrm{P}}\right|+\left|{\mathrm{R}}_{\mathrm{T}}\right|},$$

$$\mathrm{R}{\mathrm{C}}_{\mathrm{vlm}}=\frac{\left|{\mathrm{R}}_{\mathrm{P}}\right|}{\left|{\mathrm{R}}_{\mathrm{T}}\right|},$$

$$\text{ASD}=\frac{1}{2}\left(\frac{1}{n_{\mathrm{P}}}\sum _{i=0}^{n_{\mathrm{P}}}{d}_i^{P\to T}+\frac{1}{n_{\mathrm{T}}}\sum _{j=0}^{n_{\mathrm{T}}}{d}_j^{T\to P}\right),$$

where the Dice coefficient measures the overlapping ratio between the registered phantom organ region (R_P) and the target subject organ region (R_I); |·| is the region volume; ∩ denotes the overlapping parts of two regions; RC_vlm measures the ratio of the registered phantom organ volume over the target subject organ volume; ASD measures the averaged surface distance between the surface of registered phantom organ and the surface of target subject organ; n _P and n _T stand for the number of surface mesh vertices in the phantom organ and test subject organ, respectively; $d_i^{P\to T}$ is the minimum distance from the i ^th vertex of the phantom organ to the surface of the target subject organ; and $d_j^{T\to P}$ is the minimum distance from j ^th vertex of the target subject organ to the surface of the phantom organ.

Figure 6C reports the results of Dice, RC_vlm, and ASD for the 22 test CT images. Because the skeleton and skin of the target subjects include limbs, whereas the phantom does not, it is unreasonable to evaluate Dice and RC_vlm for the skeleton and body region. Therefore, the skeleton and body region (skin) only show the ASD results. Figure 6C shows that most organs have a median Dice > 0.9, a median RC_vlm between 0.85 and 1.5, and a median ASD below 1.5 mm. The heart and kidneys have RC_vlm values almost equal to 1, indicating good volume estimations for these organs. The ASDs of all organs are between 1 and 1.5 mm, which is roughly the pixel size of the training images for constructing the phantoms, meaning that the accuracy of anatomical modelling is limited by the spatial resolution of the training images.

Discussion

Phantom construction

To collect enough training images of normal subjects, we chose the health‐screening PET/CT images as the training data. Due to the low X‐ray dose used for PET/CT acquisition, only major trunk organs and bones could be segmented from the CT images. Ideally, we should use medical images with better soft‐tissue contrast, such as diagnostic CT, contrast‐enhanced CT or MRI images. However, these images are generally acquired for local diseased organs and we are trying to collect enough diagnostic CT images covering the entire torso with minimal gross organ defects. To compensate for the missing organs, we morphed a 3D template of complete anatomy to each training subject using the already segmented organs as the matching target. Similarly, Segars et al. (2013) also morphed their XCAT phantoms to CT images to create a phantom library. Such morphing takes advantage of the anatomical dependency between the segmented and unsegmented organs, yielding a reasonable estimation of the missing anatomy. It should be noted that Segars et al. used a smooth invertible transformation (i.e. the multichannel large deformation diffeomorphic mapping), whereas we used the thin‐plate‐spline (TPS) transform to map the unsegmented organs. Although the purposes were similar, Segars's method produced smoother organ deformation but was much slower than ours (6–8 h vs. a few minutes for each training subject). Nevertheless, we will consider learning from Segars et al. and use diffeomorphic transforms in future research because better phantom quality deserves the additional construction time.

To construct the phantoms, two requisite steps are the semi‐automatic organ segmentation and the marker‐based template registration. These two steps are the most time‐consuming and labour‐intensive parts of the workflow. We used a semi‐automated approach because it allows the radiologist to proofread and correct the segmentation results. To speed up the processing of more training data, an automatic organ segmentation method with less labour‐intensive proofreading must be developed. We can learn from recent methods (Wang et al. 2016).

Personalized anatomy modelling

By registering the deformable phantoms with individual test subjects, we demonstrate the feasibility of using the deformable phantom to model individual torso anatomy based on body surface data or torso CT images. Compared with many existing organ segmentation methods, a benefit of deformable phantom registration is the estimation of all torso organs, including those that cannot be segmented from CT images, e.g. cardiac chambers, skeletal muscles, and renal vessels. This feature is important for simulation applications that do not require accurate organ segmentation but demand good estimation of organ volume and comprehensive modelling of all internal structures (Divoli et al. 2009). Moreover, the results of deformable phantom registration also provide close initialization for subsequent organ segmentation, which is not our current research scope but will be investigated in a future study.

The CT‐registration experiment gives quantitative results of each organ's registration accuracy. The heart seems to be the most accurate organ, with median values for Dice, RC_vlm, and ASD of 0.92, 1.06, and 1.16 mm, respectively. The heart also has compact distributions of the three metrics, meaning that the registration of the heart is stably accurate for all test subjects. The high and stable accuracy of the heart is attributed to its spherical shape and stable position. Spherical shapes are easy to overlap, and a stable anatomical position ensures consistent registration accuracy. The kidneys also have high median Dice values (0.90 and 0.91 for the left and right kidneys, respectively), low median ASD values (1.08 and 1.05 mm for the left and right kidneys, respectively), and median RC_vlm values close to 1 (1.01 and 0.99 for the left and right kidneys, respectively) thanks to the spherical shape of the kidneys. However, the Dice and ASD distributions of the kidneys are not quite compact. This is because the positions of kidneys are rather variable (see Fig. 3B), making the registration accuracy less stable for different subjects. The spleen has a curved shape that is difficult to overlap completely; therefore, the median Dice (0.84) and ASD (1.27 mm) values were relatively lower. The anatomical position of the spleen is also quite variable (see Fig. 3B), leading to non‐compact accuracy distributions. The lungs and liver are large organs that are easy to overlap, resulting in moderate median Dice (0.87 and 0.88, respectively) and RC_vlm (0.90 and 0.91, respectively) values. However, due to their large sizes, the shape variations always occur on a large scale, resulting in relatively large ASDs (1.37 and 1.39 mm, respectively).

This study did not validate the registration accuracy of type II organs (e.g. the pancreas and gallbladder) because the radiologist could not generate reliable ground truth segmentation for these organs from the low‐dose CT images. We will keep collecting enough high‐contrast diagnostic CT images to validate these organs in future studies. However, for the small organs such as the pancreas and gallbladder, we do not expect as good a registration accuracy as for the large organs (e.g. the heart, liver, and lungs), as their shapes and locations vary noticeably even for the same person at different time points. Our objective is to obtain a reasonable estimation of their volumes.

A limitation of the current phantoms is that the SSM shape coefficients {a _i} do not correspond to intuitive anthropometry parameters such as body height, weight, and breast size. It is not feasible manually to adjust the phantom shape according to desired anthropometrical values. To solve this problem, we tried to use the method of Brett et al. (2003), which recombines SSM modes of human body surfaces to generate deformation modes related to body weight and heights. However, this method was not effective because our model includes many more organs than a single body surface. We still need to develop a more effective method to correlate the phantom deformation with intuitive anthropometrical changes. As different medical applications require different anatomical parameters, it might be appropriate to correlate the phantom deformation with application‐specific parameters, such as bone length for orthopaedics research or lung volume for respiratory simulations.

Comparison with existing deformable human phantoms

As introduced at the beginning of this paper, there are several existing deformable human phantoms incorporating intra‐ and inter‐subject anatomical variations, including the 4D NCAT torso phantom, the 4D XCAT whole‐body phantom, and the RPI deformable adult phantoms. To date, all the existing deformable phantoms have been constructed for Caucasians; we have modelled the anatomical variations of Chinese subjects for the first time. A common feature of the DCHT‐M/F phantoms and the existing deformable phantoms is the use of BREP. The RPI and DCHT‐M/F phantoms both use triangular meshes, whereas the 4D XCAT phantom uses NURBS for large organs (e.g. the liver) and sub‐division (SD) meshes for fine‐detail structures (e.g. the cerebral cortex). Compared with the triangular meshes, NURBS is more efficient for modelling large organs, while the SD mesh is smoother for representing small‐scale structures. For future improvement of the DCHT‐M/F phantoms, we will consider learning from the XCAT phantoms to use the combination of NURBS and SD meshes.

Regarding the modelling of anatomical variations, the RPI deformable phantom adapts organ volumes according to reference anthropometry values from the publications of ICRP‐89 (ICRP, 2002) and NHANES (McDowell et al. 2005); it does not include realistic variation in organ shapes. The XCAT phantoms incorporate actual‐subject respiratory and cardiac motions from gated CT images, but these motions are only for local organs rather than the whole torso range. The XCAT phantom also allows the user to adapt anatomical parameters of body height, chest measurements, diaphragm position, heart size position, and orientation to simulate inter‐subject variations, but these variations are not learned from real patient data. Our DCHT‐M/F phantoms use the SSM approach to determine realistic inter‐subject anatomical variations, including but not restricted to the changes in body height, weight, respiratory status, internal organ geometry, torso posture, male muscle size, and female breast size. No existing deformable phantom has incorporated all these variations. The training set of the DCHT‐M/F phantoms is also larger than any existing deformable phantom or phantom library. The DCHT‐M/F phantoms do not include a beating heart and therefore cannot be used to simulate dynamic cardiac imaging like the XCAT phantoms.

In terms of the modelled body range, both the XCAT and RPI deformable phantoms are for the entire body, whereas the DCHT‐M/F phantoms are for the torso. Just like the extension from NCAT to XCAT, we also plan to extend the current torso phantoms to the whole‐body range. We may learn from the strategy used by Segars et al. (2013) for extending the XCAT phantom to a phantom library. They added pseudo limbs and a head to the patient CT data and morphed the XCAT phantoms to match each individual patient. To do so, anthropometry data for Chinese limbs and heads must be obtained first.

Conclusion

In this study, deformable phantoms of Chinese adult males and females were constructed based on 79 segmented CT images of normal subjects. The SSM approach was used to learn anatomically meaningful inter‐subject variation. The evaluation results demonstrate the capability of phantoms to model personalized anatomy. Future improvements of the phantom can be achieved by using more training subjects or more advanced shape modelling methods. In particular, as we are still collecting more PET/CT data, our future studies could explore sub‐population modelling for different ages or country areas, which will hopefully lead to more meaningful results. To achieve these goals, automated methods for image segmentation and template registration must be specifically developed for low‐dose CT images to tackle the heavy burden of data processing.