FEM Human Body Model with Embedded Respiratory Cycles for Antenna and E&M Simulations

An approximate method to model respiratory motion in a CAD human model subject to electromagnetic (or acoustic, thermal) finite-element analysis is suggested and described. Its concept implies using affine transformations, which are implemented in commercial FEM software packages, in the form of a parametric sweep. This method does not require multiple copies of the CAD model or multiple project files. It enables use of arbitrary sampling times and an automatic reposition of on-body and in-body devices. The method was applied to the platform-independent full-body electromagnetic computational model Visible Human Project® (VHP)-Female v. 3.1. Examples of scattering calculations and antenna modeling are provided.

Diaphragm motion. Respiration is chiefly driven by the diaphragm with primary motion in the superior-inferior direction; total travel is estimated as 10-30 mm during quiet breathing [1]. Other studies report 20 ± 7.0 mm average [2]. A simplified 1D diaphragm motion, x(t), is non-harmonic, and the exhalation portion dominates the inhalation. Given the exhalation at origin, one has where A is the corresponding amplitude [3,4]. Furthermore, the respiratory motion often exhibits hysteresis in space, with an amplitude on the order of 2-4 mm [1]. Adjacent tissues. Closely adjacent structures (i.e., liver, etc.) show comparable motion amplitudes. Furthermore, the following motion amplitudes have been observed (cf. a review in Ref. [1]): • Motion with an average amplitude of 12 mm in the lung for targets not attached to rigid structures • 1-25 mm superior-inferior motion of the kidneys, 13 mm superior-inferior motion of the spleen, 2-8 mm motion of the heart (the heart motion is mostly a simple rigid-body translation [5,6]), and 1-7 mm motion of the trachea • 13 mm superior-inferior motion of the spleen   2 Respiratory motion captured via MRI retrospective gating and averaging over multiple cycles, after [2]. The green contour indicates lung volume at maximum exhalation Thoracic cage kinematics. During respiration, the ribs rotate about an axis through their costal necks to affect the anteroposterior and transverse diameters of the thoracic cavity as shown in Fig. 18.3 [5,7].
CAD B-Spline modeling. Modeling of the breathing cycle to date has been mostly performed via deformable NURBS surfaces (B-splines) for the lungs and surrounding tissues. The changes the phantoms undergo are then typically splined over time to create time continuous 4D respiratory models [5,8,9], which indeed utilize free-form deformations.
Challenges of FEM CAD Modeling. Commercial FEM codes do not operate with B-spline surfaces but rather with triangulated surfaces and tetrahedral/hexahedral volumes. This is in particular valid for most frequency-domain electromagnetics solvers such as ANSYS EM Suite/Maxell 3D and CST Microwave Studio. Therefore, a freeform breathing sequence has to be ultimately converted to a (large) discrete series of separate (full-body) triangulated CAD models, even if the original data were in the form of parametric B-splines. Generally, a conversion from NURBS surfaces to FEM triangular surfaces requires very significant additional meshing times.
The size of one detailed FEM full-body model is quite large (about 200-1000 Mbytes in ANSYS) and a computation with 20-30 such models would be a significant challenge from several points of view. For example, a user will need to create, run, and then post-process a number of large distinct project files, each of which must replicate his/her own excitation setup (e.g., a coil, an antenna, or a radar) and employ a new human model. Furthermore, manual repositioning is necessary for any and all on-body and in-body devices at every step, which would potentially create errors.

Methods
Built-in affine transformations. A commercial CEM package typically includes a set of nine affine transformations: Three translations (in the x, y, z directions) Three rotations (about the x, y, z axes) Three directional scaling transformations (along the x, y, z axes) applicable to any object (including a triangular tissue mesh) or to a group of objects and in the form of a parametric sweep. These transformations can be performed in  [5,7]. The ribs rotate about an axis through their costal neck either global or local coordinate systems. The user can initialize a discrete generic global variable, x n , n = 0,…,N, define object geometry parameters as certain unique functions of x n , and then move, rotate, or deform every object of a multi-object structure independently within the framework of the same project file.
Our approach. We apply built-in parameterized affine transformations to construct breathing cycles (quiet, deep, shallow) using only one base full-body human model [10] source not found and using only one project file. Along with the base static human CAD model, this project file includes a parametric sweep or sweeps modeling deformations of involved tissues. Such an approach is not exact, but it may have sufficient accuracy when the parametric sweep is carefully designed. It will allow us to employ any temporal resolution, which is impossible with discrete models. To construct an anatomically relevant breathing cycle, we will try to follow the anatomical data collected from Refs. [1][2][3][4][5][6][7][8][9] as close as possible.
Challenges. To design an FEM-compatible and anatomically justified multitissue affine parametric sweep, a very extensive preprocessing of the static human CAD model is necessary, which is a significant undertaking.

Selecting a Sweeping Variable
The natural sweeping variable x n is proportional to the diaphragm motion. Since the breathing cycle is periodic, only one period T must be considered. According to Eq. (18.1), physical time, t, is expressed through a sweep variable by This result can be programmed in MATLAB as E = 11; t_=0:E; T = 1; t = T * (pi/2-acos((t_/E).^0.25))/pi; plot(t_, t, '- * '); grid on. Sweeping variable x n runs from zero to N = 11 in 12 uniform steps. Its zero value corresponds to maximum exhalation; its maximum value of 11 corresponds to maximum inhalation. Higher N values can be considered for a better accuracy.

Static CAD Model
As a base human model at maximum exhalation, we will choose the VHP-Female v.3.1 CAD model (http://www.nevaem.com/) shown in Fig. 18.4. The source data for this model was provided by the National Library of Medicine's Visible Human Project in the form of full color cryosection images. These images were hand segmented and registered in a global coordinate frame. The model has 26 individual tissues, 270 individual tissue parts, major blood vessels and peripheral nerves, and a superior resolution in the spinal cord/cranium. All tissue structures are manifold shells and no shell intersects with any neighboring shell. The sweep for the respiratory motion will be implemented for both BASE and SMOOTH sub-models. Only the results for the BASE sub-model will be reported here.
The subject is a ~60-year-old white female with a height h of 162 cm measured from top of the scalp to the average center of both heels. The body mass M, computed using standard tissue densities [11] and assigning the average body shell, which includes internal tissues, the density of muscle, is ~88 kg. The computed BMI is ~33.5 (moderately obese). The subject has a heart pathology.

Respiratory Cycle and CAD Tissues Affected by Respiration Motion
The overall change in lung volume is set at 0.32 L, which is close to a normal-toshallow breathing sequence for this subject. Default temporal resolution includes 12 discrete uniform steps from 0 to 11 in steps of 1 from maximum exhalation to These objects are transformed so that there are no intersections between any of them at any time moment, with the minimum deformation factors. These transformations are to be performed in global or local coordinate systems.

Required Accuracy: Total Body Mass
Since the respiratory motion modeled with multiple deformed CAD objects is an approximation, a requirement should be made with regard to the total mass error. We will require that the maximum relative body mass variation shall not exceed 0.1% during the entire respiratory cycle.

Algorithm
Below, we briefly review suggested kinematics and dynamics for the individual tissues. All quantitative approximations and the final formulas are thoroughly described in Appendix A.
Lung dynamics This is the first deformation step described in detail in Appendix A. In a local coordinate system associated with the top of the lung, the lung is deformed in all three directions and is moved in one direction in order to guarantee the expected diaphragm movement of 20 mm and simultaneously the volume change of 0.32 L, while maintaining anatomically sound overall deformations.
Thoracic cage kinematics This is the second deformation step. Since the rotation axes in Fig. 18.3 are very loosely defined for the actual anatomical data, we have rotated each rib pair about a fixed axis passing through the heads of two ribs (the end parts closest to the spine). We have also rotated slightly the rib pairs about the vertical axis. Thus, every rib pair is subject to rotation about two axes. All permissible variations of rotation angles have been tested, for every rib pair, in order to satisfy two criteria: (i) avoid intersections with the lung and (ii) stay as close to the lung as possible.
Sternum/cartilage dynamics This is the next deformation step. The sternum is subject to a translation motion, without rotation. Fixed control points on its surface are introduced. Those control points, along with the rib tips, form lines, along which the corresponding cartilage parts will further be deformed (moved and expanded).

Muscles dynamics
In this case, we apply rotations, movements, and slight deformations. The goal is to minimize overall movement while avoiding intersections with the thoracic cage.
Heart kinematics The heart is moved in two respective directions without rotations and deformations. The cardiac cycle is not considered.
Liver/stomach kinematics Liver and stomach are moved in two respective directions and are slightly deformed; see Appendix A.

Outer full-body shells
This is the only case where we cannot apply affine transformations. However, we may apply Boolean operations with the tissue CAD objects. A number of deformed chests objects are created internally, and then they are united with the otherwise static full-body shells. This operation requires greater care since we have two very closely spaced (1 mm) body shells.

Polynomial Interpolation
After a discrete set of affine transformations has been established, this set was converted to polynomials applicable to any temporal resolution and reported in Appendix A. The polynomial approximations have been independently tested with a fine grid. As an example, Table 18.2 reports affine polynomial approximations for several muscles. Note that the dynamic variable t in Table 18.1 is not the actual time, but is proportional to the diaphragm motion x(t) in Eq. (18.1).

Results
The corresponding full-body VHP-Female model with the embedded respiratory motion in the form of a parametric sweep described in Appendix A has been independently realized in The maximum body mass variation during the entire respiratory cycle is 80 g, which is less than 0.1% of the total body mass. The parametric sweep may be adjusted/modified at any time in response to further anatomical evaluations and customer needs.

RF Test at 300 MHz
The problem geometry is shown in Fig. 18.5. An incident plane wave at 300 MHz has a horizontal polarization. The simulations have been performed in ANSYS HFSS with three adaptive mesh refinement passes and with the final meshes approaching 1 M tetrahedra. Figure 18.5 shows the near-field results at three observation points given a 1 V/m incident wave. The scattered field is plotted. In the illuminated zone, the co-pol near field data may vary by about 3% due to the respiratory motion. In the

Near field
shadow zone, the corresponding variation is negligibly small. Cross-polarization components may exhibit considerably larger relative near-field variations.

Muscle Deformation Sequence (Pectoralis Major, Pectoralis Minor, Abdominal Muscles, and Erector Spinae)
New local coordinate systems: A local coordinate system is defined for each muscle using a simple translation. The origins are located at (min(Px), max (Py), max (Pz)) with P being

Heart Deformation Sequence
New local coordinate systems: According to literature, the pumping motion of the heart is independent of breathing. As a result, the heart object will only be transformed to avoid intersection with lungs in breathing sequence, with respect to the origin of the global coordinate system (0, 0, 0). See Tables 18.A15 and 18.A16

Liver Deformation Sequence
New local coordinate systems: The liver object is deformed to avoid intersection with lungs in breathing sequence, with respect to the origin of a local coordinate system: (0, max (Py), max (Pz)). See Tables 18.A17, 18.A18, and 18.A19

Skin Shell Deformation
First, the skin shell deformation starts with a generation of N chest objects for each step via non-rigid transformations. This process was accomplished in MATLAB. A deformed chest region is defined as : . mm , m m P All nodes in the chest region of the skin shell are selected and transformed in the y-direction using the following equation: We chose nodes in the chest region so that P(:, 3) − min (P(:, 3)) goes from 180 to 0. Therefore, nodes that are closer to the upper and lower boundaries of the region will move less than the nodes that are closer to the center. With maximum inhalation, the center node of the chest region will move by 10 mm in the Y direction. Thus, only coordinates of nodes belonging to the chest area are changed. Also, the connectivity matrix, t, of the entire skin shell still remains the same. As a result, 11 skin shell objects with different chest regions will be generated. Second, these new skin shells are subtracted from the original skin shell in HFSS, which results in N smaller deformed chest objects. These chest objects are spaced evenly (400 mm in Y direction) in front of the original shell and then united. A moving box is carefully designed so that it covers only one chest object at any time instant t. Then, the intersection is performed. The process is illustrated in Fig. 18.A1.
Box original position is given by: −300mm, (200 − t * 400) * 10 −3 , − 350mm. An intersection operation is performed with the box and the chest array object, which results in one chest object for a particular time t. Finally, the chest object is moved and a unite operation is performed with the original skin shell (shown in Fig. 18.A2).

Fig. 18.A1
A box is carefully designed so that each iteration covers only one chest object at a time Open Access This chapter is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as 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 images or other third party material in this chapter are included in the chapter's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the chapter's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.