Development of an Interactive Software Application to Model Patient Populations in the 4D NURBS-Based Cardiac Torso Phantom

W. Paul Segars', David S. Lalush'.*, and Benjamin M. W. Tsui'.2 'Department of Biomedical Engineering and 'Department of Radiology

The University of North Carolina at Chapel Hill, Chapel Hill, NC

Abstruct The 4D NURBS-based Cardiac Torso (NCAT) phantom

was developed to provide a realistic and flexible computerized torso phantom to be used in medical imaging research. The organ shapes in the NURBS-based phantom are modeled with non-uniform rational b-splines or NURBS surfaces using the Visible Human CT data set as the basis for the formation of the surfaces. Since it is based on human data, the phantom has the ability to model organ shape and anatomical variations more realistically than phantoms based on simple geometric primitives. To this point, the NCAT phantom has been limited to simulating variations upon the anatomy of the Visible Male. We extend the abilities of the phantom to include simulation of female patients. Two breast models, simulating the prone and supine positions, were developed using 3D NURBS surfaces. As is the case with the other organs of the torso, the NURBS definition of the breasts allows a high degree of flexibility to model anatomical variations. We develop an interactive software application that will allow a user to modify the NURBS surfaces that define the different organs of the NCAT phantom in order to generate male and female patients with varying anatomy. The software application provides 3D and 2D views of the phantom and includes several transformations that can be used to alter the anatomy. It also includes the ability to import patient data from which the user can manipulate the organs of the phantom to match the specific patient anatomy. We conclude that this software application is a useful resource in creating patients with varying anatomy to be used in medical imaging research studies that involve a population of patients.

I . BACKGROUND

The 4D Dynamic MCAT phantom has been under development in our laboratory over the past decade. It is widely used in SPECT imaging research [ 1-61. Recently, the phantom was extended to permit the study of the effects of anatomical variations on cardiac SPECT images [5] and study of gated SPECT [6,7]. The 4D MCAT is based on simple geometric primitives, but uses cut planes, intersections, and overlap to form complex biological shapes. I t has the ability to model both male and female patients. For the female anatomy, the MCAT phantom

includes two models for the breasts simulating the supine and prone positions. For each position, the breasts are modeled as two modified ellipsoids. The phantom also includes the ability to model anatomical variations through modification of the parameters that define the different geometric shapes. With this ability to modify the anatomy, the MCAT program can be used to simulate a patient population involved in patient studies. However, the simplicity of the geometric primitives limits the ability of the MCAT phantom to model the anatomy realistically. Thus, a phantom that will provide a realistic and flexible model of the anatomy must rely on a different set of primitives. A primitive that will permit the kind of modeling needed is the non-uniform rational b-spline (NURBS) [8,9].

The NURBS-based cardiac torso phantom (NCAT) was developed to provide a more realistic version of the 4D MCAT phantom. The phantom was designed using 3D NURBS surfaces to define the different organ shapes [10,11]. NURBS are widely used in computer graphics to mathematically define complex curves or surfaces. Thus, they are capable of modeling the complex biological shapes in the torso. The NURBS surfaces for the organs in the NCAT phantom were formed using the Visible Human CT dataset (National Library of Medicine) as the basis. Since it is based on human data, the NCAT phantom models organ shapes more realistically than the geometry-based MCAT phantom. To this point, the NCAT has been limited to simulating variations upon the male anatomy due to its foundation from the Visible Male dataset. In order to extend the phantom to include female anatomy, breast models must be developed and incorporated with the existing organ models.

Like the 4D MCAT, the NURBS-based phantom includes the ability to model anatomical variations. The NURBS surfaces defining the different organ shapes can be altered easily via affine and other transformations to model anatomical variations. The shape of a NURBS surface can be modified through the control points that define the surface, Fig. 1 . The control points form a convex hull around the NURBS surface and determine its shape. By applying transformations to the control points, the shape of the surface can be modified or sculpted as if it were made of clay [5,6]. Each transformation is performed by simply multiplying the control points Pi,j defining the surface to be altered by the appropriate transformation matrix T as shown in equation 1.

20-5 1 0-7803-6503-8/01/$10.00 2001 IEE

A R

A B Figure 1 : Modification of the shape of a NURBS surface through its control points. (A) Frontal view of a NURBS surface definition for a sphere. The surface is composed of a 9s3 set of control . points (squares) which form a convex hull around the shape of the sphere. (B) Frontal view of the same sphere with its shape altered. Modification to the shape of the sphere is done by manipulating its control points. The shaded control points are translated to the right altering the shape of the sphere in this direction.

The NURBS basis for the phantom not only gives it the ability to realistically model anatomy, but it also offers a great deal of flexibility to model patient motion and anatomical variations. The modification of the control points to reshape a surface, however, can be a cumbersome process depending on the complexity of the desired shape.

We develop an interactive software application that allows easy and efficient modification of the NURBS organ models of the NCAT phantom to model anatomical variations that would be found among a patient population. We also extend the ability of the phantom to model female patients through the development of breast models. The software application allows the input of patient data from which to guide the modification of the surface models. The resulting software application is a usefd resource in compiling a patient population to be used in patient studies.

11. METHODS

A. Development of the Breust Models We developed simple, preliminary models for the breasts

in the prone and supine positions using the 3D NURBS software Rhino3D. Figure 2 shows the process for the development of the prone breast model. Each breast model was defined initially as a simple NURBS ellipsoid, Fig. 2A. The ellipsoid is analytically defined by the following equation

C D Figure 2: Development of the prone breast model in Rhino 3D. (A) The breast model is initially defined as an ellipsoid. (B) The ellipsoid is shaped to form a rounded off half-ellipsoid by translating the 9 highlighted control points inward. (C) The ellipsoid is placed on the NURBS surface for the body by translating and rotating the entire set of control points. (D) Individual control points are transformed manually to sculpt the breast model until it has the desired shape.

with XL, YL, and ZL specifying the radius of each dimension of the ellipsoid. The XL, YL, and ZL parameters were initially set for each breast model based on the parameters defined for that model in the original MCAT phantom. In terms of NURBS, the ellipsoid was defined by a 9x3 matrix of control points. Each ellipsoid model was initially shaped to form a rounded off half-ellipsoid. To do this, the 9 control points at the back end of the ellipsoid were translated inward, Fig. 2B. The breast model was then positioned onto the body surface by translating and rotating the entire set of control points defining it using the Rhino3D software, Fig. 2C. The control points defining the breast surface were then individually manipulated, sculpting the surface until it had the desired shape, Fig. 2D. The breast models for the supine positions were also developed using the technique shown in Figure 2.

B. Development and Application of the Sofmme The software application was written in Visual C++ using

OpenGL to display 3D and 2D views of the phantom. Figure 3 displays the graphical user interface of the software application. The application includes one 3D perspective view of the phantom as well as three 2D slice views (transaxial, coronal, and lateral). It also includes several transformations that can be applied to the control points of the NURBS surfaces defining the different organs of the phantom.

20-52

Table 1 : Priority of the Organs 1 Orean

Body Outline Lungs (left and right)

Liver

Figure 3: Graphical user interface of the phantom development application. Included are 3D (Top Left) and 2D views (Bottom) of the phantom as well as different transformations (Top Right) used to manipulate the NURBS organ models. The application can import patient data from which to guide the modification of the organ models. Sample patient data is shown in the 2D slices along with the outlines of the phantom's organs.

The organ models of the phantom were linked in the software application so that change in one organ affected the neighboring organs. This interaction was setup by two different methods. One method involved prioritizing the interacting surfaces. If a transformation caused one surface to overlap another, the overlap of the interacting surfaces was assigned to the organ of higher priority. The priority of the organs is shown in Table I . The majority of the organ models were setup to interact by this method. The second method was to link the control points of the interacting surfaces. Transformations applied to the control points of one surface were also applied to coinciding control points of neighboring surfaces. The respiratory structures (the lungs, body outline, and ribcage) were setup to interact by this method in order to model respiratory mechanics [6 ] . The linking of the different organ models allowed for efficient manipulation of the anatomy.

To demonstrate the use of the software application, three sets of patient transmission CT data (A-C) were imported into the program. The data included two males and one female of variable anatomy. Information on the three patients is listed in Table 2.

Using the patient data as a guide and the different transformations of the application, the NURBS surfaces for the NCAT phantom were altered to match the each specific patient anatomy creating four different phantoms.

0 122 3

Left Diaphragm Kidneys (left and right)

Stomach

4 5,6

7 Spleen

Sternum Backbone (2 surfaces) Right Ribs - cartilage

(1 0 surfaces) Right Ribs (12 surfaces)

Left Ribs - cartilage (1 0 surfaces)

Left Ribs (12 surfaces) I 44-55 Heart exterior I 56

8 9

10-1 1 12-2 1

22-33 34-43

Left myocardium 59 I Left inner chambers I 60 J

Patient Gender Age A Male 68 B Male 55 C Female 68

Height Weight 6' 190

6'1" 136 5'9.. 187

111. RESULTS

A. Development of the Breast Models Figure 4 shows top and lateral views of the breast models

created in the prone and supine positions. As can be seen in the images, the NURBS breast models are simplistic, but they have the potential to realistically model the female anatomy. More work will be done using patient data to refine the shape of the breast models. The simple breast models are, however, suitable for the demonstration of the software application.

B. Application of the Sofware Figure 5 displays transaxial slices of the original NCAT

phantom. Figure 6 shows the transaxial slices of the male patients (A and B) as well as transaxial slices of the NCAT phantoms modified to fit both of these patients. In order to match the anatomy of both of these patients, the NURBS surfaces defining the diaphragm, the heart, the rib 'cage, lungs, and body outline were modified.

For patient A, the height of the diaphragm in the left and right sections of the body was lowered 10 mm. The heart was translated downward 10 mm and forward 5 mm. The orientation of the heart was also modified by tilting it downward by IO". The antero-posterior, lateral, and

20-53

A 13

A B Figure 4: Surface renderings of the NURBS surfaces for the body and the breasts in the prone (Top) and supine (Bottom) positions. Top (A) and lateral (B) views are shown.

Figure 5: Transaxial slices of the original NCAT phantom (Visible Male).

longitudinal widths of the left and right lungs as well as the rib cage were increased. The antero-posterior and lateral widths of the body outline were decreased. The longitudinal width of the body outline was increased.

Patient B is underweight and of slight build; therefore, for patient B, the antero-posterior and lateral widths of the lefl and right lungs as well as the rib cage and body outline were decreased significantly. The height of the diaphragm in the left section of the body was lowered 10 mm while the height of the right diaphragm was lowered only 2 mm. The size of the heart was scaled by 95% and was translated downward IO mm, forward 5 mm, and laterally towards the right lung by 5 mm.

Figure 7 displays the transaxial slices of the female patient, patient C. Like the process involved with the male patients, fitting the NCAT phantom to the anatomy of the female patient included modification of the NURBS surfaces for the diaphragm, the heart, the rib cage, lungs, and body outline. However, additional modification of the newly developed breast models was also required. For the female patient data, the supine breast models were used and modified.

For, patient C the body outline required only slight modification. The lateral width of the body was decreased slightly as was the antero-posterior width. The right diaphragm was raised by 5 mm while the left diaphragm was

Male (Patient A) Transmission Reconstruction

NCAT Phantom Modified for Patient A

Male (Patient B) Transmission Reconstruction

NCAT Phantom Modified for Patient B Figure 6: Transaxial slices of Patients A and B and the NCAT phantom modified to match the anatomy of the two male patients.

raised by 2 mm. The heart was scaled to 95% and translated downward I O mm and forward 7 mm. The orientation of the heart was changed by tilting it downward by 5 degrees. The breast models were translated downward and inward by 5 mm. The antero-posterior width of the breast models was also decreased.

The total transformation of the phantom in each case took approximately ten to fifteen minutes. From the images in figures 6 and 7, it can be seen that the modified phantom closely models the anatomy of the sample patients.

20-54

IV. CONCLUSIONS

We have developed an interactive software application to model anatomical variations in the 4D NURBS-based cardiac torso phantom. We have also developed preliminary breast models for the NCAT phantom extending its ability to incorporate simulation of female patients. The application allows the user to easily modify the NURBS organ models of the phantom using simple affine transformations applied to the control points of the organ models. The organ models in the phantom are linked so that changes in one organ affect the others. This allows efficient modification of the organ models. Patient data can also be used to guide the modification of the organ models.

Currently, the application requires manual manipulation using different transformations to modify the organ models. Work is now being done to automate the fitting process. In the course of this work, transmission scans of patients were used as input to the application. Future work will include the use .of CT data to generate new phantoms. More work will also be done on the breast models using patient data to refine their shape making them more realistic. Despite the lack of automation, the software application was found to be a fast, efficient way to alter the NCAT anatomy. We conclude that the s o h a r e application is a useful resource in simulating a patient population for use in medical imaging research.

V. REFERENCES

[ I ] P. H. Pretorius, M.A. King, B. M. W. Tsui, K. J. LaCroix, and W. Xia. A mathematical model of motion of the heart for use in generating source and attenuation maps for simulating emission imaging. Med P l y , vol. 26, pp. 2323-2332, Nov 1999.

[2] B M W Tsui, J. A. Terry. and G. T Gullberg, "Evaluation of cardiac cone-beam Single Photon Emission Computed Tomography using observer performance experiments and receiver operating characteristic analysis." Invest Radio/. vol. 28, pp. 1101-1 112. 1993.

131 P. H. Pretorius, W Xia, M. A. King, B M W Tsui. T.-S Pan. and B J . Villegas, -'Determination of left and right ventricular volume and ejection fraction using a mathematical cardiac torso phantom for gated blood pool SPECT." J h'iicl Med, vol. 37, pp 97P, 1996.

Female (Patient C) Transmission Reconstruction

NCAT Phantom Modified for Patient C Figure 7: Transaxial slices of Patient C and the NCAT phantom modified to match the female patient's anatomy.

[4] K. J. LaCroix and B. M. W. Tsui, '-The effect of defect size. location, and contrast on the diagnosis of myocardial defects in SPECT with and without attenuation compensation," J iVtrcl hled, vol. 37, pp. 20P. 1996.

[5] K.J. LaCroix, B. M. W. Tsui, E. C. Frey, R. .I. Jaszczak. "Receiver operating characterisic evaluation of iterative reconstruction with attenuation correction in 99"Tc-Sestamibi myocardial SPECT images.'' J iVticl Med. vol. 41. pp. 502- 5 13,2000.

[6] D. S. Lalush and B.'M. W. Tsui. "Block-iterative techniques for fast 4D reconstruction using a priori motion models in gated cardiac SPECT." Phys Med B i d , vol. 43, pp. 875-887. 1998.

[7] B. M. W. Tsui, W. P. Segars, and D. S. Lalush. "Effects of upward creep and respiratory motion in myocardial SPECT," IEEE Trans. iVuc/. Sci., in press, 2000.

[SI L. Piegl, "On NURBS: A Survey," IEEE Computer Graphics andApplications, vol. 1 I , pp. 55-71. 1991.

[9] L. Piegl and W. Tiller. The NURBS Book, 2"''. Ediiion. Springer-Verlag: Berlin. 1997.

[lo] W. P. Segars, D. S. Lalush. and B. W. iM. Tsui. "A Realistic spline-based dynamic heart phantom," ,-. IEEE Trans. Nucl. Sci., vol. 46, pp. 503-506. 1999.

[ I I ] W. P. Segars. D. S. Lalush, and B.. W. M. Tsui, '-Modeling respiratory mechanics in the MCAT and spline-based MCAT phantoms." .-. IEEE 7inns. !\:ztc/. Sci.. in print 2000.

20-55