Development of a 4D Digital Mouse Phantom for Molecular Imaging Research

W. Paul Segars1, Benjamin M. W. Tsui1, Eric C. Frey1, G. Allan Johnson2, and Stuart S. Berr3

1Department of Radiology, Johns Hopkins University, Baltimore, MD, 2Duke Center for In Vivo Microscopy, Duke University, Durham, NC, and 3Departments of Radiology and Biomedical Engineering, University of Virginia, Charlottesville, VA

Abstract

We develop a realistic and flexible 4D digital mouse phantom and investigate its usefulness in molecular imaging research. The organ shapes are modeled with non-uniform rational b-spline (NURBS) surfaces, which are widely used in 3D computer graphics. High-resolution 3D magnetic resonance microscopy (MRM) data obtained from the Duke Center for In Vivo Microscopy was used as the basis for the formation of the surfaces. With its basis upon actual imaging data and the inherent flexibility of the NURBS primitives, the phantom models organ shapes realistically while maintaining the flexibility to model anatomical variations and involuntary motions such as the cardiac and respiratory motions. These motions were modeled using a gated black-blood magnetic resonance imaging (bb-MRI) dataset of a normal mouse as the basis for the cardiac model and respiratory-gated MRI and known respiratory mechanics as the basis for the respiratory model, using images obtained from the University of Virginia. In each case, the time-changing 3D surfaces are defined by a set of time curves to create time continuous dynamic or 4D NURBS surface models. We demonstrate the usefulness of the mouse phantom in initial simulation studies in single photon emission computed tomography (SPECT) and x-ray computed tomography (CT). We conclude that NURBS are an efficient and flexible way to accurately describe the anatomy and cardiac and respiratory motions for a realistic 4D digital mouse phantom. The phantom provides a unique and useful tool in molecular imaging research, especially in the development of new imaging instrumentation, image acquisition strategies, and image processing and reconstruction methods.

I. INTRODUCTION The rapid growth in genetics and molecular biology

combined with the development of techniques for genetically engineering small animals has led to increased interest in in vivo small animal imaging. With the rise of small animal imaging, new instrumentation, data acquisition strategies, and image processing and reconstruction techniques are being developed and researched. A major challenge is how to evaluate the results of these new developments. One method from which to evaluate and improve medical imaging devices and image processing techniques is through the use of simulation studies. Simulation techniques are finding an increasingly important role in medical imaging research. They

___________________________ Address correspondence to: William Paul Segars, PhD, Department of Radiology, Division of Medical Imaging Physics, Johns Hopkins University, 601 N. Caroline St., Baltimore, MD 21287-0859. E-mail: wsegars@jhmi.edu.

have become an important and indispensable complement to theoretical derivations, experimental methods, and clinical studies in medical imaging research and development. An important aspect of simulation is to have a realistic phantom or model of the subject’s anatomy and physiological functions from which imaging data can be generated using accurate models of the imaging process. The advantage in using such phantoms in simulation studies is that the exact anatomy and physiological functions are known, thus providing a gold standard or “truth” from which to evaluate and improve imaging devices, data acquisition techniques and image processing and reconstruction methods.

Much research has been done in creating digital human phantoms for medical imaging research. Existing computerized phantoms can be divided into two general classes: voxelized and mathematical phantoms. Voxelized phantoms1,2 are generally based on patient data and are thus fixed to a particular anatomy and resolution. Study of the effects of anatomical variations can be very limited, and generation of the phantom at other resolutions requires interpolation, which induces error. Mathematical phantoms3-5 on the other hand, are based on simple geometric primitives. They can allow for anatomical variation and generation at multiple resolutions. Mathematical phantoms can be made reasonably realistic, but the simplicity of the mathematical equations limits exact modeling of the organ shapes. Current developments are aimed at computer phantoms that are flexible while maintaining an accurate representation of anatomy and physiology.

One such phantom is the 4D NURBS-based Cardiac-Torso (NCAT) phantom6-8 developed in our laboratory to accurately model the human anatomy and cardiac and respiratory motions. The 4D NCAT phantom is based on state-of-the-art medical imaging data using non-uniform rational B-splines (NURBS) to model the organ shapes. NURBS are widely used in three-dimensional computer graphics to accurately describe complex 3D surfaces. NURBS surfaces are very flexible; they can be altered easily via affine and other transformations to model anatomical variations or patient motion. The particular transformation needs only to be applied to the set of control points. The 4D NCAT thus combines the realism of a voxelized phantom with the flexibility of a mathematical phantom. It provides a more realistic model of the human anatomy and cardiac and respiratory motions without sacrificing any flexibility to model anatomical variations and patient motion.

Currently, there is a lack of realistic computer generated phantoms modeling the mouse anatomy and physiological functions for use in molecular imaging research. We apply the same methods and techniques used to develop the 4D NCAT phantom to the creation of a new 4D digital mouse phantom.

The mouse phantom will provide a valuable tool for use in molecular imaging research. We demonstrate the utility of the phantom in pilot SPECT and x-ray CT simulation studies.

II. METHODS

A. Modeling the 3D Mouse Anatomy A 256x256x1024 3D magnetic resonance microscopy

(MRM) dataset of a normal 16 week old male C57BL/6 mouse was used as the basis for the anatomy of the phantom. The dataset was obtained from G. Allan Johnson of the Duke Center for In Vivo Microscopy, an NIH Resource (P41 05959/ R24 CA 92656). With a resolution of 110 microns over the whole body, this dataset is extremely detailed allowing the creation of realistic models for several different anatomical structures. Fig. 1 shows sample transaxial slices obtained from the MRM dataset.

Models for the different structures were created using the same techniques developed in our laboratory to construct the

4D NCAT phantom6-8. The anatomical structures are manually segmented using the software program SURFdriver10, a surface reconstruction application, to display and define organ contours in the MRM image slices as shown in Fig. 2A. The contours defined in the segmentation process were then used as input to the Rhinoceros NURBS modeling software11. NURBS surfaces were fit to the contours using established methods for generating relatively smooth 3D cubic NURBS surfaces from contours taken from an object12,13. Fig. 2B displays the 3D NURBS surface created for the stomach.

B. Modeling the Cardiac Motion A gated black-blood MRI (bb-MRI)14,15 cardiac data set

(Fig. 3) of a normal 15 week old male C57BL/6 mouse was used to create a 4D beating heart model for the phantom. The study was obtained from Stuart S. Berr of the University of Virginia (UVa) and consisted of twelve time frames over a complete cardiac cycle. At each time frame, the 256x256 short-axis MR images had a pixel size of 0.1 mm x 0.1 mm and a slice thickness of 1 mm. Blood was suppressed in the images causing it to appear dark and the surrounding tissue to appear bright using a double inversion-recovery preparation pulse every other heartbeat15. This technique improves the definition of the endocardial and vessel boundaries in the images as well as reduces the artifacts related to blood flow.

Due to the coarse thickness (1 mm) of the MRI short-axis image slices, these boundaries were difficult to follow accurately using only the short-axis dataset. Therefore, gated long-axis MR images were acquired. Bright-blood long-axis images were acquired from two separate normal mice. Each long-axis dataset consisted of one 0.1 mm x 0.1 mm long-axis slice defined at twelve time frames over the cardiac cycle, Fig. 4. The gated blood pool images were used to gain insight into the normal motion of the atrioventricular (AV) valve plane and the boundaries of the heart throughout the cardiac cycle.

Using the technique described above, 3D NURBS surfaces were created for the principal structures of the heart: the right and left ventricles, atria, and large vessels. SURFdriver was used to display the time-frame short-axis images and define contours for the different structures. As mentioned above,

Figure 1: Sample transaxial slices of the MRM dataset used to create the 3D anatomy for the mouse phantom.

Figure 2: (A) SURFdriver surface reconstruction program. MRM slices (Fig. 1) are segmented using the application by defining organ contours (white). (B) Contours (dashed lines) are used to define smooth 3D cubic NURBS surfaces for the structures using the Rhinoceros application. The above example shows the creation of a 3D NURBS model for the stomach.

Figure 3: One short-axis slice through twelve frames of gated black-blood MRI cardiac data.

special processing had to be done to select contours to define the boundary between the atria and ventricles and to define the apex and base of the heart. The boundaries were selected from the gated long-axis MR datasets and using the known anatomy of the heart as a guide. 3D NURBS surfaces were fit to the contours defining each heart structure at each time frame. The time correspondence between control points defining a surface over the time frames was set up based on the 4D NCAT human heart model. The cardiac twisting motion illustrated in the 4D NCAT cardiac model6-8 was scaled down to fit the smaller heart size of the mouse. Once the twisting motion was established, the radial and longitudinal contractions of the control points could be obtained by noting the epi- and endocardial borders in the gated MRI images. Using this technique, the 3D position of each control point defining a cardiac surface was determined for each time frame. Time curves were then defined for each control point’s position creating a time changing 3D surface or 4D NURBS model for each heart structure.

C. Modeling the Respiratory Motion Respiratory mechanics involve the motions of the

diaphragm, heart, thoracic cage, and lungs16-18. During inspiration, the diaphragm contracts forcing the abdominal contents downward and forward increasing the volume of the thorax, Fig. 5. In addition, the ribs rotate forcing the ribcage outward and upward further increasing the volume of the thoracic cavity, Fig. 6. The lungs inflate with air due to the change in thoracic pressure. During expiration, the opposite movement occurs decreasing the thoracic volume causing the lungs to deflate.

We incorporate these respiratory motions into the digital mouse phantom. The NURBS surfaces that define the respiratory structures in the phantom were altered through manipulation of their control points to simulate respiration.

1. Motions of the Diaphragm, Liver, Heart, Stomach, Spleen, and Kidneys

The diaphragm is defined in the phantom as the top of the liver which encompasses both left and right sections of the

body. The movement of the diaphragm was simulated by simply translating the surface defining the liver (Fig. 7). In addition to moving linearly up and down, the diaphragm was also set to move forward and backward with the changes in the anterior-posterior (AP) diameter of the chest due to the movement of the ribs. This movement was observed in human respiration8. The heart, stomach, spleen, and kidneys were translated with the movement of the diaphragm. In each case the translation was applied to the control points defining the different structures in order to move them.

2. Motion of the Ribcage, Lungs, and Body

Figure 4: One long-axis slice through twelve frames of gated MRI blood pool cardiac data.

Figure 5: Motion of the diaphragm during respiration16. During inspiration, the diaphragm contracts increasing the volume of the thoracic cavity. During expiration, the diaphragm relaxes decreasing the volume of the thoracic cavity. [From J. West, 199516]

Figure 6: Motion of the ribs during respiration16. The ribs rotate outward and upward during inspiration increasing the volume of the thorax. [From J. West, 199516]

Figure 7: Inspiratory motions of the liver (diaphragm), stomach, spleen, heart, and kidneys simulated in the mouse phantom. Expiratory motion was simulated as the reverse of the inspiratory motion.

The ribs in the mouse phantom were rotated about their transverse axes to simulate their respiratory motion (Fig. 8). Each rib must be individually rotated about its transverse axis to simulate its respiratory motion. However, if all the ribs are rotated by the same amount, a difficulty can arise in that some ribs may affect the AP diameter of the chest differently depending on their tilt angle. This complicates the positioning of the sternum, which is connected to the ribs. The rotation of each rib was individually calculated using the expansion of the AP diameter of the chest as follows. The beginning tilt angle θi of each rib was first calculated by (1)

−=

i

yyi L

CTiiarccosθ (1)

where T=(Tx, Ty, Tz) is the coordinate for the tip of the rib, C=(Cx, Cy, Cz) is the coordinate for the tip of the rib’s costal neck, Li is the AP length of the rib, and the x-axis defines the transverse axis of the rib. The tilt angle θi

new that would correspond to the change in the AP diameter of the chest ∆AP was then calculated by (2).

∆+−=

i

zynewi L

APCTii)(

arccosθ (2)

The desired rotation of the rib iRφ about the transverse axis (x-

axis) was calculated by the following equation.

newiiRi

θθφ −= (3)

Each rib was then rotated about the x-axis by the angle iRφ .

As mentioned earlier, NURBS surfaces can be altered easily via affine transformations. The particular transformation needs only to be applied to the set of control points. The rotation of each rib about the x-axis was performed by simply applying a rotation matrix to the control points defining the

rib. Each rib was rotated about the x-axis (Fig. 8) according to the following equation

jiRXrotated

ji i ,, )( PRP φ= (4)

where Pi,j are the control points in homogeneous coordinates (x,y,z,1) defining the rib surface and RX is the 4x4 matrix for the rotation about the x-axis. The rotation matrix RX is defined as

10000cossin00sincos00001

ii

ii

RR

RRX φφ

φφ −=R (5)

The origin for the rotation operation was set to be the tip of the rib’s costal neck (Cx, Cy, Cz), which connects the rib to the backbone.

The NURBS surfaces defining the lungs and body outline in the mouse phantom were set up to expand or contract with changes in the ribcage. The control points defining the lungs were scaled about the lung’s center so as to fill in the cavity formed by the moving ribcage. The control points defining the body were scaled about the backbone so as to comply with changes in the anterior-posterior (AP) diameter of the thoracic cage due to the movement of the ribcage.

The sternum was set up to move with the movement of the ribs. The amount of outward movement was determined by the expansion in the AP diameter of the chest, ∆AP, while the amount of upward movement, ∆Height, was determined by the amount of rotation of the ribs.

3. Time-Motion Curves for the Respiratory Cycle The volume curve16 for the lungs during normal tidal

breathing in a human is shown at the top of Fig. 9. The period of a typical respiratory cycle for normal tidal breathing is 5 seconds with inspiration lasting approximately 40% of the period (2 seconds) and expiration lasting the remaining 60% (3 seconds). The amount of volume change in the lungs for normal breathing in humans is 500 ml.

Using the lung-volume curve for a human, a similar curve was derived for a mouse. The period of the respiratory cycle for normal tidal breathing in a mouse is approximately 0.4 seconds19. It is assumed that inspiration lasts 40% (0.16 s) of the period with expiration lasting the remaining 60% (0.24 s) as is the case for human respiration. The amount of volume change in the lungs for normal tidal breathing in the mouse is ~0.15 ml19. The volume curve for the mouse was approximated with the piecewise cosine function in (6). The top portion of the function represents the volume change in the lungs during inspiration while the bottom portion represents the volume change in the lungs during expiration. A graph of the function is shown at the bottom of Fig. 9.

Figure 8: Respiratory motion of a rib in the mouse phantom. Lateral view showing the rotation of a rib about the transverse axis (x-axis) by φR. The origin of the rotation is the tip of the rib’s costal neck. The rib rotates upward during inspiration increasing the AP diameter of the chest by the amount ∆AP. The lateral diameter of the chest remains unaffected.

≤≤+

−−

≤≤+

−

=ststml

sttmltV

4.016.0075.0)4.0(24.0

cos075.0

16.00075.016.0

cos075.0)(

π

π

(6)

The respiratory motion in the digital mouse phantom was set up to be dependent on two time varying parameters, the change in height of the diaphragm ∆diaphr and the amount of AP chest expansion ∆AP. The height of the diaphragm controls the upward/downward motions of the liver, stomach, spleen, heart, and kidneys while the AP expansion of the chest controls the AP motions of the organs as well as the motion of the ribcage. In order to form a 4D respiratory model, these parameters have to be altered over time to produce a volume change in the lungs that closely resembles that seen at the bottom of Fig. 9.

The height of the diaphragm was set to change a maximum of 1.0mm sinusoidally for normal tidal breathing according to (7). This value was based on respiratory-gated MRI data of a normal adult mouse obtained from UVa. Fig. 10 shows a coronal slice of the data taken at end-inspiration and end-expiration. The change in the height of the diaphragm is indicated by the dotted line. The change in the height of the diaphragm was found to be 1.2mm from the images. In obtaining the respiratory gated images, however, the mouse was under isofluorane/oxygen (1%). This tends to make the mouse gasp making it easier to respiratory gate. The result is a larger diaphram movement. To offset this, the diaphragm was assumed to move slightly less than this amount.

The AP diameter of the chest was assumed to change a maximum of N mm’s sinusoidally as shown in (8). The value for the maximum AP expansion of the chest N will be determined by trial and error as discussed below.

≤≤+

−

≤≤+

=∆ststmm

sttmmtdiaphr

4.016.05.0)4.0(24.0

cos5.0

16.005.016.0

cos5.0)(

π

π

(7)

≤≤+

−−

≤≤+

−

=∆stsNtN

stNtN

tAP

4.016.02

)4.0(24.0

cos2

16.00216.0

cos2)(

π

π (8)

In order to determine the value of N in the motion equations for the mouse phantom, volume measurements of the lungs were made at end-expiration and compared to volume measurements made at end-inspiration in the following manner. The mouse phantom was first generated at end-expiration. At end-expiration (t = 0), the height of the diaphragm is raised by 1 mm (Eq. 7), and the change in the AP diameter of the chest is set at zero (Eq. 8). The liver, left diaphragm, heart, stomach, spleen, and kidneys were raised with the height of the diaphragm. The organs were simply translated upward since the AP motion was set to zero with the AP expansion of the chest (Eq. 8). The mouse phantom was voxelized to a voxel size of 0.1 mm3, and the lung volumes were approximated by counting voxels in the lungs. The phantom was then generated at end-inspiration (t = 0.16s) using different values of N to set the maximum change in the AP diameter of the chest. At end-inspiration, the height of the diaphragm and the longitudinal positions of the liver, stomach, spleen, heart, and kidneys are not changed, but the AP diameter of the chest increases by N mm’s. The ribcage in both phantoms was rotated upward to expand the chest by N mm’s, and the lungs were expanded accordingly. The organs were moved forward with the change in the AP diameter of the chest. The lung volumes in the inspiratory mouse phantom defined at each N value were compared to those from the expiratory phantom in order to approximate the volume change in the lungs. The N parameter was adjusted in each

Figure 10: Respiratory-gated MRI data taken from a normal mouse. One coronal slice is shown at end-expiration and end-inspiration. The movement of the diaphragm during respiration is indicated by the dotted line. The diaphragm moved ~ 1.2mm.

Figure 9: (Top) Change in volume of the lungs during normal tidal breathing in a human (ref). (Bottom) Change in volume in the lungs during normal tidal breathing in a mouse. Volume curve for the mouse was based on the volume curve of the human.

case until the total amount of volume change in the lungs was approximately 0.15 ml, which corresponds to normal tidal breathing in the mouse. The N value that gave the desired volume change was found to be 0.7 mm.

The respiratory time curves for the ∆diaphragm and ∆AP parameters are shown in Fig. 11. The changes in the parameters were spline-interpolated in time to create time continuous 4D respiratory models. This allows the phantom to be defined for any time resolution. The 4D time-motion curves can also be manipulated to alter the motions of the different parameters to produce different breathing patterns. By adjusting the amplitudes of the time-motion curves, heavier or lighter breathing patterns can be simulated. Also, faster or slower breathing patterns can be simulated by altering the period of the time-motion curves.

D. Initial Simulations in SPECT and x-ray CT We simulated small animal SPECT and x-ray CT data from

the newly created mouse phantom to demonstrate its utility in molecular imaging research. Using the mouse phantom software application, we generated pairs of 3D voxelized phantoms that represented average distributions of attenuation coefficients and average radioactivity concentrations in the different organs.

Using the mouse phantom, we simulated a SPECT bone scan. The organs were set to simulate the uptake of Tc-99m Medronate Disodium Phosphate (MDP). The phantom was generated into a 160x160x160 array with a pixel width and slice thickness of 0.15 mm.

Emission projection data was generated from the voxelized phantom using a realistic pinhole SPECT projection model. The projection data matrices were collapsed to 80x80 to simulate sampling. Poisson noise was added to the projection data roughly equivalent to that of a typical animal study. The emission projection data were then reconstructed using the iterative OS-EM reconstruction method. The images were reconstructed into 80x80x80 arrays with a pixel width and slice thickness of 0.3 mm.

For the x-ray CT simulation study, the mouse phantom was voxelized into a 512x512x512 array with a pixel size and slice

thickness of 50 microns. The organs in the phantom were set to model the distribution of attenuation coefficients at 140keV. Cone-beam projection data was simulated from the voxelized phantom using a Feldkamp cone-beam projection algorithm [20]. The projection data were collapsed to simulate sampling and then reconstructed using a Feldkamp cone-beam reconstruction [20] into 256x256x256 arrays with a pixel width and slice thickness of 0.1mm.

In each case, the data simulated from the phantom was compared to actual data obtained from small animal experiments in our laboratory to assess the ability of the phantom to produce realistic molecular imaging data.

III. RESULTS

A. 3D NURBS model of the Mouse Anatomy Fig. 12 displays 3D surface renderings of the digital mouse

phantom. Anterior and lateral views are shown. As can be seen in the images, the NURBS primitives can accurately model the complex organ shapes, providing the basis for a realistic model of the 3D mouse anatomy.

B. 4D NURBS Cardiac Model The top of Fig. 13 displays the cardiac model developed

for the mouse phantom. The epi- and endocardial surfaces are shown for each structure of the heart at end-diastole (ED) and end-systole (ES). Using the time curves defined for each

Figure 12: Anterior (left) and lateral (right) views of the digital mouse phantom.

Figure 11: Parameter curves for the digital mouse phantom over the respiratory cycle. Respiratory parameters are the diaphragm height and AP chest expansion.

surface, thirty time frames were generated from the original twelve base frames. The thirty frames illustrate a smoother contracting and twisting motion of the myocardium as compared to the original twelve time frames. For each of the thirty frames, the volumes and muscle mass of each of the heart chambers were calculated. The volume curves for the ventricles and atria for the thirty frames are shown at the bottom of Fig. 13. The curves follow the normal pattern for the beating heart. The total myocardial mass was found to be conserved within ± 5%.

C. 4D NURBS Respiratory Model The top of Fig. 14 displays the anterior view of the mouse

phantom during end-expiration (left image) and end-inspiration (right image). The bottom of Fig. 14 shows the left lateral view of the phantom during end-expiration and end-inspiration. These images indicate the ability of NURBS surfaces to model respiratory motion realistically. As was done with the heart, thirty time frames were generated from the respiratory phantom. The volume in each lung was then calculated at each frame. Fig. 15 shows the respiratory volume curves for the combined right and left lungs. The curves illustrate a respiratory cycle very similar to that shown in Fig. 9.

D. Initial Simulations in SPECT and x-ray CT The top of Fig. 16 shows reconstructed SPECT images

generated from the phantom simulating the uptake of Tc-99m MDP in a normal mouse without respiratory motion. The bottom of Fig. 16 shows reconstructed SPECT images

obtained from imaging a mouse with the same radiopharmaceutical in our laboratory. Coronal image slices are shown. The top of Fig. 17 shows reconstructed x-ray CT transaxial images simulated using the mouse phantom while the bottom of Fig. 17 shows similar CT images obtained from a live mouse using a microCT system built in our laboratory. In both cases, the simulated images are comparable to those obtained experimentally. This demonstrates the great potential the new 4D mouse phantom has in molecular imaging research. Combined with accurate models of the imaging

Figure 14: (Top) Anterior view of end-expiration (left) and end-inspiration (right) in new mouse phantom. (Bottom) Left lateral view at end-expiration (right) and end-inspiration (left). The dotted line indicates the movement of the diaphragm.

Figure 15: Change in volume curves calculated from the mouse respiratory phantom for the combined right and left lungs. The curve is very similar to that shown in Fig. 9 for normal respiration.

Figure 13: (Top) 3D surface renderings of the epi- and endocardial surfaces of the RV and LV for the new NURBS-based mouse beating heart model at end-diastole and end-systole. (Bottom) Volume curves for the atria and ventricles of the mouse heart phantom.

process, the phantom can be used to produce realistic molecular imaging data from which imaging devices and techniques can be evaluated.

IV. DISCUSSION We have developed a realistic and flexible 4D digital

mouse phantom for use in molecular imaging research. The phantom was based on 4D NURBS and includes a realistic 3D model of the mouse anatomy and accurate 4D models for the cardiac and respiratory motions. The 3D anatomy of the phantom was based on high-resolution MRM data obtained from Duke University. The cardiac motion was developed based on cardiac gated black-blood MRI data from the University of Virginia while the respiratory motion was developed based on respiratory-gated MRI data, also from UVa, and known respiratory mechanics. Each set of data was obtained from a normal, healthy mouse. With its basis upon actual imaging data and the inherent flexibility of the NURBS primitives, the result approaches that of an ideal phantom. The 4D mouse phantom uniquely combines the anatomical realism of a voxelized phantom with the flexibility of a mathematical phantom. It provides a realistic model of the mouse anatomy without sacrificing flexibility in modeling anatomical variations and motion. Used in combination with accurate models of the imaging process, the phantom can be used to produce realistic imaging data to serve as a gold standard or “truth” from which molecular imaging devices and techniques can be evaluated and improved. The usefulness of the mouse phantom was demonstrated in pilot simulation studies in SPECT and x-ray CT. In both cases, the phantom produced imaging data comparable to that obtained from imaging actual mice in our laboratory.

V. CONCLUSIONS We conclude that NURBS are an efficient and flexible

way to describe the anatomy and physiology for a realistic 4D digital mouse phantom. With its realistic model of the mouse anatomy and cardiac and respiratory motions, the phantom provides a unique and useful tool in molecular imaging research. The 4D digital mouse phantom has enormous potential to research new instrumentation, image acquisition strategies, and image processing and reconstruction methods

X-ray CT images simulated using the mouse phantom

X-ray CT images obtained experimentally

Figure 17: (Top) Reconstructed cone-beam x-ray CT images generated from the mouse phantom. (Bottom) Reconstructed cone-beam x-ray CT images obtained from a live mouse using a microCT system developed in our laboratory.

MicroSPECT images simulated from the mouse phantom

MicroSPECT images obtained experimentally

Figure 16: (Top) Reconstructed SPECT coronal images generated from the mouse phantom simulating the uptake of Tc-99m MDP. (Bottom) Coronal SPECT images obtained experimentally from an actual mouse.

in molecular imaging.

VI. ACKNOWLEDGEMENTS Magnetic resonance microscopy (MRM) data used in the

creation of the 3D anatomy of the mouse phantom was acquired at the Duke Center for In Vivo Microscopy, an NIH/NCRR National Resource (P41 05959).

VII. REFERENCES [1] E. J. Hoffman, P. D. Cutler, W. M. Digby, and J. C. Mazziotta,

“3-D phantom to simulate cerebral blood flow and metabolic images for PET,” IEEE Trans Nucl Sci, vol. NS-37, pp. 616-620, 1990.

[2] I. G. Zubal, C. R. Harrell, E. O. Smith, Z. Rattner, G. R. Gindi, and P. B. Hoffer, “Computerized three-dimensional segmented human anatomy,” Med Phys, vol. 21, pp. 299-302, 1994.

[3] 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 Radiol, vol. 28, pp. 1101-1112, 1993.

[4] J. Peter, R. Jaszczak, and R. Coleman, “Composite quadric-based object model for SPECT Monte-Carlo Simulation,” J Nucl Med, vol. 39, pp. 121P, 1998.

[5] 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 Nucl Med, vol. 37, pp. 97P, 1996.

[6] W. P. Segars, D. S. Lalush, and B. M. W. Tsui, “A realistic spline-based dynamic heart phantom,” IEEE Trans. Nucl. Sci., vol. 46, pp. 503-506, 1999.

[7] W. P. Segars, D. S. Lalush, and B. W. M. Tsui, “Modeling respiratory mechanics in the MCAT and spline-based MCAT phantoms,” IEEE Trans. Nucl. Sci., vol. 48, pp. 89-97, 2001.

[8] W. P. Segars. Development of a new dynamic NURBS-based cardiac-torso (NCAT) phantom., PhD dissertation, The University of North Carolina, May 2001.

[9] G.A. Johnson, et al., “Morphologic phenotyping with magnetic resonance microscopy: the visible mouse”, Radiology, 222(3): p. 789-793, 2002.

[10] D. Moody and S. Lozanoff, “SURFdriver: A practical computer program for generating three-dimensional models of anatomical structures,” Paper presented at the 14th Annual Meeting of the American Association of Clinical Anatomists, July 8-11, 1997.

[11] R. McNeil. Rhinoceros: www.rhino3d.com, Seattle, WA, 1998. [12] L. Piegl, “On NURBS: A Survey,” IEEE Computer Graphics

and Applications, vol. 11, pp. 55-71, 1991.\ [13] L. Piegl and W. Tiller, The NURBS Book, 2nd Edition, Springer-

Verlag: Berlin, 1997. [14] S. S. Berr, Z. Yang, W. D. Gilson, J. N. Oshinski, B. A. French.

Cine Magnetic Resonance Imaging of Myocardial Ischemia and Reperfusion in Mice. International Society for Magnetic Resonance in Medicine 9th Annual Meeting. Abstract number 1895. Glasgow Scotland, April 2001.

[15] F. H. Epstein, W. D. Gilson, Z. Yang, B. A. French, S. S. Berr Black Blood Myocardial Tagging in Mice. Society for Cardiovascular Magnetic Resonance. Annual Meeting, Orlando, Jan 2002.

[16] J. West, Respiratory Physiology, 5th Edition, Williams and Wilkins: Baltimore, 1995.

[17] W. O. Fenn and H. Rahn, Section 3: Respiration, Handbook of Physiology, vol. 1, 1964.

[18] Y. Wang, S. Riederer, and R. Ehman , “Respiratory motion of the heart: Kinematics and the implications for the spatial resolution in coronary imaging”, MRM, vol. 33, pp713-719, 1995.

[19] Biology of the Laboratory Mouse, The Staff of The Jackson Laboratory, E. Green, ed. 1966. Dover Publications, New York.

[20] LA Feldkamp, LC Davis, and JW Kress. Practical cone-beam algorithm. J. Opt. Soc. Am. A. 1(6): 612-619, June 1984.