A 3D Virtual Environment for Modeling Mechanical ... - CiteSeerX

A 3D Virtual Environment for Modeling ? Mechanical Cardiopulmonary Interactions Jonathan Kaye1 Dimitris N. Metaxas1 Frank P. Primiano, Jr.2 1

Center for Human Modeling and Simulation, University of Pennsylvania, Philadelphia, PA 2 ECRI, Plymouth Meeting, PA

Abstract. We have developed a computer system for modeling mechan-

ical physiological behavior in an interactive, 3D virtual environment. Such an environment can be used to facilitate exploration of cardiopulmonary physiology, particularly in situations that are dicult to reproduce clinically. We integrate 3D deformable body dynamics with new, formal models of (scalar) cardiorespiratory physiology, associating the scalar physiological variables and parameters with corresponding 3D anatomy. Our approach is amenable to modeling patient{speci c circumstances in two ways. First, using CT scan data, we apply semi{ automatic methods for extracting and reconstructing the anatomy to use in our simulations. Second, our scalar models are de ned in terms of clinically{measurable, patient{speci c parameters. This paper describes our approach, problems we have encountered, and a sample of results showing normal breathing and acute eects of pneumothoraces.

1 Introduction In an interactive, immersive virtual environment, objects need both to look and behave appropriately. Thus not only must the anatomy look realistic, but also tissue must deform properly in accordance with ongoing physiological processes or external intervention. It is essential that object deformation be accompanied by appropriate physiological response. In an eort to create such an environment, we have de ned a compact, scalar description of cardiopulmonary mechanics that drives deformable 3D anatomy to simulate mechanical behaviors of and interactions between physiological systems. The scalar description provides an ecient form with sucient degrees of freedom to express a range of normal and pathological conditions. By its de nition, the scalar description contains clinically{measurable, patient{speci c parameters. The 3D anatomy, reconstructed from CT scans, provides a vivid depiction of the simulations as well as a natural means for interacting with the ?

This work has been supported by the National Library of Medicine under contract number NO1{LM{4{3515 and the Philadelphia VAMC. The authors appreciate the contributions to this eort by Eric Homan, Janice Cook-Granroth, Cheng-Ning Chang, John Clarke, Bonnie Webber, and Douglas DeCarlo.

patient. We couple these methods by translating scalar predictions to the 3D anatomy and 3D deformation to its impact on scalar physiological properties. We envision our system ultimately assisting students to visualize and explore anatomical and physiological relationships, illustrating behavior visually on the 3D anatomy and quantitatively in terms of detailed physiological measurements.

2 Related Work We have found that related approaches focus either on the visual presentation without commensurate physiological delity, or on the behavior of physiological variables and quantities with less emphasis on the visualization using realistic 3D anatomy. Modeling realistic, 3D anatomy is currently in the domain of `anatomical atlases,' such as the many eorts involving the Visible Human Project [1]. These projects have reconstructed actual patient images to present static models that can be viewed from arbitrary angles and cross{sections. Any `physiology' typically implies they have labeled the parts or given more detailed descriptions. Recently, there has been great interest focused on endoscopic simulation and other minimally{invasive procedures. These programs are mostly developed for very speci c procedures and do not let the user explore consequences of incorrect actions. Emerson et al [2] have compiled an extensive bibliography on virtual reality in medicine. There are a number of patient simulation programs derived from complex mathematical models, with current commercial products mainly for anesthesia training [6, 10]. These approaches rely on more sophisticated mathematical models for physiological systems than the surgical simulators. The visualization of anatomy is relatively simple, such as changing skin color or using video clips. Because they are designed for anesthesia training, these models tend to center on pharmacokinetics (absorption, metabolism, and action of drugs) and pharmacodynamics (drug eects on patients) with less stress on complexities of physical movement. Generally, these systems use a simple mechanics model with a single degree of freedom chest wall (described in [5]). This can be expanded to have multiple lung compartments, but one cannot investigate the eects of dierent muscle recruitments or anomalies within the chest wall. In contrast, our approach emphasizes the mechanics.

3 Anatomy and Physiology Respiration encompasses a number of processes: the mechanical process of ventilation, or the movement of air into and out of the lungs, the biochemical processes that deliver oxygen to and removes carbon dioxide from the cells of the body, and the neurological mechanisms that regulate breathing patterns. Our focus is the mechanics. The lungs are contained within the thoracic cavity which is divided into two halves (one for each lung), separated by the mediastinum. The mediastinum is a

membranous structure that contains the heart, the major blood vessels, and the trachea. Clinically, the rib cage and diaphragm/abdomen are referred to as the `chest wall,' a unit comprising the ribs, sternum, respiratory muscles, diaphragm, abdominal contents, and abdominal muscles. The lung and chest wall are separated by a very thin layer of liquid called the intrapleural uid. The uid occupies the intrapleural space. Normally, the

uid is at a subatmospheric pressure. The intrapleural uid allows the lung to slide on the chest wall and acts to transmit forces between them. Air or blood entering the intrapleural space can cause the lung to separate from the chest wall and impede respiration. A pneumothorax is the pathological presence of air in the intrapleural space. One cause of a pneumothorax is a breach in the chest wall. If the breach allows the free bidirectional passage of air, it can be referred to as an open sucking chest wound. If a ap of tissue at the breach acts as a one{way valve, allowing air into the intrapleural space but plugging the hole to prevent air from leaving during expiration, pressure builds up and a tension pneumothorax develops. Intrapleural pressure increases in the half of the thoracic cavity in which the pneumothorax occurs. The resulting pressure gradient across the mediastinum pushes the mediastinal contents towards the opposite side. Blood ow is essential for delivering nutrients and oxygen to body tissue and removing the waste products of metabolism. Blood is pumped by the heart into the pulmonary and systemic circulation. The right ventricle of the heart pumps blood into the pulmonary circulation (through the lungs), and the left ventricle pumps it into the systemic circulation (rest of the body). The blood returning to the heart from the systemic circulation arrives via the inferior and superior vena cavae. The heart and vena cavae are located in the mediastinum. Because the vena cavae are accid and the blood pressure within very low (less than 10 mmHg), they can be greatly in uenced by changes in the pressure outside their walls, which we call the intramediastinal pressure. Changes in vessel dimensions alter ow resistance properties. Assuming that the intramediastinal pressure changes as the average of the intrapleural pressures, one can see that intrapleural pressure changes, originating from ventilation, may cause changes to cardiovascular function. With pneumothoraces, the increasing intrapleural pressure may result in collapse of the vena cavae.

4 Methods

Our work can be divided into three categories: the reconstruction of thoracic anatomy for organ geometry, the 3D modeling, and the scalar modeling. We use the reconstructed anatomy to add realism to the simulation. The 3D modeling not only depicts the 3D geometry, but also involves kinematics and dynamics, resulting in tissue deformation. The scalar modeling describes the relationship between generalized forces (pressures) and displacements (volumes).

4.1 Reconstruction of Thoracic Anatomy

We obtained sets of CT scans of the thorax for a subject breathing dierent volumes of air, courtesy of Dr. Eric Homan at the University of Iowa. The

reconstructed versions of these data sets became the boundary conditions for our 3D simulation. Using 2D deformable contours (`snakes') in a program developed by colleagues at the Hospital of the University of Pennsylvania, we segmented the images. Once we recovered the shapes, we used public{domain software by Hoppe [3] to reduce their resolution. This was a necessary step because the original shapes were too detailed computationally for our use.

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Fig. 1. Reconstruction of thoracic anatomy: (a) segmentation, (b) reconstruction

(shaded is 5% Vital Capacity [VC], wireframe is 75% VC), and (c) reduced resolution of reconstructed anatomy, for normal rest and 75% VC. Vital Capacity is the maximum lung volume change one can voluntarily produce.

Figure 1(a) shows the segmentation process, with (b) illustrating some results for reconstructed lungs. Part (c) shows the end product after resolution reduction. Once we derive the anatomy at dierent lung volumes, we t a single tessellation for each structure to the parts at dierent volumes. We do this by creating a deformable model that is attracted (through forces) to the data from the dierent volume reconstructions. Since our data sets did not include collapsed lungs, we created approximations for their shape. This tting gives us a single tessellation for each part to use throughout the range of breathing. Based on this geometry, we assign mechanical properties to the 3D system for the dynamic parts of our simulation.

4.2 3D Modeling The 3D anatomy in our environment consists of two lungs, an upper torso, a structure called the parietal pleura encasing each lung, and the inferior and superior vena cavae (IVC and SVC, respectively). We divide the parietal pleura into its medial surface, corresponding to a wall of the mediastinum, the inferior surface, corresponding to the diaphragm, and the rib cage. Currently, we have no 3D representation for the abdomen. In the lung/chest wall system, the rib cage muscles, diaphragm, and abdominal muscles provide the active, driving forces for displacements, while the lungs,

mediastinum, and mediastinal contents are passive. Because computation speed is a great concern, we cannot model all parts with 3D deformable{body dynamics. It is important to model the lungs with deformable{body dynamics because they must be able to follow and slide on the chest wall, as well as collapsing in ways that may be dicult to model realistically with pure kinematics. We have divided the modeling of structures into two categories: structures controlled by 3D kinematics and structures controlled by 3D dynamics. The structures with kinematics are updated with linear interpolation. The structures with dynamics are viscoelastic P spring{mass systems, updated with the Newtonian equation of motion f = ma (described in [5]). The rib cage, diaphragm, and mediastinum are modeled with kinematics. Their displacements are interpolated based on the values of pressure and volume variables with which they are associated. Each lung, modeled with a mixed dynamics/kinematics process, is updated with respect to body forces, contact with other structures, internal forces arising from the passive elements in the structure trying to return it to its unstressed shapes, and pressure gradients developed in the scalar modeling. The surface of the vessels is modeled as a deformable mesh.

The Lungs For small lung volume changes about an operating point, such as tidal breathing, the lung acts like an isotropic solid, i.e., it expands equally in all directions. This is true regardless of the operating point [9]. The behavior is most likely due to the expansion of the alveoli. For large volume changes, the lung cannot be modeled as an isotropic solid, because large changes involve changes in airway dimensions in addition to alveoli expansion. We model the gross shape changes by a core that undergoes the anisotropic changes the lung experiences during large volume excursions, and a surface mesh representing the lung surface which acts isotropically. Since the core represents the airways, including the main stem bronchus, we include a translational component to the core that allows it to move with the mediastinum when it shifts. We attach the lung surface to the core through core{to{surface springs. This lets the surface also translate and keeps the lung moving with the main stem bronchus. The core is connected to the surface mesh with zero{rest{length dampened springs. Currently, the core nodes are mapped to the surface in a one{to{one relationship. These core{to{surface springs act to pull the surface back to the core. The transmural pressure (the dierence between the inside pressure [alveolar] and the outside pressure [intrapleural]) is applied to the core based on interpolation. The transmural pressure is applied to the surface mesh along surface normals. In general, the core expands less than the surface, which means small changes are mostly accounted for by surface changes alone, while large changes are the product of both in uences, making it consistent with the observation about real lung changes. Our model requires us to choose viscoelastic properties for the surface mesh and the core{to{surface connections. For the surface mesh, we need properties that maintain smoothness under deformation without undue stiness that would distort the shape from its basic (core) form. For the core{to{surface con-

nections, we want stier springs that can guide the surface to make its shape approximately that of the core. The method we employ is straightforward. For the surface mesh, we assign the elastic coecient k for a spring inversely proportional to the dierence between its length at the collapsed lung state and at the fully expanded lung state (the fully expanded lung shape is the shape we would like the lung to reach at maximum expansion). For the core{to{surface mesh, we assign the elastic coecient to be inversely proportional to the distance from the core to the surface at maximum lung expansion. We compute the damping coecient d from k by assuming that the lung parenchyma is roughly critically damped (d = k=sqrt(2)).

4.3 Scalar Modeling Respiratory Mechanics We developed our ventilation model by extending

the work of Primiano [7]. The physical analog for the model we have implemented is illustrated in Fig. 2. It consists of two lungs, the mediastinum, the rib cage, the diaphragm, the abdomen, and the common junction (explained in [4]). We also provide for bilateral intrapleural spaces of non{zero volume changes to model pneumothoraces. In the physical analog, the chest wall components are represented as (massless) disks that move within a conceptual cylinder. The uppercase F (within circles) represent active muscular eorts, while the lowercase f (within squares) represent passive mechanical elements. The arrows indicate the direction of in uence an element has on a component. For example, tension in the mediastinal element fm2 resists the rib cage's positive (upward) displacement. We use the direction of the arrows to determine the signs, when the pieces are written in equation form. The tension in an element depends on the relative displacement of the named component, with zero being its value at the patient's normal rest. The diaphragm and abdomen move with a single degree of freedom because we model the abdomen as a liquid of uniform pressure. As a rst approximation, we model the mediastinum and its contents computationally as an elastic membrane. an elastic membrane. We solve the system of ordinary dierential equations corresponding to Fig. 2 explicitly over time using conventional numerical methods. The equations are derived completely from the diagram|see [4] for details. We currently model the passive elements as viscoelastic. This means that an element x in uences the change in volume vy by the following function: fx (vy ) = vy =Cx + v_y Rx , where Cx is the element's compliance and Rx is the element's resistance.

Cardiovascular Mechanics To simulate basic cardiovascular mechanics, we adapted Rideout's PF-1 model [8] which incorporates linear and non{linear (time{ varying ventricular{compliance) elements. Our model has ve segments for the systemic circulation, ve for the pulmonary circulation, and four heart chambers. We call the portion of the systemic venous circulation closest to the right atrium the vena cava, a collective representation of the inferior and superior vena cavae. In Rideout's model, the pressure outside a vessel is assumed not to change. In our model, we identify a certain section of the vasculature as being `within' the

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Fig. 2. Six degree of freedom physical analog. mediastinum and hence in uenced by changes in the pressure outside the vessels. To these vessels we apply the transmural pressure as the dierence between the pressure within the vessel and the change in intramediastinal pressure (equal to the average of the changes of the two intrapleural pressures).

4.4 Integrating Scalar and 3D Modeling The 3D and scalar models are coupled during the simulation in two ways. First, the kinematics parts are is updated with linear interpolation based on pressure gradients or volumes predicted in the scalar models. Second, the dynamics parts are sensitive to 3D forces derived from pressure gradients. We convert the scalar transmural pressure to 3D forces acting along surface normals. These 3D forces act to deform the anatomy. Collisions between the lung and the chest wall are resolved by allowing the lung to slide along the wall, but not penetrate it. The walls of the mediastinum are attached to the contents (vena cavae) by dampened springs. This means that mediastinal deformations can cause vessel deformations. Depending on the degree of vessel deformation (judged by changes to the cross{sectional area), the program may change the vessel's ow resistance (since it is inversely proportional to its cross{sectional area). To keep the scalar and 3D models consistent, we must ensure that a pressure gradient applied to the 3D model results in a volume consistent with the scalar volume predicted. This is a known problem with spring{mass systems which we will address in the future by introducing volume{preserving forces.

5 Results The system gives the user the choice of displaying over sixty scalar variables plotted against time or each other, as well as control of over sixty parameters. In our implementation, the parameters are resistances and compliances. We chose initial parameter values to produce normal responses for a healthy individual. The program lets the user orient his view arbitrarily in the 3D environment. Figure 3 shows a view of the (supine) patient from the patient's left lateral position. The prints below the anatomy are on a virtual bed sheet. The bed reminds the user of the orientation regardless of the user's viewing perspective.

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Fig. 3. Results from increasing rib cage muscle eort relative to diaphragmatic muscle

eort. We show in (a) the normal tidal expansion, and (b) the expansion with an increased rib cage muscle force.

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Fig. 4. Right sucking chest wound (a) compared with right tension pneumothorax (b). Figure 3 shows the dierence between normal breathing for the supine patient (3(a)), dominated by diaphragmatic contraction, and breathing with in-

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Fig. 5. (a) intact system at rest position; (b) tension pneumothorax at rest position. creased rib cage muscle involvement (3(b)). The user can appreciate these changes either by looking at the variable plots or adjusting the 3D view. In Fig. 3(b), the diaphragm is actually sucked up into the chest cavity slightly during breathing (second plot from top, rst column). In severe pneumothoraces, such as depicted in the right thoracic cavity in Figs. 4 and 5, the intrapleural pressure can become equivalent or greater than atmospheric pressure, causing the right lung to collapse and the mediastinum to shift markedly (compare the mediastinum in Fig. 5(a) and (b)). This has a pronounced, detrimental eect on venous return because of cardiopulmonary mechanical interactions. Figure 4 shows the dierent results from a right open sucking chest wound (Fig. 4(a)) and a right tension pneumothorax (Fig. 4(b)). The right lung is appreciably smaller in the tension pneumothorax because the intrapleural pressure is greater. Because we have not yet implemented a volume preservation scheme, the left lung separates from the chest wall.

Figure 5 compares the normal equilibrium values for the intact anatomy (Fig. 5(a)) with the values at equilibrium after inducing a right tension pneumothorax (Fig. 5(b)). Comparing the plots displayed, one can see that the blood pressure (second column, top) decreases signi cantly. Because the ow resistance in the vena cava has increased, the central venous pressure (second column, second from bottom) and the central venous volume (second column, bottom) increase. If more of the circulatory anatomy were shown, distended jugular (neck) veins, a classic clinical nding in the presentation of tension pneumothorax would be apparent. The pressure/volume plot for the left ventricle (third column, top), shows the stroke volume (amount ejected from the ventricle each heartbeat). In the tension pneumothorax, the stroke volume decreases from 70 ml to 40 ml. It is important to remember that these results are only for the mechanical consequences of the injuries. More realistic clinical presentations can be obtained with the incorporation of neurological models.

6 Conclusion

Applying techniques from computer vision, physics{based modeling, and bioengineering, we have illustrated an interactive visualization tool for the simulation of cardiopulmonary mechanics. Also, the procedure incorporates patient{speci c anatomy and mechanical properties, and can be adapted to clinical and educational applications.

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