The Center for Human Modeling and Simulation and the TraumAID project, University of Pennsylvania
Douglas DeCarlo, dmd@gradient.cis.upenn.edu, Jonathan Kaye, kaye@linc.cis.upenn.edu, Dimitri Metaxas, dnm@central.cis.upenn.edu, John Clarke, jclarke@gradient.cis.upenn.edu, Bonnie Webber, bonnie@central.cis.upenn.edu, Norm Badler, badler@central.cis.upenn.edu.
To produce analogous realism in our virtual agents' bodies, we recognize the critical relationship between the physical existence of an anatomical part with the functional role(s) it plays. This has led us to to couple our quantitative deformable model techniques [6] with models of the physiological mechanisms that produce physical changes. This allows us to design models that reflect the fact that anatomical parts have two intrinsic, interrelated existences: they are physical objects that obey physical laws, and they are part of physiological systems, so their behavior contributes to the overall functioning of the body. They are interrelated because changes to one can affect the other, both as part of the same system and as a result of physical adjacency.
Another area of medicine that can gain from models of functional anatomy is the emerging field of Virtual Surgery. To date, however, many efforts have concentrated on providing realistic images and dynamics (e.g., Noar [7] on techniques used in endoscopic simulators), neglecting functional issues. The consequence is that a necessary characteristic for virtual surgical simulators [10], reactivity, that organs must react appropriately to manipulation or cutting, such as by bleeding or leaking fluid, cannot be achieved.
We chose first to model the respiratory mechanism since it involves physiological change, such as pressures and flows, that depends on gross anatomical deformations. Ultimately, with models for other physiological systems [8], we want to demonstrate their interaction due to the physical space they share.
We currently express physiological dynamics in both a quantitative and qualitative framework. This provides us with a mixed quantitative/qualitative description of physiological behavior, which may be more appropriate for explanation than a purely quantitative model. Our system consists of two integrated levels of abstraction: (i) geometric and physics-based modeling of anatomy (shape extraction, motion, deformations, and graphical rendering); and (ii) simulation of physiological mechanisms that behave in accordance with physical laws and physiological processes.
This paper describes our ongoing effort [3] involving the procedures we have developed that graphically demonstrate organ geometry, physics, and physiological dynamics. It details our current implementation of a simplified lung during normal, quiet breathing, describing the quantitative results of our Finite Element Method implementation, based on techniques from [6].
Figure 1 goes here
Our qualitative formulation of the dynamics involved in quiet breathing is described in [3]. It makes use of the qualitative simulation paradigm QSIM [4]. Figure 1 shows the quantities we considered, assuming constant resistance and compliance.
When applying Lagrangian dynamics [6], we obtain second order equations of motion which take the general form
Mq'' + Dq' + Kq = gq + fq (1)
where q are the generalized coordinates (the degrees of
freedom) of the model,M, D, and K are the mass, damping,
and stiffness matrices, respectively, gq are inertial forces, and
fq are the generalized external forces. The vector q contains
the information needed to specify the shape of the lung. If the
equation of motion (1) is integrated over time, the
dynamic deformation of the model is observed.The shape and viscoelastic properties of the lungs are modeled by using isoparametric finite elements [13]. Because we currently lack detailed data on the elastic properties of the viscoelastic material of the lung, we use linear finite elements. However, our methodology is general and is also applicable to non-linear finite elements.
We incorporate the isoparametric finite elements into the Lagrange equations of motion (1). The finite elements are used to compute internal elastic forces that arise due to the deformation of the lung. This deformation is caused by applied forces that include pressure and collision forces.
We can now use this model to create dynamic simulations of inhalation and exhalation, and also of a simple pneumothorax. Our model of the lung interacts with the surrounding chest cavity by applied forces. This type of representation of the lung lends itself to a modular approach, where this lung model could be incorporated into a larger model of human anatomy without changing the implementation. For instance, the addition of a second lung or heart would not require changes in the implementation of the first lung. The first lung need not "know" about the other lung or the heart directly. Their effects could be dealt with through applied forces.
This lung model will react to external forces that include pressure forces (due to the difference in pressure between the lung and intrapleural space), and contact forces caused by the lung rubbing against the chest wall.
The lung is contained within the chest cavity. For this implementation, the chest cavity is given two degrees of freedom, which correspond to diaphragm and chest wall deformation. This simplified chest model is suitable currently, for the purpose of demonstration. However, because of the modularity of our lung model, we could add a more complex chest wall model without disturbing our model of the lung. This chest cavity model contains what is necessary for simulation of inhalation and exhalation. Figure 2 shows kinematic motion of the chest wall at the extremes-(a) at rest, and (b) fully inhaled.
Figure 2 goes here
Within this chest wall is the finite element mesh for the lung and intrapleural space. The initial model can be constructed by creating the lung in its unstretched shape shown in figure 3(a), and then setting the intrapleural pressure to its negative value (with respect to atmospheric pressure), resulting in the lung at rest in (b) (recall that the lung is stretched in its normal resting state due to the negative intrapleural pressure). In this (and all following) model diagrams, the lung is shaded with a light gray, and the intrapleural space with a darker gray. A diagram of the finite element mesh used is shown in figure 3(c).
Figure 3 goes here
The forces that arise due to pressure differences occur at the boundaries of the intrapleural space, which is the only location where two adjacent elements will differ in pressure. For such an element, we can compute the pressure force at a node along an element edge as
force = (P/l) * n (2)where P is the pressure of an element, l is the length of the edge, and n is a normal pointing out of the element that is perpendicular to the edge. This is a 2-D analog of the f = P / area relationship. When considering the sum of all pressure forces, the net contribution of force for each edge is related to the pressure gradient across the edge.
The contact forces due to collision of the lung with the chest wall are implemented as in [5].
Figure 4 goes here
To simulate a simple pneumothorax, we can set the intrapleural pressure to be equivalent to body surface pressure (atmospheric pressure) in our model. This will eliminate any pressure forces holding the lung close to the chest cavity. The resulting collapsing motion of the lung is shown in figure 5. The location of the injury is indicated by the gap in the chest wall. Notice how the lung returns to its unstretched shape, as shown in figure 5(a).
Figure 5 goes here
In this paper, we have examined one aspect of our project, the Finite Element Method implementation of a two-dimensional, idealized lung. This preliminary work will be used as the basis for our continuing physics-based three-dimensional modeling which we will apply to simulating normal respiratory physiology and related pathologies. It will also serve as a basis for considering the interaction of physiological systems due volume constraints.
[1] N. Badler, C. Phillips, and B. Webber. Simulating Humans: Computer Graphics, Animation, and Control. New York: Oxford University Press, 1993. [2] Clarke, J.R., Webber, B., Niv, M., Rymon, R., Gertner, A. and Kaye, J. The Care of Injured Patients: An architecture of Medical Knowledge. Der Chirurg (Special issue on surgical decision-making), April 1994. [3] J. Kaye, D. Metaxas, J. R. Clarke, B. Webber. Lung Modeling: Integrating Anatomy and Physiology. First International Symposium on Medical Robotics and Computer-Assisted Surgery (MRCAS-94), Pittsburgh, 1994. [4] B. Kuipers. Qualitative Simulation. Artificial Intelligence, 29: pp. 289-338, 1986. [5] D. Metaxas. Physics-Based Modeling of Nonrigid Objects for Vision and Graphics. Ph.D. thesis, Department of Computer Science, University of Toronto, 1992. [6] D. Metaxas and D. Terzopoulos. Shape and Nonrigid Motion Estimation Through Physics-Based Synthesis. IEEE Trans. Pattern Analysis and Machine Intelligence, 15(6): pp. 569-579, June 1993. [7] M.D. Noar. Endoscopy Simulation: A Brave New World? Endoscopy, 23: pp. 147-9, 1991. [8] G. Provan, S. Neumann, J. R. Clarke, and J. Kaye. A Mixed Qualitative/Quantitative Acute Cardiovascular Model: Preliminary Report, for the AAAI Spring Symposium, AI in Medicine, Stanford, 1994. [9] Rymon, R., Webber, B. L. and Clarke, J. R., Progressive Horizon Planning - Planning Exploratory-Corrective Behavior. IEEE Transactions on Systems, Man, and Cybernetics 23(6). Special issue on Planning, Scheduling and Control, November 1993. [10] R. M. Satava. Virtual reality surgical simulation: the first steps. Surgical Endoscopy, 7: pp. 203-205, 1993. [11] D. Terzopoulos and D. Metaxas. Dynamic 3D Models with Local and Global Deformations: Deformable Superquadrics. IEEE Trans. Pattern Analysis and Machine Intelligence, 13(7): pp. 703-714, 1991. [12] Webber, B., Rymon, R. and Clarke, J.R. Flexible Support for Trauma Management through Goal-directed Reasoning and Planning. Artificial Intelligence in Medicine 4(2): pp. 145-163, April 1992. [13] O. Zienkiewicz. Finite Element Method. McGraw-Hill, 1977.
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