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Ann Thorac Surg 2002;73:1032-1034
© 2002 The Society of Thoracic Surgeons
a Division of Cardiothoracic Surgery, Department of Surgery, Washington University School of Medicine, St. Louis, Missouri, USA
* Address reprint requests to Dr Pasque, Division of Cardiothoracic Surgery, Washington University School of Medicine, Suite 3103 Queeny Tower, One Barnes-Jewish Hospital Plaza, St. Louis, MO 63110, USA
e-mail: pasquem{at}msnotes.wustl.edu
Taken at first glance, the article by Gnaneswar and associates [1], which describes a complex engineering analysis of the aortic root, appears to be just another foray into the details of a topic dear to the hearts of most cardiothoracic surgeons—aortic root reconstruction. If you probe a little deeper, however, the true significance of this manuscript, which weds the unlikely partners of structural engineering and heart surgery, is readily appreciated. It represents, in fact, nothing less than a vital component of a clinical tool of the future that has the very real potential to change our subspecialty practice. The clinical tool to which I am referring is a different kind of total artificial heart than the one that is grabbing all of the headlines these days. This different kind of total artificial heart, to the contrary, will reside entirely in the mathematical depths of the desktop computer. Specifically, I am describing what most myocardial mechanics investigators might call the Holy Grail of cardiac physiology, a fully interactive, three-dimensional, computer-based model of the in vivo human heart.
That this study by Gnaneswar and associates [1], and for that matter this total artificial heart of the future, sits squarely in the realm of mathematics need not worry all of us nonmath types. I have not a clue how my personal computer works, but I use it every day. Likewise, most of us will not have a clue about the mathematical foundation of the computer-based heart models of the future. Nonetheless, I would predict that even the most mathematically challenged of us will, in the not too distant future, use it on a regular basis. Mathematical theory and applied mathematics are the building blocks of this model. Although the mathematics is what scares us the most about it, it is exactly that dreaded math that gives our futuristic model its many unique strengths. Mathematics supplies not only the common structural framework on which each of the many components can be suspended, but also represents the only manner in which to adequately model the complex interactions among these various components. It is also the mathematics that is already allowing the development of a surgeon-friendly, interactive framework that will allow real-time modification of the various model components, as well as the descriptions of their interrelationships. This is the key to the model’s potential as a clinical tool. It will allow us to enter clinical problem-specific or patient-specific variables and then test the various therapeutic options that are available to us.
It is also the mathematics that will display the answers to our inquiries of this heart model in the interactive, three-dimensional visual field of the computer workstation. Cardiothoracic surgeons are visual animals. We need to visualize solutions to clinical problems. There is no use spewing out a list of numbers for us to analyze. Give us the pictures. Let us see the heart in front of us in full living color. Display it in three dimensions using variable degrees of transparency, with a dynamic, rotatable display of the contracting and relaxing ventricles with their opening and closing valves and tensing and relaxing papillary muscles. But, of equal importance, let us visualize the results of our proposed surgical intervention. Let us see the results of surgically altering the left ventricular shape or of remodeling the various components of the subvalvular apparatus of the mitral valve—before we do it.
The studies like those of Gnaneswar and associates [1] are the cornerstone building blocks on which this computer-based total artificial heart will be built. Each component of this model will be assembled at its individual assembly plant in the laboratories across this country and around the world. They will be built in the common language of mathematics, which will allow their subsequent assembly into larger subcomponent assemblies that will ultimately all come together into the total heart model.
An engineering tool, based entirely in the language of mathematics, finite element analysis (FEA), was used by Gnaneswar and associates [1] to model and analyze the aortic root. Finite element analysis, in one form or another, will almost certainly be the backbone of any computer-based model of the human heart. Finite element analysis simply breaks up the complex anatomy of the object into finite geometric regions of study referred to as elements. These elements are smaller subdivisions of the whole object that are more mathematically manageable and whose relationships to each other are known and mathematically defined. Finite element analysis was developed by the aerospace industry to model the complex geometry that has characterized high-performance aircraft. It really comes into its own, however, when it is used to model truly complex geometry, such as that of the human heart. It was exactly this complex geometry of the heart, which requires too many compromising assumptions when modeled with simplistic geometric models, that has prompted many mechanics investigators to embrace FEA.
Accordingly, the first of three key inputs to FEA, and therefore to our total artificial heart model, is an accurate description of the time-dependent, three-dimensional geometry of the object to be studied. The basic default geometry input of the proposed heart will be a compilation of hundreds of human hearts averaged into a single representative geometric shape. Initial anatomic renderings have been founded on complex postmortem examination of individual subcomponent geometry. For instance, a subcomponent of the aortic root is the aortic valve itself, whose leaflets are further subcomponents that must be modeled.
Cardiac geometry, however, can vary to the extremes, as all pediatric cardiac surgeons can attest. The strength of FEA is that it can accurately model all such variation. There will be, almost certainly, many different geometry subgroup models describing patients with variant geometry such as is found in tetralogy of Fallot or the various single-ventricle subgroups. This interactive heart model will offer even more than this, however. It will be robust enough to allow input of individual patient-specific geometry. Indeed, methodologies that are already in use, in our laboratory and in others, allow for a generalized model, which resides permanently in the modeling program, to be tweaked or morphed into the desired patient-specific input geometry simply by importing the individual patient’s magnetic resonance imaging scan data.
The second key component of the proposed heart model (and of FEA) is an accurate description of the boundary conditions applied to the various geometric surfaces of the model. These boundary conditions describe how the cardiac model is attached to, and interacts with, its surroundings. They include not only constraints that hold the heart components to the surrounding mediastinal and vascular tissues, but also the pressures applied to the individual endocardial and epicardial surfaces. Once again, each component can be modeled as an aggregate average compiled from an extensive examination of a group of patients or can be individual patient-specific information, such as that obtained in the catheterization suite. These boundary conditions, whether they be such factors as the afterload against which the ventricle ejects during systole, the load applied to the aortic valve leaflets during diastole, or the pericardial attachments to the lungs and other mediastinal tissues, are vital to supplying the descriptions of the time-dependent relationships between the model and the rest of the living organism in which it resides and functions.
The third component of the model, the material property description, relies heavily on precise experimental science to supply a mathematical description of how the various tissues react or deform under a range of physiologic loading conditions. Almost all normal human tissues have a nonlinear, anisotropic deformation within the normal physiologic range of loads. This means that the rate of deformation changes as load is increased and that the deformation is different depending on the direction in which the load is applied. The material property description of the previously mentioned aortic valve leaflet will, for example, incorporate the anisotropic influences resulting from the directionality of the elastin fibers in the leaflet. As our model gets more and more sophisticated over the years, the component modeling will involve smaller and smaller subcomponents with a requirement for more and more sophisticated testing methodologies. This is why this model will never be finished.
So what would we actually do with our computer-based cardiac model? Specifically, what kind of output can we expect from it? These questions lead us to another unique attribute of the backbone of the model—FEA. The classic forward FEA solution allows one to compute stress and strain when each of its three input components—geometry, boundary conditions, and material properties—are known. This forward solution for wall stress and regional wall strain may be useful in approaching clinical problems, as we will discuss later. It is also possible, however, to reverse this solution process. Specifically, algorithms are in use today [2–4] that allow one to inversely determine values for material variables such that FEA model-predicted strains best approximate measured strains that are obtained by other means (such as magnetic resonance imaging). In other words, the inputs to the model can be supplied by the investigator or solved for by the investigator if the normal output from solution of the model is known.
Let us explore the ramifications of this unique capability of FEA inasmuch as it applies directly to the robustness of our model in solving clinical problems. The easiest way to illustrate this capability is to orient around the unknown variable of the particular clinical situation. For example, let us examine the patient with severe left ventricular dilatation and myocardial depression secondary to long-standing aortic insufficiency. The degree of ventricular recovery that can be expected after aortic valve replacement is difficult to predict clinically but would obviously have direct clinical implications regarding choice and timing of therapy. Most investigators suspect that the extent and type of fibrotic replacement of the ventricular musculature that occurs over time with chronic aortic insufficiency may be one predictor of potential for ventricular functional recovery. This fibrotic replacement of the myocardium would clearly be expected to change the ventricular myocardial material properties. Thus, determination of patient-specific diastolic material properties of the left ventricular myocardium might reveal how far this patient has progressed down the path of irreversible injury. As previously described, determining the global diastolic material properties of the left ventricular myocardium can be performed by reversing the normal FEA process. Geometry and boundary conditions are input into the FEA model, as usual. This time, however, the usual output information, myocardial strain (obtained by tracking radiofrequency tissue-tagging grid points through diastole by sequential magnetic resonance imaging scanning), is imported into the algorithm as input—and the material property description is obtained. As mentioned, these semiautomatic, computer-based algorithms used to infer myocardial material properties from this known patient-specific data have been developed [2–4], and the relevance of various material property descriptions to ventricular recovery is already under investigation.
Moreover, the model may be able to take us even one step further. The forward FEA model solution, as previously mentioned, provides stress and strain information. What if a specific global or regional left ventricular myocardial stress level is identified that, once it is reached, is associated with myocardial pump failure in all cases? Many mechanics investigators suspect that a critical myocardial stress level may well be uniform across all clinically relevant pathophysiology and may, indeed, be the defining line that, when crossed, determines the point of cardiovascular collapse. This level, theoretically, may be applicable regardless of the inciting pathophysiology, whether valvular, viral, or atherosclerotic in its origins. In fact, FEA is already being used clinically to render accurate estimates of ventricular wall stress. With this tool, one could use a simple forward FEA solution to predict whether the patient’s heart is going to fail (wall stress exceeds tolerable level) if you perform a specific intervention. In other words, procedures like surgical ventricular remodeling of akinetic areas [5, 6] could, theoretically, be tested for each individual patient before they are performed. Known (by magnetic resonance imaging scanning) preoperative geometry can be modified in the computer by simple computer-aided design techniques such that the specific details of the operation (such as the dimensions and shape of the patch and the amount and shape of the excluded myocardium) could be tested. The FEA solution strain data could be used to visualize expected ventricular deformation with overlay stress contour mapping to discern regional stress singularities. Various pericardial patch sizes, shapes, and intraventricular attachment configurations could be modeled with comparison of predicted stress reduction (relative to preload required to maintain physiologic output). The details of the patient-specific operation could be planned and known before actual surgical application.
Ultimately, the complete assembly of our computer-based, total artificial heart model will move us to a new level in our understanding of cardiovascular physiology. Indeed, the value of the assembly of the components of the heart—just like with a high-performance aircraft—will be far higher than their mere sum. The full integration of all of these components will open our eyes to unknown relationships that are otherwise indiscernible—with incalculable clinical results. The usefulness of this grand venture, however, will be apparent at every step of its development. Indeed, the fundamental first steps in the building of this model have yielded, and will continue to yield, important clinical insights, such as those offered by Gnaneswar and associates [1] in this issue of The Annals.
References
This article has been cited by other articles:
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  J. H. Dayan, A. Oliker, R. Sharony, F. G. Baumann, A. Galloway, S. B. Colvin, D. C. Miller, and E. A. Grossi Computer-generated three-dimensional animation of the mitral valve J. Thorac. Cardiovasc. Surg., March 1, 2004; 127(3): 763 - 769. [Abstract] [Full Text] [PDF]
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