SoftHeart: A Mathematical and Software Simulation for Heart Restyling SR Amendolia", A Barsottib,AM Calafioreb,MG Bisogini', U Bottigli", MA Ciocci", P Delogu', ME Fantacci', V Marzulli", P Maestroc,E Pemigottid,N Romeoc,V Rosso", A Samaritani', A Stefanini", S Sturribo' "Istituto di Fisica dell'universita, Sassari xnd Sezione, I.N.F.N., Pisa, bDipartimentodi Cardiologia Medica e Chinugica, Univlersita degli Studi G D' Annunzio, Chieti, 'Dipartimento di Fisica dell'universita and Sezione, I.N.F.N., Pisa, dEuropeanLaboratory for Particle Physics (CERN), Geneve, Switzerland and Sezione I.N.F.N., Pisa, Italy
ability to pump. In doing so, the heart actually becomes less effective in performing its job: in these conditions the patient is diagnosed with Congestive Heart Failure (CHF). Treatment varies with the severity of CHF, ranging from medications for mild cases to heart transplants for severe cases. Cardiovascular surgeons [ I ] have begun performing a new surgical technique (Batista's procedure BP) on
Abstract The le@ ventricular reductiori culled Butista 's procedure ( B P ) is CL surgical techriique able to improve the ventr'iculcrr fiinction in the heart disease k n o w cis the Congestive Heart Fuilure (CHF). Front u geonietrical point of view the BP is n restyling of the left ventricle from a spherical configuration to an ellipsoidal one. We have written n prograni ("SoftHeart") which siniulates the response of the heart @er the B.P. The main products of our program are the new ejection fraction and the tiew stroke volume as a function of the equatorial surgical reduction. Usitig these curves it is possible to classifi the patierits into three categories corresponding to ci goussim-like curve, ~i$at curve atid a inonotonic descending curve, respectivelj. A clitiicnl trial pevorined ori 165 patierits allows a good correlation between the three categories built b j "SoftHetirt" arid three different clinical situations. An explanation of the three categories produced by "SoftHenrt" using the Lapluce and the Frank-Starling lnws is reported
1.
Figure 1. Surgical heart restyling in Batista's procedure certain patients with CHF. Medical doctors hope that for some patients this operation may be an alternative to heart transplant. The procedure, also called left ventricular reduction, involves removing a slice of the muscle from the enlarged heart and sewing the heart back together ( F i g l ) . By reducing its size, the heart can pump more efficiently and
Introduction
When its pumping function decreases, the left ventricle becomes larger in an effort to compensate for its reduced
0276-6547/98 $10.00 0 1998 IEEE
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Computers in Cardiology 1998 Vol25
vigorously. The CHF can also be combined with the heart assist devices. These devices, which take over most of the heart's pumping function, allow the heart to rest, heal, and grow stronger. After this, the assist device can be removed, and a left ventricular reduction can be performed. Thus far, the results are encouraging. However, surgeons are still collecting data to determine how long the benefits last and which patients will benefit from the surgical procedure rather than from transplant [231. This paper describes a mathematical tool which, starting from geometrical input data, is able to connect the physical behaviour to the physiological performance of the heart. This parameterization can optimize the selection of the patients for the BP.
60% of the accumulated work alters the elastic strain of wall, while the remaining 40% is converted in mechanic work. Then the strain of the wall T$ph$,e (using Laplace's formula) and the ejected volume AVsphele can be computed. The same calculations are applied to the ellipsoid which is obtained reducing the equatorial circumference of the sphere by a fixed percentage, yelding the corresponding strain of the wall Telllps,,,d and the ejected volume AVell,psold. Finally, the global variations
and
2.
Mathematical model
Our model takes into account the accumulated work obtained in a restyling of the heart from a spherical configuration to an ellipsoidal one. If we consider a sphere and an ellipsoid having the same volume, we can write 4
--Er.?
3
are computed. The model produces for each patient three curves versus equatorial reduction: increment of Ejection Fraction (EF), new EF, stroke volume.
4 =-n(ubc) 3
where r, a, b and c are the radius of the sphere and the half-axes of the ellipsoid respectively. Then, for the same amount of contraction, a better change of surface will occur in the case of the ellipsoid, and since, in our model, the accumulated energy, i.e. the work that can be done, is proportional to the variation of the surface, the ellipsoid is more efficient than the sphere. In detail, starting from echo-cardiographic data we obtain the radius of the sphere that approximate the shape of the cardiac muscle. Calculation of heart surface and volume are then carried out. The surface is divided in 1000 little areas which can be approximated by a plain surface. Each little area is contracted of a given quantity. After contraction the new total surface and volume are computed. The accumulated work W is computed using the formula for the potential energy of the mainspring
3.
The program has a user friendly interface realized in LabWindows/CVI and, for the calculations described by the previous model, uses a library written in C. The program input consists of echo-cardiographic data. The output is a data-sheet containing a summary of the most relevant cardiographic parameters, a patient identification section, and a graphic section where, as a function of the equatorial reduction, the three curves described above are shown. Such information, together with the echo-cardiographic data of the patient, can be printed on paper or saved either as a ASCII file or as a PostScript file, which gives the cardiologist the possibility to create an easy and rapid to access database and to exchange information, via e-mail, with colleagues all around the world (tele-medicine). Given the large amount of different methods used to calculate heart volumes starting from echo-cardiographic data, there is the option to calculate this figure according to Dodge formula [4]. A clinical trial was performed on 165 patients [5-61. Among them 150 were affected by CHF of different gravity and 15 were healthy patients (in blind) as a test group. Running the program on the test group it is possible to distinguish three differents typology of response based on geometrical shape of the curves
where K is the elastic constant. The corresponding change of pressure AP is given by:
AP =
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increment EF versus equatorial reduction and a increment in the stroke volume curve (Fig:2). To this
obtained for increnzerit EF and stoke volume. The first category, named A, presents a gaussian-like curve for the
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Figure 2. Typical shapes for increment EF, riew EF and stroke volume versus equatorial reduction curve for a patient of class A. The thick line on the stroke volume curve, represents the initial value of the stroke volume. The program suggests a surgical solution in cases like this 21 0-
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Figure 3. Typical shapes for iricrement EF, new EF ntid stroke volume versus equatorial reduction for a patient of class B. The thick line on the sfroke volume curve, represents the initial value of the stroke volume
Starling's law foresee a small reduction of SV. In these conditions the sum of both contributions is an increment of SV ((case A). On the contrary if the heart is normal or with a 'small dilatation, the reduction of SV due to FrankStarling's law is more significant than the increment due to the Laplace's law, and the SV decrease along with the reductim of the heart circumference (case C). Cases B can be interpreted as the ones in which heart's dilatation is so significant that the gain in SV due to Laplace's law is of the same order of magnitude of the small reduction of SV due to the Frank-Starling's law. Results expected for patients used in the clinical trial have been compared with post-operatorial echocardiographic data in 40 cases among the 150[5]. In 33 of the 40 cases patients belong to the class we named A. Among them 8 patients died: 4 due to cardiac problems and 4 because of different complications. In the 4 patients whose death was due to cardiac problems it was later verified that the surgical equatorial reduction was greater (2 cases) or smaller ( 2 cases) than the one suggested by
category belong 107 patients among the 150 affected by CHF. The second category (B) is characterized by the patients which present a flat shape for the iricremeizt EF curve and a consequent low descending trend for the stroke volunie curve (Fig:3). This category is populated by 24 patients. The third category (C) is characterized by patients which present an iricrenzerit EF and a stroke volume curve with a dramatically monotonic descending trend (Fig:4). To this category belong the last 19 patients plus the 15 healthy patients considered as a test group.
4.
Discussion and conclusion
The behaviours produced by the model and reported in Fig: 2-4 can be explained using the Laplace and FrankStarling laws. If the heart dimension is significatively bigger than normal, as a consequence of the heart circumference reduction, Laplace's law foresee an increment of the stroke volunie (SV), while the Frank-
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from the curves generated by SoftHenrt. If we consider as a cause for failure both the death of a patient and the absence of improvement of ventricular functionality, we can assert that SoftHenrt shows a sensitivity of 60% and a specificity of 95% with a positive
SoftHenrt, placing the SV in the region at the righiileft of the peak. In the remaining 25 patients was observed an increase of the SV and they actually have a good outcome. In 5 of the 40 cases of patients belonging to class B, 3 died and 2 survived without showing any benefit. In the two cases that belong to class C, the patients died as expected
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Figure 4. Typical shapes for iricrenient EF, riew EF, stroke volume versus equatorial reduction for a patient of class C. Thick line on stroke volume curve, represents the initial value of the stroke volume.
predictive value of 86% and negative of 83%. Both serisitivity and negative predictive value are 100% if we consider that the only decess of patient belonging to class A was due to an excessive reduction of the equatorial heart circumference, in according with SoftHenrt response. In conclusion SoftHeart can be used as a valid method to operate a selection of patients affected by CHF to be submitted to Batista's procedure.
[4] H.T. Dodge er d.Hemodynamic aspects of cardiac failure in "The myocardium : failure and infarction" E.Braunwald (editor) New York H.P. Publishing Co., 1974,70-79 [SI A. Barsotti et al. Criteri di selezione dei pazienti con
scompenso cardiac0 terminale da sottoporre a cardiomioplastica riduttiva ventricolare sinistra (operazione di Batista). Cardiologia 1997;42(Suppl. 3):37-41. [6] A. Barsotti et al. Ventricular remodelling in dilated cardiomyopathy. (Author's reply) Lancet 1997,350,1706-7.
References R.J.V. Batista er al. Partial left venticulectomy to improve
left ventricular function in end stage heart disease. J. Card. Surg. 1996, 1 1 :96-96
Address for correspondence:
G.D. Angelini et nl.Left ventricular volume reduction for end-stage heart failure. (abstr.) Lancet 1997, 350:489.
Simone Stumbo. Dipartimento di Fisica, p.zza Torricelli 2 , 56100 Pisa Italy. E-mail address:
[email protected]
R.B. Bestetti. Partial ventriculotomy (Batista's procedure) reduces heart failure in dilated cardiomyopathy. (letter) Lancet 1997, 350,1706.
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