Abstract
The author outlines from an historical point of view the mathematical problems, which were the main topics of his scientific collaboration with Enrico Magenes. A full account of the joint work on mathematical models for electrocardiology is given. The paper ends commenting few original letters Magenes wrote to the author: it gives a clear description of the work method, and also of the “gentle” pressure to which Magenes’s collaborators were exposed.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Colli Franzone, P., Magenes, E.: On the inverse potential problem of electrocardiology. Calcolo XVI(IV), 459–538 (1979)
Colli Franzone, P., Guerri, L., Viganotti, C., Macchi, E., Baruffi, S., Spaggiari, S., Taccardi, B.: Potential fields generated by oblique dipole layers modeling excitation wavefronts in the anisotropic myocardium. Comparison with potential fields elicited by paced dog heart in a volume conductor. Circ. Res. 51, 330–346 (1982)
Colli Franzone, P., Guerri, L., Viganotti, C.: Oblique dipole layer potentials applied to electrocardiology. J. Math. Biol. 17, 93–124 (1983)
Colli Franzone, P., Guerri, L., Magenes, E.: Oblique dipole layer potential for the direct and inverse problems of electrocardiology. Math. Biosci. 68, 23–55 (1984)
Colli Franzone, P., Guerri, L., Viganotti, C., Taccardi, B.: Finite element approximation of regularized solution of the inverse potential problem of electrocardiography and applications to experimental data. Calcolo XXII(I), 91–186 (1985)
Corbin, L.V. II, Scher, A.M.: The canine heart as an electrocardiographic generator: dependence on cardiac cell orientation. Circ. Res. 41, 58–67 (1977)
Guerri, L., Magenes, E.: On the inverse problem of electrocardiology. In: Alekseev, A.S. (ed.) Current Problems of Numerical and Applied Mathematics. Collection of Articles (Aktual’nye Problemy Vychislitel’noj i Prikladnoj Matematiki. Sbornik Statej), pp. 59–72. Izdatel’stvo “Nauka” Sibirskoe Otdelenie, Novosibirsk (1983) (in Russian). [B] Akademiya Nauk SSSR, Sibirskoe Otdelenie. Vychislitel’nyj Tsentr., 208 p. R. 2.00
Magenes, E.: Sui problemi di derivata obliqua regolare per le equazioni lineari del secondo ordine di tipo ellittico. Ann. Mat. Pura Appl. (4) XL, 143–160 (1955)
Magenes, E.: Su alcune recenti impostazioni dei problemi al contorno, in particolare misti, per le equazioni lineari ellittiche del secondo ordine. Ann. Sc. Norm. Super. Pisa, Cl. Sci. (3), X(I–II), 75–84 (1956)
Magenes, E.: Il problema della derivata obliqua regolare per le equazioni lineari ellittico-paraboliche del secondo ordine in m variabili. Rend. Mat. 16(3–4), 363–414 (1957)
Magenes, E.: Su un problema inverso di teoria dei potenziali logaritmici. Calcolo XXII(I), 31–46 (1985)
Martin, R.O., Pilkington, T.C.: Statistically constrained inverse electrocardiology. IEEE Trans. Biomed. Eng. 22(6), 487–492 (1975)
Nedelec, C.: Curved finite element methods for the solution of singular integral equations on surfaces in R 3. Comput. Methods Appl. Mech. Eng. 8, 61–80 (1976)
Rudy, Y., Oster, H.S.: The Electrocardiographic Inverse Problem. CRC Press, Boca Raton (1993)
Taccardi, B., Macchi, E., Lux, R.L., Ershler, P.R., Spaggiari, S., Baruffi, S., Vyhmeister, Y.: Effect of myocardial fiber direction on epicardial potentials. Circulation 90, 3076–3090 (1994)
Tentoni, S.: Analisi numerica di problemi ai limiti ellittici, connessi con l’Elettrocardiologia, mediante potenziali di superficie. Master Thesis, Pavia (1980)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Italia
About this chapter
Cite this chapter
Colli Franzone, P. (2013). Inverse Problems in Electrocardiology. In: Brezzi, F., Colli Franzone, P., Gianazza, U., Gilardi, G. (eds) Analysis and Numerics of Partial Differential Equations. Springer INdAM Series, vol 4. Springer, Milano. https://doi.org/10.1007/978-88-470-2592-9_4
Download citation
DOI: https://doi.org/10.1007/978-88-470-2592-9_4
Publisher Name: Springer, Milano
Print ISBN: 978-88-470-2591-2
Online ISBN: 978-88-470-2592-9
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)