Stent a rilascio di farmaco: una storia di successo per la matematica applicata

Formaggia, L. ; Minisini, S. ; Zunino, P.

La Matematica nella società e nella cultura, Série 1, Tome 3 (2010) no. 2, pp. 181-200.

Riassunto (VO)

L'uso di modelli matematici a supporto della ricerca in medicina ha visto negli ultimi decenni un grosso impulso, stimolando l'attività di numerosi matematici applicati. Da un lato la migliore comprensione dei fenomeni fisici e biologici e dall'altro la disponibilità di strumenti di calcolo sempre più potenti a costi decrescenti ha fatto sì che la simulazione numerica possa effettivamente affiancarsi, anche se non sostituirsi, alla sperimentazione su animali e a trials clinici. Nel caso preso in esame da questo lavoro, che riguarda particolari dispositivi a rilascio di farmaco usati nel trattamento dell'arteriosclerosi, essa permette di poter valutare l'effetto di differenti configurazioni del dispositivo, o diverse tipologie di farmaco. Nell'articolo si dà una rassegna dei modelli matematici utilizzati nell'ambito degli stent a rilascio di farmaco, partendo dai modelli più semplici, basati su formule con forte carattere empirico o equazioni differenziali ordinarie, fino a modelli basati su sistemi di equazioni alle derivate parziali che accoppiano i fenomeni di rilascio con quelli di diffusione e trasporto nei tessuti biologici e nel flusso sanguigno.

Abstract

In the last decades the adoption of mathematical models to support medical research has found a considerable increase of interest, stimulating the activity of applied mathematicians. A better understanding of the physical and biological phenomena together with the availability of powerful and affordable computers has prompted the use of numerical simulation as a complement, even if not yet as a substitute, of animal experimentation and clinical trials. In the case considered here, namely that of particular drug eluting devices used in the treatment of arteriosclerosis, it allows for the evaluation of the effect of different designs of the device, or different type of drugs. In this article we give a review of mathematical models used for simulating the functioning of drug eluting stents. We start by considering the simplest models, based on empirical formulae or ordinary differential equations, up to models based on systems of partial differential equations that describe the drug elution processes coupled with the diffusion and transport of the drug in biological tissues and blood flow.

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