Multidisciplinary and multiobjective design optimisation of coronary stents

Abstract

Coronary stents are tubular type scaffolds that are deployed, using an inflatable balloon on a catheter, most commonly to recover the lumen size of narrowed (diseased) arterial segments. Even though numerous stent designs, of varying geometrical and material complexity, are used in clinical practice today, the adverse biological responses post-stenting are not completely eliminated. In-stent restenosis (IR), reduction in lumen size due to neointima formation within 12 months of procedure, and stent thrombosis (ST), formation of a blood clot inside a stented vessel, are the two most common adverse responses to stents. Such adverse responses are multifactorial and their causes are not completely understood. However, the geometric design of a stent, which is a common differentiating factor between the numerous commercially available stents, is known to be a key factor influencing adverse responses. In light of the above, this thesis exploits stent geometry parameterisation in both constrained and multiobjective optimisation. Gaussian process surrogate modelling is used to cost effectively (a) understand the influence of stent geometry parameters on metrics indicating adverse response, and (b) obtain families of stent designs which are potentially more resistant to such responses.

Various computational models are developed to evaluate the efficacy of a stent in terms of the factors influencing the adverse responses. In particular, two finite element analysis (FEA) models and two computational fluid dynamics (CFD) models are developed. The FEA models are used to simulate the balloon-expansion of stents in a representative coronary artery and bending of stents on application of bending moments. On the other hand, the CFD models simulate haemodynamic flow in the stented artery and the associated drug-release into the tissue. The expansion FEA models are validated against manufacturer provided pressure-diameter relationship and the flexibility FEA models are validated against the numerical studies found in literature. The numerical models are then used to extract metrics which are related to the adverse responses. Six metrics are formulated: (i) acute recoil, which measures the radial strength of the stent; (ii) volume average stress, which measures potential arterial injury caused by the stenting procedure; (iii) haemodynamic low and reverse index, which measures the haemodynamic alteration relevant to IR; (iv) volume average drug, which measures the amount of anti-proliferative drug delivered into the tissue; (v) drug deviation, which measures the uniformity of drug-distribution in the tissue; and (vi) flexibility metric, which measures the deliverability of the stent. These metrics are then used to compare the performance of different geometric stent designs. Two parameterisation techniques – one for a generic ring and link topology of stents, and one for the commercial CYPHER (Cordis corporation, Johnson & Johnson company) – are proposed to study the effect of geometrical variation in stent design on the formulated metrics of efficacy. These techniques are then combined with surrogate modelling to perform stent design optimisation studies and study the effect of stent geometry on the evaluation metrics. Finally, three paradigms to choose optimal stent designs from a set of non-dominated solutions, in terms of the evaluation metrics, are proposed, and optimal designs under such paradigms are identified.

The last part of this thesis concerns surrogate assisted optimisation, and is not specific to the problem of stent design. Here, the use of analytically available gradient information in widely used Kriging predictors is explored. A search algorithm to locate all stationary points of a Krig, using a combination of an iterative sequence of the Krig derivative and a low-discrepancy sequence is proposed.

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