The unexplained success of stentplasty vasospasm treatment : Insights using Mechanistic Mathematical Modeling

Abstract

Background: Cerebral vasospasm (CVS) following subarachnoid hemorrhage occurs in up to 70% of patients. Recently, stents have been used to successfully treat CVS. This implies that the force required to expand spastic vessels and resolve vasospasm is lower than previously thought.

Objective: We develop a mechanistic model of the spastic arterial wall to provide insight into CVS and predict the forces required to treat it.

Material and methods: The arterial wall is modelled as a cylindrical membrane using a constrained mixture theory that accounts for the mechanical roles of elastin, collagen and vascular smooth muscle cells (VSMC). We model the pressure diameter curve prior to CVS and predict how it changes following CVS. We propose a stretch-based damage criterion for VSMC and evaluate if several commercially available stents are able to resolve vasospasm.

Results: The model predicts that dilatation of VSMCs beyond a threshold of mechanical failure is sufficient to resolve CVS without damage to the underlying extracellular matrix. Consistent with recent clinical observations, our model predicts that existing stents have the potential to provide sufficient outward force to successfully treat CVS and that success will be dependent on an appropriate match between stent and vessel.

Conclusion: Mathematical models of CVS can provide insights into biological mechanisms and explore treatment approaches. Improved understanding of the underlying mechanistic processes governing CVS and its mechanical treatment may assist in the development of dedicated stents.

Keywords: Mathematical modeling; Stent; Stentplasty; Vascular smooth muscle cells; Vasospasm.

Figure 1:

Figure 1a: The arterial geometry is approximated as a nonlinear elastic cylinder with unloaded radius R and thickness H (left) which is pressurized and axially pre-stretched to mimic in vivo conditions (right). Figure 1b: Diameters, internal pressures and constituent stretches at different phases of our model of vasospasm. In the pre-vasospasm phase (1), arterial diameter at systolic blood pressure is 2.9mm, VSMC stretch equals its attachment stretch. In the early phase of vasospasm (2), the constriction is chemically driven and VSMCs haven’t remodelled yet. Following remodelling (3), VSMCs have returned to their attachment stretch while elastin hasn’t remodelled so its stretch hasn’t changed from phase (2). Finally, if a stent provides enough pressure to exceed a critical value, a dilatation threshold (4) is reached at which VSMCs are brought to mechanical failure and incapacity to bear the pressure load. This signifies successful treatment of CVS.

Figure 2

Pressure-diameter curve for a middle cerebral artery (solid curve). Physiological systolic blood pressure of 16kPa corresponds to healthy diameter of 2.9mm (red dashed lines). The non-solid curves represent the contributions of the individual load-bearing constituents: elastin, collagen (medial+adventitial), passive response of VSMCs and active response of VSMCs.

Figure 3

Pressure-diameter curve for a vasospastic middle cerebral artery with original systolic diameter 2.9mm that contracted to a systolic diameter of 1.46mm. The non-solid curves represent the contributions of the individual load-bearing constituents.

Figure 4

Pressure-diameter curve for the vasospastic artery before and after VSMC damage. When the dilatation threshold is reached, VSMCs cease to contribute to load bearing and only elastin and collagen are bearing the pressure load (thinner solid curve).

Figure 5

Effectiveness of two stent-retrievers in resolving vasospasm in a middle cerebral artery with 50% stenosis. The stent is effective if its related curve remains above the solid curve up until the dilatation threshold. In this example, Solitaire 6mm would be successful, whereas Trevo 4x20mm would not because mechanical equilibrium would be reached at point E, which is well before the dilatation threshold.

Figure 6

Effectiveness of four stent-retrievers in vasospastic arteries of physiological diameters 1.5mm (Fig. 6a), 2mm (Fig. 6b), 2.9mm (Fig. 6c) and 4mm (Fig. 6d), at 50% stenosis. In the 1.5mm artery all the stents expand the wall beyond the dilatation threshold. In the 4mm artery, they open the artery to new diameters, which are less than the dilatation threshold and are therefore not effective in treating vasospasm.

Figure 7

Plot of the parameter pairs f_a vs f_p that solve mechanical equilibrium for a vasospastic middle cerebral artery at 50% stenosis. The represented values cover all possible solutions.

Figure 8

Plot of the critical pressure (above) and additional pressure (below) vs increase in passive response in vasospasm at 50% stenosis. The critical pressure is defined as the amount of pressure necessary to be applied to the arterial wall to reach the dilatation threshold, while the additional pressure is the amount of pressure an interventional device should provide to reach such dilatation threshold. Equivalently, the additional pressure equals the critical pressure after subtraction of systolic blood pressure (16 kPa). The case considered in the main text is shown in red.

Figure 9

Chronic outward force vs diameter relationships for four commonly available stents: Solitare 6mm, Solitaire 4mm, Capture 3mm and Trevo 4mm. Note the forces rapidly fall to zero as the stent expands.

Figure 9

Chronic outward force vs diameter relationships for four commonly available stents: Solitare 6mm, Solitaire 4mm, Capture 3mm and Trevo 4mm. Note the forces rapidly fall to zero as the stent expands.

Figure 10

Pressure-diameter curves for four commonly available stents: Solitaire 6mm, Solitaire 4mm, Capture 3mm and Trevo 4mm.

Figure 11

Constituent stretch vs diameter relationship for elastin, medial collagen, adventitial collagen and VSMCs. Given the different mechanical roles, constituents begin to bear the pressure load at different diameters and are configured at different stretches at the physiological diameter (vertical dashed line).