Modelling and analysis

The present study is a patient-specific case study of a 58-year-old female patient who had reported with a hemorrhagic stroke (sudden subarachnoid hemorrhage due to aneurysmal rupture) with a broad necked aneurysm arising from the bifurcation of the left ICA, while the right ICA bifurcation appeared to be normal. The location of the broad neck aneurysm and normal ICA bifurcation is highlighted in three different views, as shown in Fig. 2. The grid sizes of the 3D FSI models for the LICA as shown in Fig. 3 consist of 35230 and 21270 hexahedral elements for the fluid and solid models, respectively, while the RICA consists of 36480 and 22450 hexahedral elements for the fluid and solid models, respectively.

Different views of CT scan of ICA bifurcation. a: Normal; b: Giant aneurysm

Carotid bifurcation FSI models (left and right side). The left side has giant aneurysm at the ICA bifurcation and the right side is normal

The pressure waveform in a typical carotid artery bifurcation is in the range 110–120/70–80 mmHg, as per clinical observation [38]. However, assuming the peripheral resistance from the arteries in downstream side, a pulsatile pressure waveform was applied at the outlet, as shown in Fig. 4(a) [39, 40]. The velocity spectrum obtained from patient specific ultrasound carotid Doppler was considered as pulsatile velocity waveform at the inlet, as shown in Fig. 4(b) [38, 39]. In the present study, focus is on understanding the haemodynamics for three conditions, that is, SL, ST and HD positions. Hence, the applied numerical boundary conditions at inlet and outlet should follow physiology of postural changes. Therefore, effect of gravity on blood flow during SL is nil, however to counter the gravity, during ST and HD position, 1G and -1G force is applied downwards and towards the head respectively [20, 25]. Hence, considering these assumptions, the pulsatile velocity waveform (normalized) as shown in the Fig. 4(b) is applied at inlet for various postures [25, 34].

Various applied waveforms in the fluid domain. a: Outlet pulse pressure waveform; b: Inlet velocity waveform for different postures

The considerable increase in the flow is at peak systole, particularly during the HD position [34]. Thus, in the present investigation of transient FSI analysis, laminar flow is adopted in the SL and ST posture, while the k–ω turbulence model (medium intensity factor) is prescribed for the HD posture (Reynolds number is greater than 3000). The flow properties of viscosity and density are assumed to be 0.004 Pa and 1060 kg/m³, respectively. The elastic properties of arterial wall assumed to have Youngs modulus of 5 × 10⁵ Pa, density of 1200 kg/m³ and Poisson’s ratio of 0.48 [39, 41]. The entire simulation was performed for five pulse cycles, and each pulse cycle (0.8 s) was discretized into 250-time steps and the results captured during the last cycle was presented. Although the physiological influence of postural change during transition time is quite complex, however the stabilized flow behavior due to autoregulation is assumed in the present investigation.