A fluid-structure interaction model of the internal carotid and ophthalmic arteries for the noninvasive intracranial pressure measurement method

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Abstract

Accurate and clinically safe measurements of intracranial pressure (ICP) are crucial for secondary brain damage prevention. There are two methods of ICP measurement: invasive and noninvasive. Invasive methods are clinically unsafe; therefore, safer noninvasive methods are being developed. One of the noninvasive ICP measurement methods implements the balance principle, which assumes that if the velocity of blood flow in both ophthalmic artery segments – the intracranial (IOA) and extracranial (EOA) – is equal, then the acting ICP on the IOA and the external pressure (Pe) on the EOA are also equal.

To investigate the assumption of the balance principle, a generalized computational model incorporating a fluid-structure interaction (FSI) module was created and used to simulate noninvasive ICP measurement by accounting for the time-dependent behavior of the elastic internal carotid (ICA) and ophthalmic (OA) arteries and their interaction with pulsatile blood flow.

It was found that the extra balance pressure term, which incorporates the hydrodynamic pressure drop between measurement points, must be added into the balance equation, and the corrections on a difference between the velocity of blood flow in the IOA and EOA must be made, due to a difference in the blood flow rate.

Introduction

Today, severe traumatic brain injury (TBI) is one of the leading causes of disability and death worldwide, especially among children and young adults. Each year, around 7 million cases of TBI are recorded, and it is calculated that by the year 2020, this threat will become number one among fatal injuries [1]. Intracranial and central nervous system tumors are the 17th most common cancer type worldwide, with more than 256,000 new cases diagnosed in 2012 [2]. Infections after cranial surgery are also very serious threats that require immediate recognition and treatment [3]. Microgravity conditions could affect the human body’s fluidic system, which in turn affects intracranial pressure (ICP), leading to vision deterioration or even vision loss [4]. In these cases, adequate patient monitoring is required to prevent secondary brain damage and to select the available treatment option in a timely manner. After experiencing TBI, or in a case of an intracranial tumor, a patient’s brain begins to swell; this swelling could be monitored indirectly by measuring ICP.

ICP is the pressure inside the human skull and thus in the brain tissue and cerebrospinal fluid. The increase in ICP could be acute or chronic [5]. For a healthy patient in the supine position, normal ICP values are in the range between 7 and 15 mmHg [6], and for pathological patients, ICP can exceed 25 mmHg [7]. Pathways leading to an increase in ICP are due to intracranial tumors, blood vessel anomalies, infections, TBI, etc.

A human skull, once the sutures and fontanelles have closed, becomes a structure that permits no further expansion; consequently, the dependence of internal volume on ICP is negligible [8]. ICP is a result of interactions among internal constituents such as arterial blood, venous blood, cerebrospinal fluid, and brain tissue. Brain tissue is sensitive to blood flow dynamics, and several mechanisms (metabolic, myogenic, and neurogenic) are involved in maintaining the appropriate cerebral blood pressure. Within certain limits, a human body utilizes autoregulatory mechanisms of ICP, which is also known as the Monro-Kellie hypothesis [9]. When the autoregulatory mechanism fails, secondary brain damage may occur.

The gold standard for ICP measurement is the use of intraventricular catheters that are connected to an external pressure transducer; nevertheless, this invasive method greatly increases the risk of complications [10]. Therefore, an accurate and certified noninvasive method of ICP measurement is needed. Although there are several proposed noninvasive ICP measurement methods, such as numerical modeling, medical imaging, the implementation of the impedance mismatch principle, etc. [5], [11], [12], our study only focuses on the noninvasive ICP measurement method, which implements the balance principle that works without any calibration needed and uses the ophthalmic artery (OA) as the main sensor [13], [14] to estimate the value of ICP.

OA supplies oxygenated blood to the eye. In most cases, it is the first intracranial bifurcation of the internal carotid artery (ICA), which in turn arises from the common carotid artery, which bifurcates from the aorta. OA starts inside the cranium and traverses the optic nerve canal to the eye socket located outside the skull [15] (Fig. 1).

The noninvasive ICP measurement method is based on simultaneous measurement of blood flow velocity in the OA at two points using the two depth transcranial Doppler ultrasound (TDTCD) technique: in the intracranial space of the OA (IOA) and in the eye socket, where the extracranial segment of OA (EOA) lies, by introducing an additional external pressure Pe in the cushion, tightly enclosing the area around the eye by placing a special mask on the patient’s head. The mask surrounds the eyeball so that Pe can be applied on the eye, as also on the extracranial segment of the OA, while the IOA segment is affected by ICP (Fig. 1). At any given moment, the blood flow rate in different arterial segments is equal, but velocity differs, as it depends on the blood flow resistance and OA lumen diameter, which is influenced by ICP, Pe, mechanical properties of the OA, and the surrounding environment (tissue, fluids). In most cases, the pressure in the eye socket is zero (i.e., equal to atmospheric pressure). Because OA is affected by ICP inside the cranium, the diameter of OA inside the cranium is smaller than that on the outside of the cranium, and the respective blood flow velocity is larger. As the external pressure Pe in the mask enclosing the face increases, the diameter of the segment of the artery located in the eye socket decreases and the velocity of blood flow increases. The velocity of blood flow in both segments becomes close when the added Pe becomes close to the ICP. The condition of ICP and Pe balance is described by the following equation:ICP=Pe+Pekwhere Pek is the extra balance pressure term incorporating the influence of the hydrodynamic pressure drop (between the measurement points) of blood flow pblood and other sources, such as any constrictions in movement due to bifurcation or prescribed displacements, material model, calculations errors etc., which affect the balance principle.

It is assumed that the OA’s mechanical properties do not vary longitudinally because of its short length (~3 mm), but circumferential mechanical properties vary because of the OA’s structure, which can be divided roughly into three parts: the tunica intima, tunica media, and tunica adventitia. Tissue or fluid enveloping OA influences its ability to change the diameter. During in vivo ICP measurements, residual blood velocity depends on the artery’s mechanical behavior as well as all the other enclosing (tissue, fluid) properties and resistance to flow. The measured blood flow velocity values are used to calculate the comparative nondimensional indices, for example, PI (pulsatility index), RI (resistivity index), etc.

A working device for noninvasive ICP measurement was created and is already patented [13], [16], [17]. The device was practically tested and validated through in vivo TDTCD measurements and the results compared with those obtained using the invasive methods [14], [18], [19], including the “gold standard” ventricular ICP method [20]. In order to use the device in clinical practice, the accuracy of noninvasive ICP measurement must be improved, because according to the ANSI/AAMI standards, the error of the ICP measuring device should not exceed ±2mmHg in the range of 0–20 mmHg, and in the range of 20–100 mmHg, the maximum error should not exceed ±10% [21]. That requires a fundamental understanding of the blood flow in the OA and its interaction with the surrounding tissues when the EOA wall is exposed to varying external pressure Pe. Experiments are too expensive or even impossible, while numerical simulation of blood flow in OA in situations close to those encountered during the measurements will allow us to estimate the factors that influence the measurement accuracy.

The main objective of the present work was to create and validate a numerical model suitable for investigations of the noninvasive ICP measurement method.

A three-dimensional FSI numerical model was created that incorporated the ICA segment, just after the bifurcation from the common carotid artery, then following the bone segment and the inner cranial segment of ICA and OA (OA bifurcates from ICA), then following the optic nerve canal of the OA and EOA segment. The model accounted for three degrees of freedom for deformation and stresses and a pulsating blood flow condition.

Section snippets

Computational model and methods

The numerical investigation of pulsating blood flow in an elastic artery requires a model that incorporates the mechanical behavior of an elastic vessel, the dynamics of time-dependent blood flow, and a model of moving boundary of the fluid-structure interaction. On the creation of the model, the following main assumptions were made:

  • The blood flow in ICA and OA is laminar.

  • The blood can be treated as homogenous, incompressible Newtonian fluid.

  • ICA and OA can be treated as a homogenous, isotropic,

Results and discussion

In order to assess the developed model, a mesh verification, a calibration of the vessels wall elastic properties, and an estimation of the balance point were performed. Mesh verification was performed in the case of stationary blood flow to ensure mesh independency of the calculations of the cross-sectional area. Lame parameters were calibrated to ensure that the model’s lumen cross-sectional area change was comparable in value to those of available experiments [29]. Finally, the balance of ICP

Conclusions

The heartbeat pulse averaged blood flow velocity ΔU had to be corrected, due to blood flow rate difference ΔQ between IOA and EOA. ΔQ was 0.02 ml/min, which was responsible for a shift in ΔU values by 0.02 cm/s, which shifted the balance point by 1.75 mmHg.

The ICP=Pe balance was achieved, although some nonmarginal extra balance pressure term Pek={PeS,PecU,PeuncU} had to be added. For heartbeat pulse-averaged cross-sectional areas PeS0.5 mmHg, while for corrected and uncorrected

Conflict of interest statment

None of the authors have any conflicts of interest to declare.

Funding

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

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