Modeling the effect of tumor compression on airflow dynamics in trachea using contact simulation and CFD analysis

Highlights

• Power loss for breathing in patients with tracheal lesions is studied in this work.

• Stenosis of 3D models is mimicked by contact simulation with ellipsoidal tumors.

• Turbulent airflow in the stenosed trachea models is simulated using CFD.

• For 50% stenosis, the power loss during inhalation rises to more than 66%.

• Using a tumor growth model, the proposed method may predict when to operate on the patient.

Abstract

Malignant central airway obstruction can cause severe breathing difficulty in a patient that requires surgical intervention or stent implantation to alleviate it. A predictive model to identify the onset of this event as the central airway is progressively compressed by tumor growth will be helpful for clinicians to plan for medical intervention. We present such a model to simulate tumor compression of the trachea and the resulting change in airflow dynamics to estimate the level of stenosis that will cause severe breathing difficulties. A patient-specific model of trachea was generated from acquired Computed Tomography (CT) scans for the simulations. The compression of this trachea due to tumor growth is modeled using nonlinear contact simulations of ellipsoidal tumors with the trachea. Computational fluid dynamics (CFD) is employed to simulate the turbulent airflow during inhalation in the stenosed trachea. From the CFD simulated flow fields, the power loss due to airflow through the domain is calculated. The results show that when the obstruction in the trachea reaches 50%, compared to the undeformed model, the power loss can rise to more than 66%. A measure of breathing difficulty can be derived by correlating it with the power loss. Thus, medical intervention can be predicted based on the degree of stenosis if the induced power loss exceeds a threshold that causes severe breathing discomfort.

Introduction

The trachea, or windpipe, performs the role of transporting air to and from the lungs during breathing. It is a tube having a length of 10–13 cm and a diameter of 2–2.5 cm in most adult humans, extending from larynx to carina [1]. As an integral part of the airway, any tracheal disorder can potentially cause severe difficulty in respiration. Central airway obstruction (CAO) is one such disorder of the trachea. CAO is referred to as the condition when a mechanical obstruction in the central airway impedes the airflow to the two main bronchi. It is a serious disorder that affects patients with chest disease. Approximately 20–30% of patients with lung cancer are affected by airway obstruction, although not all of them are attributed to CAO [2,3].

In general, there are two ways in which the central airway is obstructed [4]. The first kind occurs when a tumor compresses or extends into the airway lumen. This tumor can originate from a range of sources, such as enlarged lymph nodes, goiter, large vessels or other mediastinal structures [5]. The second mechanism is when tumors metastasize into the airway. Malignant CAO can be extraluminal (extrinsic), endoluminal (intrinsic), or mixed [6]. The extraluminal lesion obstructs the airway by compressing it from the outside. Endoluminal obstruction occurs as a result of tumor growth on the inside, and a mixed lesion is a combination of both. These three types of lesions are shown in Fig. 1.

Due to the obstruction, a decrease in the cross-sectional area of the tracheobronchial airway occurs, which is referred to as stenosis. Patients with tracheal stenosis generally develop difficulty in breathing including dyspnea (shortness of breath), stridor (high-pitched whistling during inspiration), wheezing and other conditions [7]. Although surgical intervention is generally the best treatment for CAO, it might not be suitable for all patients [8], e.g. patients with irremovable tumors. Stent implantation, albeit palliative in nature, can help alleviate the breathing difficulty by providing an outward pressure to counteract the compression created by lesions. In general, extraluminal lesions are treated with stent implantation or dilation [6]. Stenting may also be required in endoluminal and mixed cases, typically after surgically removing the tumor [6].

In order to alleviate the breathing difficulty, a thorough understanding of airflow dynamics in the trachea, and its relationship with different structural and flow properties are essential. Using principles of fluid mechanics, the role of airway constriction on breathing difficulty can be explained. Poiseuille's equation states that the flow resistance in a cylindrical vessel is proportional to the length and the viscosity of the fluid, and inversely proportional to the radius to the fourth power. With the progressive increase of tumor volume due to growth, the flow area in a patient with CAO disorder will decrease over time. Consequently, when other factors are constant, the airway constricted by tumor growth will require more effort from the patient to overcome the increased resistance to transport air to the left and right bronchi. It is to be noted that a patient's ability to create negative pressure difference across the tube also contributes to breathing difficulty for a patient [6].

Taking advantage of more advanced fluid dynamics models than Poiseuille's equation can help in obtaining useful information regarding the flow field in the trachea and its effect on the patient. For example, the power required to overcome the resistance is a measure of breathing difficulty [9], which can be conveniently calculated using computational fluid dynamics (CFD). CFD is a powerful tool that has been widely employed to furnish useful information to clinicians prior to performing surgery. Researchers have used CFD to investigate flow patterns in idealized [10,11] and patient-specific [12] trachea, as well as stenosed and post-operative ones [13,14]. In general, some assumptions regarding the flow condition (steady, unsteady, or quasi-steady) and boundary conditions (inlet, outlet, and wall) are made to investigate velocity and vorticity field, pressure loss, and wall shear stresses in the domain of interest. The organs of the human respiratory system have highly complex geometry with varying cross-sections. Flow with different regimes is observed at different parts of this respiratory system. Air enters the system through the nasal cavity, and because of its complex geometry, even at low flow rates the airflow can become translational or turbulent in this region [15] When air moves into the larynx, it encounters a constricted flow passage. As a result, the laryngeal region is dominated by a jet, which makes the flow turbulent there [16]. Eventually, as air travels further into the bronchial tree, the flow gradually gets converted into a laminar one [17]. Thus, in order to simulate the airflow during respiration accurately, it is necessary to choose an appropriate turbulence model. Using CFD, Chen et al. [18] calculated the pressure drop before and after vascular ring surgery. Brouns et al. [19] found resistance to airflow through an artificially stenosed trachea increased significantly as constriction in the tracheal lumen is increased. Bates et al. [20] considered the effect of curvature and constriction in realistic trachea models, and found that curvature induces an increased work of breathing. Mason et al. [21] applied CFD simulation to model airflow in an obstructed trachea before and after surgical intervention, which showed increased wall shear stress and flow resistance in the former case. By investigating the flow patterns in a progressively compressed trachea, Xiao et al. [22] verified that the narrowest region of a stenosed trachea offers the most resistance to airflow. Gunatilaka et al. [23] concluded that to obtain more representative results from CFD simulations of tracheal airflow, the geometry must be extracted from medical images during the required breathing phase of interest for a patient.

The present study aims to propose a procedure to predict a time-frame for surgical intervention. The basic goal is to provide an estimate of the time when the extrinsic lesion will become too large to cause significant difficulty in breathing. This is the time elapsed after the detection of early signs of the tumor. We assume a tumor of idealized geometry, placed at the site where the tumor is detected. In the present work, the volume of the tumor is increased gradually by changing its geometric parameters. With an appropriate model, a relation between time and those parameters can be established. As the tumor grows, it will obstruct the cross-sectional flow area in the trachea by the extraluminal lesion. This will gradually increase the pressure drop, which in turn will increase the flow resistance in the domain, which is a measure of breathing difficulty. At a higher degree of stenosis (more than 50%), the patient will start to experience difficulty in breathing [24]. In this work, we create stenosed models of the trachea from an undeformed patient-specific model. This task can be achieved using geometric operations, for example by subtracting a tumor body from the trachea. However, the resulting geometry is likely to be unrealistic because it does not take into account the change in area and curvature of the trachea near the site of the tumor compression. Hence, we employ contact modeling to simulate realistic deformation of trachea models by tumor compression, where we gradually increase the stenosis up to 50%. Additionally, using CFD, the power loss in the domain is calculated, which is indicative of the added effort required to overcome the flow resistance. Since a patient has to expend more energy to breathe in the same amount of air than in normal conditions, power loss can be used to measure breathing difficulty. When this power loss increases beyond a threshold, a clinical intervention will become necessary. With a representative population of patients having similar lesions, the parameters of an appropriate tumor growth model and this threshold value of power loss can be determined. Therefore, starting from a patient-specific trachea geometry, and a tumor growth model, a conservative estimate of the time when the patient will experience such a high level of breathing difficulty can be obtained. This may help in a more informed evaluation of the patient. Fig. 2 depicts the workflow of the present work.

The remainder of the paper is structured as follows: Section 2 details the process of modeling the tumor and its growth with time, and settings for the contact simulation. In section 3, the procedure for conducting CFD simulation in the normal and stenosed trachea models are documented. The results of the CFD simulation are provided in section 4, where the pressure, velocity magnitude, turbulence intensity, wall shear stress (WSS), and power loss in the trachea models are discussed. Finally, in section 5, the work is summarized, along with its limitations and scope for future work.