What is the Effect of COVID -19 Transmission on Human Lungs

By Dr. Sharad N. Pachpute

Flow Physics of Respiratory Systems

• Our respiratory system consists of nose, mouth, airways, and lungs. Surrounding air enters through the nose and mouth. After then it passes down through the throat, trachea, bronchi and smaller airways.
• The entrance to the larynx is covered with a small flap of tissue that automatically closes while swallowing and prevent food or drink from entering to the airways.
• There are two lungs. Each lung is divided into multiple lobes. The right and left lung have three and two lobes, respectively. The left lung shares space for chest with the heart.
• Overall, the left lung is a slightly smaller in size compared to the right lung. The human lungs consist of a complex structure of airways. The cross-sectional size of airways decreases from large portion (trachea) to smaller portion (alveoli).
• The bronchi are further divided into many smaller airways, and at end it is the narrowest airways (bronchioles). Their size is around 0.5 mm. The lung airways resemble an upside-down tree which is also names as the bronchial tree.
• Semi-flexible, fibrous connective tissues (cartilage) hold large airways. Smaller airways are held by the lung tissue. The walls of smaller airways are a thin with a circular layer of smooth muscles. The airway size of airways changes while muscle relax or contract

Weibel’s Lung Model

• Weibel (1963) simplified the tracheobronchial system using a dichotomous branching network of pipes
• A simplified system consists of a total of 23 levels of bifurcations or airways
• The numbering of bifurcations is based their downstream distance from the trachea
• A simplified Weibel’s model of lung is presented below. This model is well accepted for CFD modelling with an acceptable range of accuracy
• The geometry of human lung is divided into three main regions
  • Conductive zone: G0–16
  • Respiratory bronchioles: G17–19
  • Alveoli ducts and alveoli: G20–23
• As per this human model:
  • G0 is the trachea
  • G1 is the left and right bronchi
  • Four branches of airways are noted after the bronchi G1 are G2. These four branches continue until the last section which is called as alveoli (G20–G23)
  • The airways (bifurcations), the ratio of length-to-diameter ratio (L/D) is constant (~3)
  • The ratio of diameters for parent and child airways (D_n/D_n+1) is constant which varies from 1.17 to 1.5

Effect of COVID-19 on Lungs

• The latest global pandemic of new coronavirus (COVID-19) is easily transmitted through respiratory droplets during cough or sneezing
• Children, aged people, and those with weakened immunity systems are more susceptible to the adverse effects caused by coronavirus (COVID-19) transmission
• The coronavirus (COVID-19) is the most respiratory viruses. Effect face mask is discussed in the previous post. Without a facemask, the covid patient spreads corona virus by droplets from someone’s cough or sneeze to others.
• Most of COVI-19 patients, experience mild or moderate symptoms of fever and cough. However, sometimes the virus can make deep into the lungs and causes pneumonia.
• Lungs consists of clusters of tiny air sacs (alveoli). During the breathing, oxygen fills the air sacs and passes directly into blood vessels
• Pneumonia occurs when viruses cases the infection and inflames the alveoli
• In serious cases they fill with mucus (highly viscous fluid), dead cells and other debris
• They oxygen cannot pass from through small air ways

• The following image shows a CT scan from of 65-year-old man with COVID-19 symptoms
• Pneumonia caused by the corona-virus (COVID-19) is presented with distinctive hazy patches around the outer edges of both lungs

 

Effect of COVID-19 on Air Flow

• Human lungs consist of millions of microscopic spongy air vessels. These balloon-shaped air vessels called are called as alveoli
• At the alveoli, the exchange of gases takes place between the air sac and blood vessel take place
• In healthy lungs, an alveolus permits the oxygen exchange with blood flow and carbon dioxide is expelled out to the air airways
• However, for infected lungs, the alveolus restricts exchange of gas with blood stream due to inflammation and fluid inside the air sac
• Most of COVID-19 patients suffer with a serious inflammation of the lungs after which the alveoli are filled with water like fluid, pus or debris. The inflammation and fluid significantly restrict air flow and the immune system comes down

 Steps of CFD Modelings of Lungs

• The computed tomography (CT) visualize lung structure after extracting lung and bronchial structures for modeling
• This method provides the image derived from patients to generate a 3D model
• A CT scan creates a volumetric image of the lung with high resolution. It shows a clear difference between air and body tissue.
• Using the images of CT scan, Software are used for the automatic extraction of the upper and central airways

• Using advanced CFD modeling  software we can get the geometry of lungs airways
• After creating the CAD model, it is meshed and solved numerically to get pressure velocity, and particle deposition inside the lung’s airways

• Simplified models of lungs up to generation number  G3 has been studied in the literature

CFD Modeling of an Elastic Lung Model

• Yu Feng et (2018) carried out a transient CFD simulation of human respiratory systems considering an elastic lung model
• The elastic lung model was developed by Computational Bio-fluidics and Biomechanics Laboratory (CBBL) at Oklahoma State University to accurately predict anisotropic lung motions
• The considered transient simulation for airflow velocity and pressure fields by Fluid-Structure Interaction (FSI) modelling
• The SST Transition turbulence model used for fluid flow (CFD) modeling and finte element method (FEM) models for structural analysis to consider elasticity of lungs
• The transient from laminar-to-turbulence airflow is observed in the virtual respiratory system
• In their CFD model, the human respiratory system covers from nose and mouth to generation 13 (G13)
• The elastic lung model made computationally efficient to characterize lung motion using pulmonary function test (PFT) results
• Multi-phase CFD models like Euler-Euler and Euler-La grange models can be integrated with the existing flow model to predict particle deposition predictions in the airways

• Total air taken during inhalation is distributed across the lung’s airways

• Pressure distribution of lungs
• Pressure is high in the trachea after that decreases in the airways. The air pressure is very small across the small airways of the lung.

 CFD Modelings of COVID-19 affected Lung

• Zhang and Papadakis (2010) represented the human airway affected by asthma They considered a circular cross-section surrounded with several sinusoidal folds along the circumference of airways. The radius of such airways is expressed in the polar coordinate system as

• where r, θ and R present the radial coordinate, angular coordinate, and effective radius of the affected cross-section. Here, A_fold and n are for the amplitude of the folded (centimeter) and number of folds in the affected cross-section of airways, respectively
• A typical asthmatic airway has 40% of normal lumen area and 10 folds
• The airways affected by Chronic obstructive pulmonary disease (COPD) or COVID-19 are simplified with axisymmetric constriction with one or more of the bifurcations
• For COVID affected people, the size of airways is small and using the CFD analysis air flow rate per lungs duct can be determined

• Human Lungs are very delicate, and they get easily affected due to particle or mucus deposition
• The following figures show CFD results for the airways affected by Chronic obstructive pulmonary disease (COPD or COVID-19.
• Airflow rate is low for infected airways compared to healthy airways

 

Case Study CFD Analysis of a Simple Lungs Model

Objective of Simulation

• To carry out CFD simulation of human lungs to assess turbulence (RANS)  models for unsteady turbulent flow through airways considering elastic deformation of human airways
• The assumption for numerical simulation of airways

• • Flow in airways is assumed to be incompressible due to less variation in temperatures
  • Flow rate is calculated based on 15-minute volume with a corresponding male surface area of 2.0 m2. Mass flow rate is a sinusoidal function of time.
  • For numerical simulations, only the trachea and upper parts of airways is considered based on a simplified Weibel model
  • Elastic deformation of breathing wall is taken with 20 mm displacement due to visco-elastic vibration considering the statistically unsteady flow

Modeling Approach 

• A simplified Weibel’s model of the lung is used for simulation. This model is well accepted for CFD modeling with an acceptable range of accuracy

Calculation of Flow Rate in Breathing

• The functional form of the flow rate during breathing is expressed as

 

• • Where respiration frequency (RF), minute volume (MV), and tidal volume (TV) depend on the subject and body surface area (BSA) of humans.

• Change in minute volume (MV) with the body surface area (BSA) for male subjects is calculated as per Gupta et al., (2009).
• The amount of minute volume of air (MV) corresponds to the body surface area (BSA) 2-meter square area is selected. For the present simulation, 15 Minute volume (MV) is considered for the CFD simulation

 

Variable	Values	Unit
Minute volume, MV	15	litre
Respiratory Frequency (IN), RF1	15	per minute
Respiratory Frequency (Out), RF2	15	per minute
Tidal volume, TV =MV/RF	1	litre/sec
β  =∏*RF/30	1.57
a = β*TV/2	0.785	Litre/s
Flow rate, = a *sin(β*t) for t = 1 sec	0.785*sin(1.57*t)	Litre/s
density of air,ρ	1.20	Kg/m3
mass flow rate = ρ*a *sin(β*t) *10-3	0.000942*sin(1.57*t)	kg/s

 

Computational Domain

• Inlet is specified with a time-dependent mass flow rate using user defined functions
• The outlet is specified with zero gauge pressure
• The breathing wall is specified as a dynamic motion considering an elastic surface with a local displacement of 5 mm

• The computational domain is discretized finite number of volumes
• Poly-hexahedral  elements were used of mesh count of 2.1 M cells
• High mesh density is used near the breathing wall

 

Numerical Schemes

The details of numerical schemes are given in the section of the basic CFD modeling. Second-order schemes for the discretization of convective and diffusion terms using pressure-based unsteady solver.

• The unsteady pressure-based solver was for simulation
• Turbulence model: SST k-w
• Numerical Scheme: Second order upwind for momentum, Turbulent kinetic energy, and specific dissipation rate
• Pressure – Velocity Coupling:  coupled (SIMPLE and PISO) algorithm used for simulation.

CFD Results

• Numerical results obtained from the simulation of the simple lungs model is presented in this section
• The Static  Pressure is high near the main branch (trachea) and then decreases as air passes through branches of the lungs

• The velocity contours of a simple human lung are presented below. A mass flow rate of air varies as per pressure difference across each branch.
• Air velocity is higher in a small branch

• High turbulent kinetic energy is  near the point of bifurcation of main branches  due to more fluctuations during respiration

 

Future Scope for CFD Analysis of Lungs

• Many research institutes have been doing research to find solutions for infected patients, but more areas need to be explored
• Many hospitals have a shortage of ventilators. Hence, design and manufacturing patient effective ventilation is essential nowadays
• Effect of different ventilation techniques can be studied to study its effect of air distribution inside the lungs
• CFD modeling will help for optimization of design parameters of ventilation like pressure, velocity, and flow rate of breathing

Summary

• During coronavirus transmission, human lungs are affected by viruses and which may reduce or block airflow inside the lungs. It is important to understand the flow pattern and effect of blockage on it.
• The creation of a 3D model of the actual lung is difficult due to large variation in length scale and complex structure of lungs parts. However using scanning data, an approximate 3D model of human lungs can be developed.
• CFD analysis of human lungs is possible using a simple lungs model using commercial or open-source simulation software.
• Statistical turbulence Model can not predict the details of flow physics inside the lungs but we can get only averaged velocity and fluctuation only in the main branch. This model can not resolve flow physics in smaller branches considering fluctuating motion of the lungs wall. Large-eddy simulations (LES) or Direct numerical simulations will help to predict flow physics inside the lungs

References

1. J. K. Mutuku, W.C. Hou, W. H. Chen, An Overview of Experiments and Numerical Simulations on Airflow and Aerosols Deposition in Human Airways and the Role of Bioaerosol Motion in COVID-19 Transmission, Aerosol and Air Quality Research, 20 (2020) 1172–1196
2. B. Soni, S. Aliabadi, Large-scale CFD simulations of airflow and particle deposition in lung airway, Computers & Fluids, 88 (2013) 804-812