01 - Publication - A use friendly Mutliscale lung modeling suite and applications

A User Friendly Multiscale Lung Modeling Suite and Application

A Thesis

Submitted to the Faculty

of

Drexel University

by

Viraj Nignesh Leena Shah

in partial fulfillment of the

requirements for the degree

of

Master of Science in Biomedical Engineering

December 2007

Multiscale Lung Modeling ii Shah Viraj

Dedications

First I shall like to thank my parents Mr. Nignesh and Mrs. Leena Shah from the bottom

of my heart for their love, affection and guidance for the pursuit of my studies at Drexel

University.

I shall take this opportunity to thank my brother Naishal and the rest of my family for

always being there for me.

Next I shall like to thank my friends Smiral, Shivani, Abi, Heman, Ashish, Nirali and all

my other friends at Drexel and from India for making me a better person each day with

their suggestions and guidance. Finally I shall pay homage to my Grandmother’s and my

brother Jay who always showered their blessings from wherever they are.

Multiscale Lung Modeling iii Shah Viraj

Acknowledgements

I would like to thank my Thesis advisor Dr. Andres Kriete for his outstanding guidance

and vision throughout this accomplishment and without whom this Project would not had

been possible. I shall also like to thank Saloni Shah for being an associate for the setup of

this Project and the previous collaborators Thorsten Denhard and Andreas Schmidt who

were the pioneers and developers of the foundations of this software. I shall also look

forward to Udaykiran Thummalapalli for continuing this project. Lastly I shall thank my

committee members, Dr Rami Seliktar, Dr. Fred Allen and Dr. Todd Doehring to share

their insights about the Project.

Multiscale Lung Modeling iv Shah Viraj

Table of Contents Dedications ......................................................................................................................... ii

Acknowledgements............................................................................................................ iii

Table of Contents............................................................................................................... iv

Lists of Tables.................................................................................................................... vi

List of Figures ................................................................................................................... vii

Abstract .............................................................................................................................. xi

Chapter 1. ........................................................................... 1 Background and literature

1.1. .............................................................................. 1 The anatomy of human lungs

1.2. .............................................................................. 8 Lung volumes and capacities

1.3. ................................................................................... 10 Mechanics of respiration

1.4. .................. 11 Structural change in the respiratory part of the lung (emphysema)

1.5. ..................................................... 16 Surface to volume (SV_Ratio) ratio change

Chapter 2. ..................................... 19 Previous computational models and assumptions

2.1. ....................................................................................................... 20 Introduction

2.2. ................................................................................................ 21 Previous models

2.2.1. ........................................................................ 22 Computer reference model

2.2.2. ............................................................................. 23 Modeling gas transport

2.2.4. ............................................................. 31 Benefits of QT for lung modeling

2.3. .............................................. 32 Design of user interface and steps in simulation

Multiscale Lung Modeling v Shah Viraj

2.4. ................................................................. 39 Example of modeling a normal lung

2.7 ....................................................................................................... 40 Emphysema

2.5. .................... 41 Measurement of histological and micro CT on lung emphysema

2.6. ............................................ 43 Extension of user interface to handle emphysema

Chapter 3. ....................................................................................................... 45 Results

3.1. ......................................... 45 Results of gas transport simulation in normal Lung

3.2. ....................................................................... 46 Results for emphysematic lungs

3.2.1. .......................................... 51 Emphysematic data with change in SV_Ratio

Chapter 4. ................................................................................................. 59 Discussion

4.1. ........................................................................ 61 Future extensions of the model:

List of References ............................................................................................................. 62

Vita.................................................................................................................................... 68

Multiscale Lung Modeling vi Shah Viraj

Lists of Tables Table 1: Parameters for the j airway segmentth .......................................................................24

Table 2: Quantitative analysis of the lung (Coxson, Rogers et al. 1999) ...............................41

Multiscale Lung Modeling vii Shah Viraj

List of Figures Figure 1: A) Lung anatomy, B) External anatomy of lungs (Machen 2007)............................2

Figure 2: A) Surface area of airway branching, B) Structure of a lung lobule (Machen

2007) ................................................................................................................................................3

Figure 3: Tree classification using different orderings (a) Weibel generations, (b) Strahler

Ordering and (c) Horsfield ordering (Tawhai 2001) ...................................................................4

Figure 4: Hierarchy of airways in human lung (Tawhai 2001) ...................................................5

Figure 5: A) Microscopic alveoli structure (Machen 2007), B) Cross section of Alveoli

(Greer 2007)....................................................................................................................................7

Figure 6:Lung volumes and capacities, TLC –Total lung capacity, VC – Vital capacity, IRV

– Inspiratory reserve volume, ERV – Expiratory reserve volume, RV – Residual volume, FRC

– Functional residual capacity, TV – Tidal volume (Nosek 2007)............................................10

Figure 7: Types of airflow (Wilmot C Ball Jr. 1996).....................................................................11

Figure 8: Types of emphysema; A) Normal acinus; B) Centrilobular emphysema C)

Panacinar emphysema; D) Paraseptal emphysema; E) Irregular emphysema (Roy 2007)

.......................................................................................................................................................14

Figure 9: Air trappings in Expiration due to emphysema A) Normal expiration; B) Impaired

expiration due to decreased elastic recoil (Nosek 2007).......................................................16

Figure 10: A) terminal airspaces composed of hemispheres; B) Airspaces dilate

concentrically shown with 2 positions; C) One hemisphere joins with another to form a

spherule; D) Circumferential segment of tissue with known diameter and length (L)

(Carton, Clark et al. 1964) ..........................................................................................................19

A model lung can be visualized as consisting of a large number of communicating

spaces of equal volume which are the alveoli. Assume that the spaces are hemispheres,

(Figure 10) which dilates equally and concentrically under a distending pressure, and

that their expansion is opposed only by fibers circumferentially distributed in their walls.

Multiscale Lung Modeling viii Shah Viraj

Two hemispheres can be grouped together as one spherule (Figure 11). The work of

expansion per hemisphere is half that of the spherule. The restraining fibers lie along

segments of great circles. To calculate work done on expansion, these can be grouped

together as a circumferential band or a segment (L) of known diameter..........................19

Figure 12: An airway bifurcation used in modeling gas concentration and uptake in

airways. Airway segments s1 and s2 are daughter segments of j; C is the concentration in

the segment; L is the length of the segment; A is the cross sectional area at the entrance

of the segment(Mercer, Anjilvel et al. 1991) ............................................................................26

Figure 13: Conical segments used to model a ventilatory unit. Gas flow from parent

airway generation is represented by leftmost segment. Alveolar ducts correspond to

darkened region of each conical segment where A - alveolar duct cross-sectional

area; A - alveolar plus alveolar duct cross-sectional area; L - length of each conical

segment. Ventilation-induced changes in ventilatory unit size are followed by increase in

length and cross-sectional area of conical segments.(Mercer, Anjilvel et al. 1991)

Dj

j

..........27

Figure 14: Flowchart of the simulation.......................................................................................32

Figure 15: Top) Graphical User Interface (GUI) for loading a tree geometry using the

software Bottom) Graphical User Interface (GUI) for opening a data file using the

software ........................................................................................................................................34

Figure 16: A tree structure of the lung loaded using the software and the path of gas flow

on the tree structure highlighted using the color blue............................................................35

Figure 17: A) Describes the lung physiology parameters; B) Describes the respiratory unit

(acinus geometry) .......................................................................................................................36

Figure 18: Display of approximate duration of simulation after the process is initiated .....37

Figure 19: Left) Open the result file; Right) Select the output file to open............................38

Figure 20: Left) Write the results; Right) Results data analysis time duration and acini data

selection option ...........................................................................................................................39

Multiscale Lung Modeling ix Shah Viraj

Figure 21: Log file of the simulation with the model parameters and duration of simulation

.......................................................................................................................................................40

Figure 22: 1) Micro CT of normal lung; 2) Histogram of figure 1; 3) Contrast stretched figure

2; 4) Thresholded figure 3............................................................................................................42

Figure 23: 1) Micro CT of Centrilobular emphysema; 2) Thresholded figure 1; 3) Results of

the SV_Ratio for figure 2..............................................................................................................43

Figure 24: Change in SV_Ratio to handle emphysema with other parameters on the GUI

interface .......................................................................................................................................44

Figure 25: A) Concentration (%) to time (sec) for a healthy lung with a mean +/- std. dev

of 3.753+/- 6.10; B) Concentration (%) to time (sec) for an Emphysematic lung with a

mean +/- std. dev of 2.87 +/-5.99; C) Difference in Concentration (%) to time (sec) from a

healthy to an emphysematic lung with a mean +/- std. dev of 0.883+/-1.40 .....................45

Figure 26: A) Surface to volume ratio to disease conditions of emphysema (Coxson,

Rogers et al. 1999) .......................................................................................................................46

Figure 27: 1, 3) Difference of each repetition with the first repetition showing the

repeatability of software output; 2, 4) Change in concentration for 7 generation of acini

with a mean +/- std. of 0.81+/- 0.44...........................................................................................47

Figure 28: 1, 3) Difference of each repetition with the first repetition showing the

repeatability of software output; 2, 4) Change in concentration for 7 generation of acini

with a mean +/- std. of 0.87 +/- 0.46..........................................................................................48

Figure 29: Difference in normal lung (T_V is 500 mL and S_V ratio is 34.6 mm ) to

emphysematic lung (T_V is 250 mL and S_V ratio is16.5 mm ) concentration with 1.4 +/-

0.95 (mean +/- std. dev.)

-1

-1

............................................................................................................49

Figure 30: Difference in normal lung (T_V is 500 mL and S_V ratio is 34.6 mm ) to

emphysematic lung (T_V is 500 mL and S_V ratio is16.5 mm ) concentration 0.757 +/-0.79

(mean +/- std. dev.)

-1

-1

....................................................................................................................50

Multiscale Lung Modeling x Shah Viraj

Figure 31: Normal lung uptake with a men +/- std. dev. of 2.57 +/- 0.11 for acini segment

98 and 7 generations of acini for 20 breathing cycles (4sec *20 = 80 sec)..........................51

Figure 32: Uptake for mild emphysema disease condition with a mean +/- std. dev. of

1.55 +/- 0.05 for acini segment 98 and 7 generations of acini for 20 breathing cycles (4sec

*20 = 80 sec) .................................................................................................................................52

Figure 33: Severe emphysema uptake with a mean +/- std. dev. of 0.48 +/- 0.01 for acini

segment 98 and 7 generations of acini for 20 breathing cycles (4sec *20 = 80 sec) .........53

Figure 34: Left to right, normal lung (12.08 +/- 0.28), mild emphysema (13.81 +/- 0.24) and

severe emphysema (15.39 +/-0.21), acini segment 98 and 7 generations of acini for the

20 breathing cycleth ....................................................................................................................54

Figure 35: Difference in the normal lung to mild emphysema of 1.74 +/- 0.06 for 20

breathing cycle of 4 sec (The negative sign is due to mild emphysema being greater in

concentration compared to normal lung)

th

..............................................................................55

Figure 36: Difference in normal lung to severe emphysema of 3.31 +/- 0.12 for 20

breathing cycle of 4 sec (The negative sign is due to severe emphysema being greater in

concentration compared to normal lung)

th

..............................................................................56

Figure 37: Concentration ratios for 1) Normal to mild 1 breathing cycle with a mean +/-

std of 1.2 +/- 0.3; 2) Normal to mild for 20 breathing cycle with a mean +/- std of 0.87 +/-

0.005; 3) Normal to mild for 1 breathing cycle with a mean +/- std of 1.833 +/- 1.88; 4)

Normal to mild for 20 breathing cycle with a mean +/- std of 0.78 +/- 0.009

st

th

st

th ....................57

Multiscale Lung Modeling xi Shah Viraj

Abstract A User Friendly Multiscale Lung Modeling Suite and Application

Viraj Shah Andres Kriete, Ph.D.

The development of computational lung models and the functional simulation of gas

transport is a promising avenue to investigate the effects of structural alterations as they

relate to disease and aging on the lung function. Since many changes such as emphysema

originate from the respiratory units (acini), which are the end units of the bronchial tree,

predictions about the impact on the lung function on this level of organization critically

rely on a precise modeling of the entire lung. The computational modeling suite, which

extends previous versions by a user friendly interface based on QT, allows modifying

structural properties and executing functional simulations of the entire lung including the

respiratory units. Application of this utility is demonstrated for emphysema, a disease and

aging related condition with an abnormal permanent enlargement of air spaces with the

destruction of cell walls leading to decrease in the alveolar surface area to volume ratio.

The results demonstrate the predictability of loss in function such as oxygen uptake and

change in gas concentration profiles over the breathing cycle with the severity of the

disease.

Multiscale Lung Modeling 1 Viraj Shah

Chapter 1. Background and literature

1.1. The anatomy of human lungs

The lungs are respiratory organs which are marvelously efficient and beautifully

constructed. The ventilating passages are compact and symmetrical, but there is no

conformity with regards to the finer branches and ramifications at the level of acini

(respiratory units) and alveoli and about their physiological impact on aging and disease

conditions. The development of computational lung models and the functional simulation

of gas transport is a promising avenue to investigate the effect of structural changes on

the lung function. Since acini constitute the end units of the bronchial tree, predictions

about structural changes on this level of organization critically rely on a precise modeling

of the entire lung. Therefore we first describe the structural hierarchy of the lung, which

is considered in the computational model and subsequently an approach to represent the

respiratory units in this model, suitable for simulation. While the essential steps for the

simulation process and the structural analysis of human lungs have been published

elsewhere (Mercer and Crapo 1987; Kriete 1998; Schmidt, Zidowitz et al. 2004), here we

extend the software with a user friendly interface, that allows to run simulations and

modify structural properties related to disease and aging.

As shown in figure 1 the respiratory system consists of the upper respiratory system

(mouth, nasal cavity, pharynx, and larynx) and the lower respiratory system (trachea,

bronchi, and lungs). The lower respiratory system is enclosed in the thorax, bounded by

ribs, spine and diaphragm. Each lung is conical in shape with its base resting on the

diaphragm and its apex extending superiorly to a point approximately 2.5 cm superior to


each clavicle. Lungs have a tree like structure where the trachea is the stem and there are

bronchioles, ducts and sacs which divide using bifurcation or trifurcation.

Figure 1: A) Lung anatomy, B) External anatomy of lungs (Machen 2007)

The trachea branches into two lobar bronchi, one to each lung. These primary bronchi

divide into secondary bronchi as they enter their respective lungs. The secondary

bronchi, two to the left lung and three to the right lung, conduct air to each lung.

Secondary bronchi give rise to tertiary bronchi which extend to the lobules. There are

nine lobules in the left lung and ten lobules in the right lung (Greer 2007). Bronchioles

divide numerous times to become terminal bronchioles which then divide into respiratory

bronchioles. As show in figure 2 the internal airway diameter falls from 500 µm to 270

µm between acinar generations 0 and 10, whereas the outer diameter remains constant at

700 µm. Each respiratory bronchiole branches approximately 22 more times to form

alveolar ducts that end as clusters of air sacs called alveoli. Alveolar sac is composed of


two or more alveoli that share a common opening. Each cluster of alveoli is surrounded

by elastic fibers and a network of capillaries.

Figure 2: A) Surface area of airway branching, B) Structure of a lung lobule (Machen 2007)

A terminal bronchiole is a bronchiole at the end of the conducting zone. Alveoli surface

at the transition into the respiratory zone. When the parent divides into two it is a

bifurcation or dichotomy; division into three daughter branches is a trifurcation. Different

ordering schemes have been developed to define the branching hierarchy; an overview is

given by the following methods:


Figure 3: Tree classification using different orderings (a) Weibel generations, (b) Strahler Ordering and (c) Horsfield ordering (Tawhai 2001)

Weibel Generations:

As shown in figure 3a the positions are defined in relation to the stem branch which is the

trachea. It continues towards the peripheral branches. The trachea has the lowest

generation number and each subsequent branch division produces daughter branches

which are one generation higher than the parent branch.

Strahler Ordering:

It was originally used on river systems. As shown in figure 3b it begins at the terminal

bronchiole which is usually 1. In the first part it classifies the parent branch as one order

higher than the two daughter branches of the same order or as the same order as the

highest ordered daughter branch. The second stage replaces the parent and daughter

branches of the same order with a branch of the same order.

Horsfield Ordering:

As shown in figure 3b it is an ordering system based on Strahler ordering which is more

appropriate for a lung tree. It assigns the lowest order to the terminal branches and the


parent branches are one order higher than the daughter branch of the highest order. It

produces more branches and orders than Strahler ordering for asymmetrical trees. It has

the number of orders same as the number of Weibel generations. It is better than Weibel

generations in grouping functionally similar branches in asymmetrical trees. Horsfield et

al. (Horsfield and Cumming 1968) developed the concept of delta which is the difference

in Horsfield order of two daughter branches that arise from the same parent branch. A

tree with delta = 0 is symmetric, delta = 1 describes a tree with regular asymmetry of one

order difference between daughters and higher delta values describe more asymmetrical

trees.

Figure 4: Hierarchy of airways in human lung (Tawhai 2001)

As shown in figure 4 the entrance to the exchange zone of gases begins at the respiratory

bronchioles, which is after the conducting airway zone. They are distal to the terminal


bronchioles and continue into alveolar ducts which are distal to the respiratory

bronchioles.

Alveolar ducts are the bronchioles which have alveoli on their walls in which the process

of respiration takes place. Alveolar ducts are densely studded with alveoli which form the

major part of the terminal air passages (Schulze 1871).

Approximately 40 % of the alveoli of the acinus are located on respiratory bronchioles,

including alveolar ducts, whereas 60 % are on the alveolar sacs. A similar ratio exists

between the volumes of the respiratory branches and the alveolar sacs. The size of alveoli

increases and clusters of alveoli become more numerous at the periphery. The pulmonary

alveolus comprises complex alveolated airways connected to a first order respiratory or

transitional bronchiole wherein all airways participate in gas exchange, whereas all

airways proximal to the transitional bronchiole are purely of a conducting nature. Alveoli

are functionally the largest unit in which all airways participate in gas exchange. Bulk of

acinar air moves along the intracinar airways mostly by molecular diffusion into the

residual air, whereas some oxygen diffuses radially into the alveoli.

Each alveolus is about 0.1 or 0.2 mm in diameter and each is surrounded by capillaries.

Gases are exchanged between the air and the blood by diffusion. A pair of human lungs

has about 300 million alveoli - (Dunnil 1962), providing a respiratory surface of about 70

m2 (Weibel 1963). The part of the airway that participates in gas exchange with the

pulmonary capillary blood consists of the respiratory bronchioles, alveolar ducts, and the

alveoli themselves.

Acini are complex alveolated airways distal to the terminal bronchioles, beginning with

the first order respiratory or transitional bronchiole. The longitudinal path length of


acinar airways which is defined as the distance along the ducts from the transitional

bronchiole to the alveolar sacs is on an average 8.8 mm. To model the O2 transfer from

the transitional bronchiole to the alveolar sacs the branching pattern, airway diameters

and the total length of the pathway from the entrance into the acinus to the terminal sacs,

as well as its variation between different pathways within the tree is required - (Haefeli-

Bleuer and Weibel 1988).

Figure 5: A) Microscopic alveoli structure (Machen 2007), B) Cross section of Alveoli (Greer 2007)

The acinus geometry is divided into number of generations (n), length of segment of each

acinus generation (L), acinus duct area (Ad) for each individual acinus generation and the

cross section of each acinus generation (A). The acinus includes the terminal bronchiole

and all other branches of airways (respiratory bronchioles) and air spaces (alveolar ducts,

alveolar sacs, and alveoli) distal to the terminal bronchiole. A branch is an airway or air

space with a single axial direction. A terminal bronchiole (TB) is an airway immediately

proximal to the respiratory bronchiole; its walls are covered with bronchial epithelium. A


respiratory bronchiole (RB) is an airway with RB or ducts as major outlets; its walls have

a significant amount (> 5 %) of bronchial epithelium and a few alveoli and/or sacs. A

duct (alveolar duct or AD) is an air space with several outlets: one or more sacs or ducts

and one or more alveoli. Except for limited (< 5 %) patches of bronchial epithelium, its

walls consist entirely of the margins of orifices of its single inlet and several outlets. It is

not an air space with only alveoli as outlets. A sac (alveolar sac or AS) is an air space

with only alveoli as outlets. An alveolus (A) is a terminal air space without outlets. If a

terminal air space has low partitions (i.e., mean partition height is 10 % or less than mean

orifice diameter), it is defined as a sac with daughter alveoli. An alternate definition

would be to call this terminal airspace a complex alveolus. In numbering generations, the

number increases as one move’s distally. Siblings belong to the same generation;

daughters and progeny are distal; parents are proximal. One can begin counting

generations at several different sites in the lung, e.g., at the start of any new type of

airway or air space. Thus the same duct might be identified as a 22nd generation branch

of the pulmonary tree, a 7th generation branch of the acinus, and a 3rd generation branch

of ducts.

1.2. Lung volumes and capacities

As shown in figure 8 the air in the lung is classified in two divisions, which are the lung

volumes which can be breathed by the subjects and the lung capacities which include two

or more primary volumes.

Tidal volume is the volume of air inhaled and exhaled with each breath and it is 500

(milliliter) mL in a resting human. It signifies the normal depth of breathing.


Inspiratory reserve volume is the additional amount of air which can be inspired at the

end of normal inspiration and 3300 mL is a normal value.

Expiratory reserve volume is the amount of air that can be expired out forcefully after

normal expiration and 1000 mL is the normal value.

Residual volume is the air that remains in the lungs even after the forced expiration and it

helps to aerate the blood in between breathing and expiration and 1200 mL is the normal

value.

Inspiratory capacity is the maximum volume of air that can be inspired starting from end

expiratory position. It includes tidal volume and inspiratory reserve volume and 3800 mL

is the normal value.

Vital capacity is the maximum amount of air which can be expelled out forcefully after a

maximal inspiration. It includes the inspiratory reserve volume, tidal volume and

expiratory reserve volume and 4800 mL is the normal value.

Functional residual capacity is the volume of air remaining in the lungs after normal

expiration. It includes expiratory reserve volume and residual volume, and 2200 mL is

the normal value.

Total lung capacity is the amount of air present in the lungs after a maximal inspiration

and it includes all the volumes and 6000 mL is the normal value.


Figure 6:Lung volumes and capacities, TLC –Total lung capacity, VC – Vital capacity, IRV – Inspiratory reserve volume, ERV – Expiratory reserve volume, RV – Residual volume, FRC – Functional residual capacity, TV – Tidal volume (Nosek 2007)

1.3. Mechanics of respiration

Air flows into and out of the lungs when air pressure within the lung differs from the

pressure of external air. As shown in figure 7 when alveolar pressure is less than

atmospheric pressure, air flows into the lungs, and inspiration occurs. The pressure in the

lungs is varied by changes in the volume of the thoracic cavity. These changes are

brought about by the contraction and relaxation of the muscular diaphragm and the

intercostal muscles. Inhalation is accomplished by contracting the diaphragm, which

flattens it and lengthens the thoracic cavity and by contracting the intercostal muscles that

pull the rib cages up and out. These movements enlarge the thoracic cavity, the pressure


within it falls, and air moves into the lungs. Air is forced out of the lungs as the muscles

relax, reducing the volume of the chest cavity and increasing the pressure.

Figure 7: Types of airflow (Wilmot C Ball Jr. 1996)

During quiet breathing, laminar flow exists from the medium-sized bronchi down to the

level of the bronchioles. During exercise, when the air flow is more rapid, laminar flow

may be confined to the smallest airways. Transitional flow, which has some of the

characteristics of both laminar and turbulent flow, is found between the two along the rest

of the bronchial tree.

1.4. Structural change in the respiratory part of the lung (emphysema)

Emphysema is a condition of the lung characterized by abnormal, permanent enlargement

of the air spaces distal to the terminal bronchiole, accompanied by destruction of their

walls (ATS 1962). Similar definitions have been adopted by the World Health

Organization (WHO 1961). Destruction of emphysema is classified with parameters of

fenestrae (the presence of abnormal holes), the destructive index, the loss of alveolar


surface area, mean linear intercept (Lm), air space wall per unit volume (AWUV) and

loss of alveolar attachments (Thurlbeck and Muller 1994).

Fenestrae are discontinuities of alveolar walls seen on thick sections of human lungs

(Boren 1962). These structural alterations can be diagnosed histopathologically or by

using micro – CT imaging techniques (Watz, Breithecker et al. 2005)

The destructive index (DI) is a recent innovation (Snider) suggested as a criterion for

alveolar wall destruction. The DI has three components:

1) Breaks in alveolar walls (DIb)

2) Type II cell metaplasia of alveolar walls, often accompanied by some

alveolar wall fibrosis (DIf)

3) Classic emphysema (DIe)

Loss of alveolar surface area is a good method of measuring destruction. Lm is the length

of a test line placed over histologic slides of the lung divided by the number of times the

line crosses alveolar walls (not surfaces). It is an approximation of air space (alveolar

ducts, alveolar sacs, and alveoli) size; it is not the mean chord length of alveoli. Alveolar

surface area (SA) is calculated from (Weibel 1963; Underwood 1970).

SA = 4V / Lm …Equation 1

In this formula, V is the volume of the lung in which Lm is measured. Rearrangement of

this formula shows that SV_Ratio (AWUV) is 4/Lm. Lm and AWUV (Gillooly and

Lamb 1993; Gillooly and Lamb 1993)) are thus reciprocals. Lm will increase if alveolar

walls are destroyed, because their loss results in fewer intercepts, or if there is over

inflation, which causes a greater distance between intercepts.


Loss of alveolar attachments is considered to be a cause of airflow obstruction in

emphysema (Pratt, Haque et al. 1961; Anderson and Foraker 1962), especially on

expiration, loss of alveolar attachments to bronchioles has recently been described as

representing “an early stage of the destruction of lung parenchyma”(Saetta, Ghezzo et al.

1985). Bronchioles are thought to be tethered by their attachment to alveolar walls, and

associations have been described between loss of alveolar wall attachments and the

percentage of alveoli destroyed (Wright 1989) or the presence and severity of

macroscopic emphysema (Petty, Silvers et al. 1986; Nagai A 1991). There is progressive

destruction of alveoli and the surrounding tissue that supports the alveoli. With more

advanced disease, large air cysts develop where normal lung tissue used to be. Air is

trapped in the lungs due to lack of supportive tissue which decreases oxygenation.

Destruction may be recognized by the disorder of the respiratory airspaces. The major

mechanism of airflow limitation is loss of elastic recoil.

Primary emphysema:

It is commonly linked to an inherited deficiency of the enzyme α1 – antitrypsin which is

a major component of α1 – globulin which is a plasma protein and as seen from figure 5.

It inhibits the action of many proteolytic enzymes and so individuals with the deficiency

of this enzyme have a greater likelihood of developing this disease.

Secondary emphysema:

It is caused due to the inability of the body to inhibit proteolytic enzymes in the lungs due

to cigaratte smoke and air pollution.


A

D B

C E

Figure 8: Types of emphysema; A) Normal acinus; B) Centrilobular emphysema C) Panacinar emphysema; D) Paraseptal emphysema; E) Irregular emphysema (Roy 2007) Types of emphysema classified according to the portion of the acinus first involved with the disease (University 2005)

1.) Centrilobular (Centriacinar) emphysema: As seen from figure 8b there is

septal destruction in the respiratory bronchioles and alveolar ducts usually in the

upper lobes of the lung. The alveolar sac which is distal to the repiratory

bronchiole remains intact. It occurs mainly in smokers with chronic bronchitis. It

involves the proximal part of the acinus. The destroyed and enlarged respiratory

bronchioles form airspaces that are separated from each other and from lobular


septa by normal alveolar ducts and sacs. It is most common and most severe in the

upper zones of the lung (upper lobe and superior segment of lower lobe).

2.) Panacinar (panlobular) emphysema: As seen from figure 8c it involves damage

in the entire acinus which is more randomly distributed and involves lower lobes

of the lungs. It occurs in patients with α1 – antitrypsin deficiency. Panacinar

emphysema is often associated with centrilobular emphysema where the

panacinar form tends to occur in the lower zones of the lung and centrilobular

emphysema is seen in the upper ones.

3.) Paraseptal (subpleural) emphysema: As seen from figure 8d it involves the

alveolar ducts and sacs at the emphysematous areas. It is seen typically in a young

adult with history of a spontaneous pneumothorax and is also seen in older

patients with centrilobular emphysema.

4.) Irregular emphysema: As seen from figure 8e there is no consistent relationship

to any alveoli, bronchioles and ducts but is always associated with fibrosis.

Effects of emphysema:

1.) As seen from figure 9 expiration becomes difficult because loss of elastic recoil

reduces the volume of air that can be expired passively.

2.) There is development of large air spaces in alveoli and air spaces adjacent to

pleura because of hyperinflation.

3.) Thus the increased residual volume in the alveoli and the diminished caliber of

the bronchiole causes the part of the inspiration to be trapped in the acinus.


A B

Figure 9: Air trappings in Expiration due to emphysema A) Normal expiration; B) Impaired expiration due to decreased elastic recoil (Nosek 2007)

4.) Damaged alveolar walls do not support and hold open the airways, so alveoli lose

their property of passive elastic recoil. All these contribute to collapse during

expiration.

1.5. Surface to volume (SV_Ratio) ratio change

The total alveolar surface area is a first estimate of the overall area available for gas

exchange in the lungs. The surface area is proportional to the air tissue interface.


Morphometric (Haefeli-Bleuer and Weibel 1988; Verbeken, Cauberghs et al. 1992;

Kitaoka, Takaki et al. 1999) studies have consistently found an increase in the average

distance between airspace walls (mean linear intercept (Lm)) and a decrease in the

surface area of airspace wall per unit of lung volume (SV_Ratio) beginning in the third

decade of life. The decrease in SV_Ratio is approximately linear and continues

throughout life, resulting in a 25 ± 30% decrease in nonagenarians (Thurlbeck 1967;

Gillooly and Lamb 1993). Although these changes are histologically different from

emphysema (no destruction of alveolar walls), they result in similar changes in lung

compliance. These changes have been designated as "senile emphysema" (Verbeken,

Cauberghs et al. 1992). A consequence of the reduction in supporting tissues around the

airways is a tendency for the small airways (<2 mm) to collapse. Premature closure of the

airways may, therefore, occur during tidal breathing. Furthermore, the flattening of the

internal surface of the alveoli is associated with a reduction in alveolar surface (75 m2 at

age 30 yrs and 60 m2 at age 70 yrs, a reduction of 0.27 m2.yr-1) (RO 1993).

Most lungs with minimal emphysema are thought to have elements of both panacinar and

centracinar emphysema while the panacinar type predominated in the three more severely

affected lungs. The gross appreciation of emphysema generally agrees well with

decreases in SV_Ratio determined from histologic sections. The distinction between

normal lung parenchyma and mild emphysema, particularly of the panacinar type, is not

always easy to make and determination of the SV_Ratio may be the best objective

method of detecting mild alveolar destruction (Niewoehner, Kleinerman et al. 1975)

The overall elastic behavior of the lung results from the complex interrelationship of

many factors including surface tension at the air-liquid interface, the material properties


of individual tissue elements, particularly collagen and elastin, and the arrangement of

these protein fibers in space and with each other. The elasticity of complex meshworks is

imparted not only by the elastic properties of individual fibers but also by their

organization. A frequently cited example to illustrate this point is the stiffness of single

nylon fibers compared to the compliant behavior of woven nylon. There are similar

examples in biological tissues (Thurlbeck 1967; Masaryk University 2005). The close

relationship observed between SV_Ratio and elasticity is consistent with the concept that

alveolar shape may be an important determinant of a lung’s elastic properties. This idea is

also supported by the observation that the relationship between SV_Ratio and elasticity

pertains for both normal and emphysematous lungs. The basic morphological processes

in aging and in emphysema are generally considered to be different. With aging the

alveolar duct increases in diameter while subtending alveoli become wider and shallower.

The outer diameter of this basic parenchymal subunit does not change significantly

(Weibel 1963). The anatomical change in emphysema is distinct in that extensive

destruction of alveolar walls occurs.


Chapter 2. Previous computational models and assumptions

The modeling and functional simulation has to consider the inherent hierarchies of

biological structures, their properties and interdependencies from cellular organelles to

macroscopical anatomical structures. The lung requires an investigation of some

thousand air conducting bronchial segments, respiratory units (acini) at microscopic

resolution. A symmetric model assumes the dichotomy at each level of branching which

is not the true case (Weibel 1963) and the asymmetric model is essential for increasing

the accuracy of lung morphology (Horsfield, Dart et al. 1971). An asymmetric tree

comprises of uneven airway paths, but emulates the process of gas exchange at the

alveolar level of the lung generation.

Figure 10: A) terminal airspaces composed of hemispheres; B) Airspaces dilate concentrically shown with 2 positions; C) One hemisphere joins with another to form a spherule; D) Circumferential segment of tissue with known diameter and length (L) (Carton, Clark et al. 1964)

A model lung can be visualized as consisting of a large number of communicating spaces

of equal volume which are the alveoli. Assume that the spaces are hemispheres, (Figure


10) which dilates equally and concentrically under a distending pressure, and that their

expansion is opposed only by fibers circumferentially distributed in their walls. Two

hemispheres can be grouped together as one spherule (Figure 11). The work of expansion

per hemisphere is half that of the spherule. The restraining fibers lie along segments of

great circles. To calculate work done on expansion, these can be grouped together as a

circumferential band or a segment (L) of known diameter.

2.1. Introduction

Beginning with the plastic cast of the human lung, the topology of the lung is analyzed

with classification schemes of Strahler ordering. The bronchial tree can be modeled by

regular dichotomic branching pattern, but that way it does not reproduce the cast

completely. The segments of identical order should have identical length while the distal

segments have less asymmetry. There is a relation between step size, branching angle,

length and diameter which are incorporated in the model. All these parameters provide

the database before the modeling can commence. The branching pattern of the conductive

part ends in a more dichotomic form, where the transition is from monopodial to

dichotomic branching pattern. To model the morphology of complete lung a combination

of main stem bronchi, lobes and respiratory units are modeled in unison. An iterative

method is used to determine the gas concentration. The gas concentration is described as

the mass transport due to convection, molecular diffusion and uptake. Each bronchial

segment gains mass from the distal segments and losses mass due to transport or gas

uptake in the daughter segment. The parameters used for computation are diffusion

coefficient, difference of concentration across segment and gradient, flow partitioning


and dispersion coefficient. The respiratory units are classified by a SV_Ratio and gas

uptake coefficient.

For each of the segment an equation describes the conservation of mass. An iterative

method is used as a solution for the complete bronchial tree, with 10,000 time steps

necessary for a stable solution. For each segment at each time step the mass transport

equation is a differential equation which is solved by Gauss Seidel iteration. The

calculation are performed from the first order to the more distal order branches down to

the respiratory units and concentrations is stored for each segment. A stable solution is

reached after several calculations. The gas uptake can be determined at different tidal

volumes.

2.2. Previous models

User friendly software was developed, implementing previously developed models for

the structural and functional simulation of gas transport. The models previously

developed include a dichotomic branching pattern (Fleming, Halson et al. 1996; Kitaoka,

Takaki et al. 1999; Lazaridis, Broday et al. 2001; Schroeter, Fleming et al. 2002), a

representation that has its origin in the so-called trumpet model (Weibel 1963) that is

used with geometric adjustments introduced later (Erichsen, Lau et al. 1979). This is a

simplification of the lung geometry that assumes a spatially symmetric branching, a fixed

relation of the cross sections of a parent branch with the daughter branches, and a

constant length of all possible spatial trajectories between the trachea and any terminating

bronchiole. This model is self-similar regarding spatial scaling properties and as such it

reveals fractal properties. Even though the human bronchial tree, at least for the first six


generations, exhibits a most symmetrical branching if compared to a wide variety of

species, irregular and asymmetric branching pattern cannot be neglected (Schlesinger and

McFadden 1981; Patra 1986). Therefore, regular symmetric models do not predict gas

flow and particle deposition reliably, and more realistic models are needed to increase

accuracy. Dichotomic branching models also tend to fill space in a spheric fashion and

cannot be adapted to the form and volume of the human lung (Sciurba, Rogers et al.). For

the local analysis of air flows, more sophisticated models are in use to show that many of

the transport processes within the airways depend quite sensitively on the geometry of the

bronchial bifurcations and the structure of the boundaries (Balásházy 1999; Darquenne

2001; Martonen 2001). But in the global modeling of the tracheobronchial tree, efforts

rely on stochastic models (Koblinger 1990; Martonen 2000) or synthesize the underlying

structure from fixed scaling laws (Kitaoka, Takaki et al. 1999) based on a small number

of anatomic examinations. These models meant to represent a mean adult lung, rather

than describing the lung of a specific individual.

2.2.1. Computer reference model

The reference model - (Schmidt, Zidowitz et al. 2004) of the bronchial tree of a normal

lung is based on high resolution computer tomography (HRCT) imaging of an in – vitro

preparation (Schmidt 2006). The software is designed on the lines of the parse tree which

has nodes which are roots, branches or leaves. The nodes are either parent or children

which get connected by branches. The lungs have a tree like structure where the trachea

is the stem and the branches arising from it are the bronchi, bronchioles, ducts and sacs. It

further handles the model parameters and the coefficients. The model takes the input


parameters from the segmented data which includes the drain area, edges of the

generations, co – ordinates, length, volume, Strahler order, predicted and successive

generation for each branch. The parent branch gives rise to daughter branches and the

process continues in hierarchy.

2.2.2. Modeling gas transport

The central purpose in implementing the mass transport is to assess the significance of

the measured variation in ventilatory unit size on the uptake of inhaled gases by the gas

exchange region of the lungs. For this purpose, some simplifying assumptions were

made:

(1) The influence of radial concentration gradients on the axial dispersion of gas in

the airways is not included.

(2) The influence of radial diffusion on the axial dispersion of gas from alveolar ducts

to the adjacent alveoli is not included.

(3) The influence on transport in the airways by interactions among convection,

diffusion, and uptake in the walls is approximated by using an effective diffusion

coefficient based on empirical measurements (Scherer, Shendalman et al. 1975).

(4) Uptake at the airway walls is governed by a single mass transport coefficient that

is the same for all airways.

(5) The partitioning of flow at airway bifurcations is proportional to the distal

alveolar volume.

(6) The non alveolated conducting airways do not change dimensions with lung

inflation and deflation.


Thus, the results based on the simplifying assumptions will give a conservative estimate

of the variations in ventilatory unit uptake of inhaled gases. For this implementation,

follow previous model implementation (Mercer, Anjilvel et al. 1991), which have

been developed to simulate portions of murine lungs. Hereby, the transport of gas is

governed by diffusion (mostly in the acini), convection and uptake, and for each time step

the following formulation applies.

… Equation 2

Aj Area in mm2

Cj Average gas concentration in % or µg / m3

Dj Effective diffusion coefficient in mm2 / sec

Kaw Mass transport coefficient in mm / sec

Lj Length in mm

mij Mass in segment j at time step i

SV_Ratioj Surface to volume ratio in mm-1 (mm2 / mm3)

Uj Velocity in mm / sec (> 0 for inspiration and < 0 for expiration)

ΔUC Difference in concentration across segment

ΔDC Difference in concentration gradient

Δt Difference in time between steps I and i+1 in sec

Table 1: Parameters for the jth airway segment


An airway segment (j), which supplies two distal segments, is illustrated (Figure 12). The

general equation for mass balance (Equation 1) can be expressed as a function of the

fluxes across interfaces with its proximal airway segment (j - 1) and distal segments (s1

and s2). This mass balance, in terms of concentrations (C) at time step i, in Equation 2,

gives the change in mass due to transport by diffusion (D), convective flow of gas (U),

and loss from the segment by uptake at the wall (Kaw) as follows:

…Equation 3

Where,

… Equation 4

In Equation 4, A*j refers to the area of a cylinder with the same volume and length as

airway segment j and is computed in Equation 3 on the basis of the upstream cross

sectional area (Aj) and the total cross-sectional areas of the two daughter segments (As1

and As2).


Figure 12: An airway bifurcation used in modeling gas concentration and uptake in airways. Airway segments s1 and s2 are daughter segments of j; C is the concentration in the segment; L is the length of the segment; A is the cross sectional area at the entrance of the segment(Mercer, Anjilvel et al. 1991)

The use of cross-sectional area in Equation 4 is mathematically equivalent to assuming

that the airway segments are tapered and allows simulations to be run for previously

published single-equivalent path models of ozone dosimetry (Miller, Menzel et al. 1978;

Miller 1985), which are specified in terms of the variations in cross-sectional area vs.

distance.

Flow partitioning to the daughter airway segments was based on the distal ventilatory

unit volume (Vvudistal) for the daughter relative to the total ventilatory unit volume

(Vvutotal) as given in the example for daughter segment s1.

… Equation 5


Equation 3, when solved for Ci+l, can be used to explicitly determine the concentration in

one segment at time step i + 1 without knowledge of the concentration at the next time

step i, adjacent segments.

Gauss-Seidel iteration (Flannery B.P. 1988) is used to simultaneously solve the set of

equations giving concentration in each jth segment at the i + 1 time step. For this iteration

process (Mercer, Anjilvel et al. 1991) appropriate values for each airway segment (and

corresponding equations for the alveolar segments of each ventilatory unit) was

iteratively solved using the most recently computed values for concentration at the i+1

time step used in adjacent segments. Computations were terminated when successive

iterations through the entire system of segments changed by a maximum of 0.1 % in any

segment to simultaneously giving concentration (and corresponding equations for the

alveolar segments).

Figure 13: Conical segments used to model a ventilatory unit. Gas flow from parent airway generation is represented by leftmost segment. Alveolar ducts correspond to darkened region of each conical segment where ADj - alveolar duct cross-sectional area; A - alveolar plus alveolar duct cross-sectional area; Lj - length of each conical segment. Ventilation-induced changes in ventilatory unit size are followed by increase in length and cross-sectional area of conical segments.(Mercer, Anjilvel et al. 1991)


The corresponding mass transport equation for each segment of the ventilatory unit is

similar to that given for the airways. As illustrated (Figure 17), the model for the

ventilatory unit is specified by a series of tapered cones where the taper is specified by

the measured changes in cross-sectional area vs. distance for the alveolar ducts and

alveolar subdivisions.

The principal differences from the airway segment equation correspond to the addition of

an alveolated compartment around the alveolar ducts and the variation in length and

cross-sectional area of each segment with ventilation. In this model, gas convection and

diffusion are assumed to occur at the interfaces between segments formed by the alveolar

ducts (cross-sectional area, AD) while the total volume of the segment includes both-the

alveolar and alveolar duct subdivisions (volume-equivalent cross-sectional area, A*).

Chemical reactions occur at the alveolar walls, which are distributed in the segment

volume. The amount of uptake is proportional to the total alveolar surface per segment,

which depends on the volume of the segment (A*L), and the alveolar surface-to-volume

ratio (SV_Ratio) times a mass transfer coefficient (Kalv)

Initially, the concentration in all airway and alveolar segments is assumed equal to the

tissue concentration of the gas (which is CV for oxygen). The concentration at the airway

segment that was the input to the model was fixed at 21% for O2. To obtain a solution for

uptake by the ventilatory units, the simulation is run until the changes in uptake by the

ventilatory units in successive breaths was 1%. A concentration of 5.26% was used for

tissue oxygen back pressure (CV). The uptake of oxygen in the airways was assumed to

be negligible. A molecular diffusion coefficient of 17.3 mm2 /sec was used for O2.


2.2.3. Qt GUI features

In order to develop a user friendly interface for the computational modules of this

software, we have considered QT. It has the features for robustness and easy object

oriented programming toolkits which add to the reusability. QT supports the development

of cross platform GUI applications with its “write once, compile anywhere” approach.

Using a single source tree and a simple recompilation, applications can be written for

many operating systems. Qt introduces a unique inter-object communication mechanism

called “signals and slots”. Qt applications can be built visually using Qt Designer, a

flexible user interface builder with support for IDE (Integrated Development

Environment) integration (Trolltech 2007).

2.2.3.1. QObject Class

The QObject class is the base class of all Qt objects and is the heart of the Qt object

model. The central feature in this model is a very powerful mechanism for seamless

object communication called signals and slots. QObjects organize themselves in object

trees. When a QObject is created with another object as parent, the object will

automatically do an insertChild ( ) on the parent and thus show up in the parent's children

( ) list. The parent takes ownership of the object i.e. it will automatically delete its

children in its destructor. Every object has an object name ( ) and can report its

className ( ) and whether it inherits ( ) another class in the QObject inheritance

hierarchy. The QObject macro is mandatory for any object that implements signals, slots

or properties and also the moc program (Meta Object Compiler) has to be run on the

source file. Using this macro in all subclasses of QObject regardless of whether or not


they actually use signals, slots and properties, prevents functions to exhibit undefined

behavior.

2.2.3.2. Signals and Slots:

Signals and slots are used for communicating between objects. The signal/slot

mechanism is a central feature of Qt and probably the part that differs most from other

toolkits. In GUI programming, there are changes in one widget which are to be notified to

other widgets. The objects of any kind should be able to communicate with one another.

Older toolkits achieve this kind of communication using callbacks. A callback is a pointer

to a processing function. Callbacks have two fundamental flaws. Firstly they are not type

safe, where there is no certainty that the processing function will call the callback with

the correct arguments. Secondly the callback is strongly coupled to the processing

function since the processing function must know which callback to call. An alternative

to the callback technique is signals and slots. A signal is emitted when a particular event

occurs. Qt has widgets which have many pre-defined signals and there can be addition of

new subclasses. A slot is a function which is called in response to a particular signal. It

even has widgets which have many pre-defined slots and there are benefits of adding

slots so that handling any signal can be easily maneuvered. The signals and slots

mechanism is type safe, where the signature of a signal must match the signature of the

receiving slot. In fact a slot may have a shorter signature than the signal it receives

because it can ignore extra arguments. Since the signatures are compatible, the compiler

helps to detect type mismatches. Signals and slots are loosely coupled where a class

which emits a signal is independent of the slots which receive the signal. Qt's signals and


slots mechanism ensures that if a signal is connected to a slot, the slot will be called with

the signal's parameters at the right time. Signals and slots can take any number of

arguments of any type. All classes that inherit from QObject or one of its subclasses (e.g.

QWidget) can contain signals and slots. Signals are emitted by objects when they change

their state in a way that may be interesting to the outside world. This is all the object does

to communicate. It is independent about whether anything is receiving the signals it

emits. This is true information encapsulation, and ensures that the object can be used as a

software component. Slots can be used for receiving signals, but they are also normal

member functions. Just as an object does not know if anything receives its signals, a slot

does not know if it has any signals connected to it. This ensures that truly independent

components can be created with Qt. There can be as many signals connected to a single

slot, and a signal can be connected to as many slots after that. It is even possible to

connect a signal directly to another signal which will emit the second signal immediately

whenever the first is emitted. Together, signals and slots make up a powerful component

programming mechanism.

2.2.4. Benefits of QT for lung modeling

The library provided by Qt has the modules for functionality, GUI classes and Open GL.

Qt designer has an advantage to use icons to stand for data which have a powerful GUI

layout and forms builder. It has advanced features for preview, widget layout and

property editor. For designing the user interface for changing the simulation parameters,

statistics layout, results, parameters and the graphics parameters Qt has the versatility to

design each window with a new feature within it.


It provides for easier memory management because child objects are automatically

deleted when their parents are, this approach largely combines the ease of use of garbage

collected languages with the efficiency and lower resource consumption of C++. GUI

layout can specify which parts of the layout should be grouped, which should stretch and

which should be constrained.

2.3. Design of user interface and steps in simulation

Figure 14: Flowchart of the simulation

1. Load the tree geometry: Open the data file as shown (Figure 15) using the File

option menu. After hitting that option the browser takes to the root directory of


software, where the data files are stored. Using the select tool, select one of the

files needed for the operation. The data files are in the format of the segmented

tree data structures with the number of nodes and edges. Within the structure of

the file the nodes and edges are separated for the number of generations and

ordering of the tree structure. QT uses this organization to extract the data from

the input files.


Figure 15: Top) Graphical User Interface (GUI) for loading a tree geometry using the software Bottom) Graphical User Interface (GUI) for opening a data file using the software

Depending on the complexity of the data the number of generations in the display shall

display the hierarchy of the tree structure.

2. Highlight the path for modeling the gas uptake: Select the path as shown in figure

16 for simulation and use the palette of controls to perform additive, subtractive,

logical operations, branch selection, pan, zoom, x, y and z rotation at each level of

branching.


Figure 16: A tree structure of the lung loaded using the software and the path of gas flow on the tree structure highlighted using the color blue

3. Select the simulation parameters: Using the GUI, select the parameters for the

simulation as shown in figure17. Except the surface to volume ratio all the

physiological parameters remain constant for the test conditions of emphysema.

Change the acinus geometry in some instances to check for the dimensional

changes.


A: Physiological Parameters B: Acinus Geometry

Figure 17: A) Describes the lung physiology parameters; B) Describes the respiratory unit (acinus geometry)

4. Start the simulation: Start the simulation for the gas uptake and concentration

profiles at inspiration and expiration. As seen from figure 18 the display window

shows the time span of the simulation with an estimated wait time for execution,

after which it displays a successful completion of the process.


Figure 18: Display of approximate duration of simulation after the process is initiated

5. Open the result file: After the simulation is completed go to the file menu and

open the output file as shown in figure 19 with concentration profiles for the

entire tree path of the simulation. It holds information for the number of

generations of acini and number of branches.


Figure 19: Left) Open the result file; Right) Select the output file to open

6. Analyze and write the results: Select the analyze option and write the results for 0

to 4 sec interval as shown in figure 20 or whatever duration of breathing cycle the

process was initialized for the branches and all the acini for selected branches.


Figure 20: Left) Write the results; Right) Results data analysis time duration and acini data selection option

2.4. Example of modeling a normal lung

The log file gives the information for the parameters selected for the simulation. It gives

the file selected for performing the operation, end time of each respiratory cycle in

seconds (End time), time step for each simulation (Delta T), actual output delta in

seconds (OutputDelta), initial concentration of the trachea in percentage of gas

(C_Trachea), tidal volume of intake in milliliters (mL) (V_tidal), maximum speed in

trachea in mm/sec (U_trachea), period of one breathing cycle which is inspiration with

expiration in seconds (Period), alveolar diffusion coefficient in mm2/ sec (D_alv),

surface to volume ratio in mm-1 (SV_Ratio), venous backpressure in mmHg (C_v), initial

concentration of gas in % (C_initial) and the total time of simulation in seconds.


Figure 21: Log file of the simulation with the model parameters and duration of simulation

2.7 Emphysema

In order to extend the model of a normal lung with a simulation of an emphysematic

lung, the structural properties of the respiratory units needs to be changed. The required

data was published in - (Coxson, Rogers et al. 1999) and was collected from a group of

patients with CT scan analysis performed and SV_Ratio was collected from patients with


control and emphysema groups. The separation into three groups was based on the

percent of the lung that was determined to be emphysematous using the “density mask”

technique. For the process of simulations the below data (Table 2) is used for the surface

to volume ratio for the normal, mild emphysema and severe emphysema groups. This

entire setup is used to check the change in concentration at each stage of disease with the

influence from the change in surface to volume ratio which is the main change seen in

emphysema and aging which has the similar modification. The data used for the

measured cases is used for the calculation.

Table 2: Quantitative analysis of the lung (Coxson, Rogers et al. 1999)

2.5. Measurement of histological and micro CT on lung emphysema

In addition to the data provided in the literature, we also measured SV_Ratio in

histological and micro CT images. The image data has been used previously to perform a


visualization of the fine structure of the bronchial tree (Watz, Breithecker et al. 2005).

Micro tomography uses X - rays to visualize smaller objects with cross section of the

pixels in the micrometer range to give high spatial resolution and exceptional speed of

operation. The internal structures are reconstructed as a set of flat cross sections where

the process is non destructive. The micro CT of normal lung in fig. 27.1 clearly

demarcates the alveoli of a normal lung parenchyma, where a respiratory bronchiole is

dividing two alveolar ducts.

1 2

3 4

Figure 22: 1) Micro CT of normal lung; 2) Histogram of figure 1; 3) Contrast stretched figure 2; 4) Thresholded figure 3


The successive figures show the histogram of the original, followed by the contrast

stretching and thresholding with Image J toolkit which gives a SV_Ratio of 27.59 mm-1

for a normal lung. The alveoli are enlarged and the alveolar septa are missing in fig. 28

which highlights the features of emphysema. The SV_Ratio is calculated by thresholding

the original image using Image J toolkit and then calculating the perimeter and area of the

fig 28.3 which gives a ration of 4.84 mm-1.

Figure 23: 1) Micro CT of Centrilobular emphysema; 2) Thresholded figure 1; 3) Results of the SV_Ratio for figure 2

31 2

The data measured is along the lines of the measured data (Coxson, Rogers et al. 1999)

and the SV_Ratio from the published data is used for the simulation in the model.

2.6. Extension of user interface to handle emphysema

Change in the surface to volume ratio is the main characteristic of emphysema (see figure

8). The SV_Ratio we are using for our simulations changed from 34.6 mm-1 to 16.5 mm-1

to 4.3 mm-1 for normal to mild emphysema to severe emphysema conditions of the lungs

respectively. We assumed a situation of panacinar emphysema (see figure 8c) with equal


changes in all segments of the respiratory model. Thus the change in SV_Ratio is entered

as a single parameter (see figure 24). The simulation process is repeated for 20 breathing

cycle for achieving a stable condition.

Figure 24: Change in SV_Ratio to handle emphysema with other parameters on the GUI interface


Chapter 3. Results

3.1. Results of gas transport simulation in normal Lung

In the Figure 25, the normal lung gas uptake for a single breathing cycle with a tidal

volume of 500 mL and surface to volume ratio of 34.6mm-1 is compared to an

emphysematic lung with a surface to volume ratio of 16.5 mm-1 and tidal volume of

250mL.

Figure 25: A) Concentration (%) to time (sec) for a healthy lung with a mean +/- std. dev of 3.753+/- 6.10; B) Concentration (%) to time (sec) for an Emphysematic lung with a mean +/- std. dev of 2.87 +/-5.99; C) Difference in Concentration (%) to time (sec) from a healthy to an emphysematic lung with a mean +/- std. dev of 0.883+/-1.40


3.2. Results for emphysematic lungs

Figure 26: A) Surface to volume ratio to disease conditions of emphysema (Coxson, Rogers et al. 1999)

In fig. 26 the measured and predicted data (Coxson, Rogers et al. 1999) for normal lung

and emphysematic lung with change is surface to volume ratio are compared. In fig. 30

and 31 the repeatability of software is tested for 20 repetitions and the variability for 7

generations of acini is tested for mild and severe conditions of emphysema. The mild


emphysema and severe emphysema have a SV_Ratio of 16.5 mm-1 and 4.5 mm-1

respectively.

1 2

3 4

Figure 27: 1, 3) Difference of each repetition with the first repetition showing the repeatability of software output; 2, 4) Change in concentration for 7 generation of acini with a mean +/- std. of 0.81+/- 0.44


1 2

43

Figure 28: 1, 3) Difference of each repetition with the first repetition showing the repeatability of software output; 2, 4) Change in concentration for 7 generation of acini with a mean +/- std. of 0.87 +/- 0.46


Figure 29: Difference in normal lung (T_V is 500 mL and S_V ratio is 34.6 mm-1) to emphysematic lung (T_V is 250 mL and S_V ratio is16.5 mm-1) concentration with 1.4 +/- 0.95 (mean +/- std. dev.)

In figures 27 and 28 the reproducibility of the software is tested for 20 repetitions. The

variability is none in the software. The mild emphysema has SV_Ratio of 16.6 mm-1 and

severe emphysema has 4.3 mm-1 where there is change in concentration for an acini

tested. The branches 23, 29 and 88 belong to the 5th, 8th and 12th generations respectively

for fig. 32 and 33. The branches from the 5th and 8th generations belong to the upper and

lower lobes of the right lung respectively and branches from the 12th generation belong to

the left lower lobe.

Minute Volume = [Tidal volume × Respiration rate]… Equation 6

Where, respiration rate is 15 breaths / min


Figure 30: Difference in normal lung (T_V is 500 mL and S_V ratio is 34.6 mm-1) to emphysematic lung (T_V is 500 mL and S_V ratio is16.5 mm-1) concentration 0.757 +/-0.79 (mean +/- std. dev.)

The alveolar ventilation rate which is the volume of entering respiratory bronchiole and

alveoli during a minute changes from 5.25 mL/min to 1.5 mL/min in emphysema. So

when the dead space to tidal volume ratio reduces the effective ventilation reduces.

Alveolar Ventilation Rate (mL/min) = [(Tidal volume – Dead space) × (Respiratory rate

/ min)] … Equation 7

In fig 31 to 33 there are 7 generations of acini compared for concentration to time from a

normal to mild emphysema to severe emphysema conditions. The fig. 44 and 45 compare

the difference of normal lung to emphysematic conditions and fig 46 shows the ratio of

disease conditions to normal lung for first and twentieth breathing cycles.


3.2.1. Emphysematic data with change in SV_Ratio

Figure 31: Normal lung uptake with a men +/- std. dev. of 2.57 +/- 0.11 for acini segment 98 and 7 generations of acini for 20 breathing cycles (4sec *20 = 80 sec)


Figure 32: Uptake for mild emphysema disease condition with a mean +/- std. dev. of 1.55 +/- 0.05 for acini segment 98 and 7 generations of acini for 20 breathing cycles (4sec *20 = 80 sec)


Figure 33: Severe emphysema uptake with a mean +/- std. dev. of 0.48 +/- 0.01 for acini segment 98 and 7 generations of acini for 20 breathing cycles (4sec *20 = 80 sec)


Figure 34: Left to right, normal lung (12.08 +/- 0.28), mild emphysema (13.81 +/- 0.24) and severe emphysema (15.39 +/-0.21), acini segment 98 and 7 generations of acini for the 20th breathing cycle


Figure 35: Difference in the normal lung to mild emphysema of 1.74 +/- 0.06 for 20th breathing cycle of 4 sec (The negative sign is due to mild emphysema being greater in concentration compared to normal lung)


Figure 36: Difference in normal lung to severe emphysema of 3.31 +/- 0.12 for 20th breathing cycle of 4 sec (The negative sign is due to severe emphysema being greater in concentration compared to normal lung)


1 2

3 4

Figure 37: Concentration ratios for 1) Normal to mild 1st breathing cycle with a mean +/- std of 1.2 +/- 0.3; 2) Normal to mild for 20th breathing cycle with a mean +/- std of 0.87 +/- 0.005; 3) Normal to mild for 1st breathing cycle with a mean +/- std of 1.833 +/- 1.88; 4) Normal to mild for 20th breathing cycle with a mean +/- std of 0.78 +/- 0.009


In figure 34 the normal lung with SV_Ratio of 34.3 mm-1, mild emphysema with a

SV_Ratio of 16.5 mm-1 and severe emphysema with an SV_Ratio of 4.3 mm-1 is

calculated for the 20th breathing cycle for an acini. For figure 35 and 36 the difference in

normal to mild and severe cases of emphysema are compared for a single acini. For

figure 35 there is ratio of normal to mild and normal to severe compared for the 1st and

20th breathing cycle.


Chapter 4. Discussion The important outcomes from this study are the changes in surface to volume ratio and its

effects on the uptake and concentration profiles in structural segments of the bronchial

tree. The movement of gases across the respiratory surface occurs mainly by diffusion

and some part by convection and direct uptake. The rate of diffusion is proportional to the

surface area across which the diffusion occurs. Since the alveoli do not collapse

completely, some air remains in the lung and is called as the residual volume. Thus the

lungs are unable to empty with each breath cycle and there is inhaled air mixed with the

residual air. So, the oxygen concentration in alveoli is considerably less than the

atmosphere. The reduction in surface area decreases the area for gas exchange for

conditions of emphysema. It greatly affects dead space, alveolar gas uptake and effective

ventilation.

In emphysema the tidal volume reduces and the surface to volume ratio decreases

considerably due to the reduced alveolar functional surface area. The air coming in the

trachea is increased with the change of tidal volume from 500mL to 250 mL, but the

residual volume increase due to air trapping in the alveoli.

All lungs judged to contain emphysema had an SV_Ratio of less than 16.5 mm-1 while

the SV_Ratio in all nonemphysematous lungs was greater than 25.6 mm-1.

In the Figure 29, the normal lung gas concentration is 3.75 +/- 6.10 % with the tidal

volume as 500 mL and surface to volume ratio is 34.6mm-1, while in the emphysematic

lung the surface to volume ratio is 16.5 mm-1 and tidal volume is 250mL and the gas

concentration is 2.87 +/- 5.99 % and the difference in normal to emphysematic

concentration is of 0.88 +/- 1.4 %. Thus due to emphysema the available gas for


exchange reduces by 0.88% for the first breathing cycle and it increase for the successive

breathing cycles.

As seen from figure 32 and 33 the functional residual capacity which is related to

expiration increases with the progress of emphysema. The residual air in the lungs also

increases with the progress of emphysema. Since the tidal volume changes from 500 mL

to 250 mL the minute ventilation changes from 6 liters (L) to 3.75 L for normal to

emphysematic conditions.

The software output is very stable with no variability seen for 20 repetitions. The

concentration in the 7 generations of acini changes from 0.81% to 0.87% for mild to

severe conditions of emphysema. Thus the gas exhaled is affected with the change in

surface to volume ratio parameters.

Going from the normal lung to emphysematic conditions the uptake of the gas in the acini

decrease from, 2.57 % to 1.55 % to 0.48 % for normal, mild emphysema and severe

emphysema conditions respectively over 20 breathing cycles. For the twentieth breathing

cycle the concentration of gas in the lungs increases from 12.08 % for normal to 13.81 %

for mild emphysema to 15.39 % for sever emphysema conditions. This way the residual

volume of the lung increases and uptake decreased causing shortness of breath even with

mild exercises due to less oxygen available for circulation. From the first breathing cycle

to twentieth breathing cycle the ratio of normal to mild changes from 1.19 to 0.87 and for

normal to severe conditions of emphysema changes from 1.83 to 0.79. Thus the

efficiency reduces for conditions of emphysema from 13 % to 21 % for mild and severe

conditions of emphysema respectively.


It takes 38 hours of computational time (134454 sec) for running a simulation of 20

breathing cycles of 4 sec each. With the complexity of hierarchy and increase in the

number of breathing cycles the time required for simulation increases.

4.1. Future extensions of the model:

Improvements in the model with more realistic parameters of elasticity and pressure shall

make the model handle more conditions of diseases. There is a significant decrease in

SV_Ratio with age even in nonemphysematous lungs (Thurlbeck 1967). Although

functional change associated with the decrease in SV_Ratio is very similar in both the

aged and the emphysematous lung. The elastic behavior of the aging lung also changing

due in part or solely to other factors including changes in the mechanical properties of

individual fibers. Thus with the incorporation of elasticity parameters the conditions of

aging can be simulated more realistically using this model. It shall be incorporated as a

GUI feature like the SV_Ratio which can allow to evaluate aging and emphysema which

have the similar pattern of effects. Pulmonary resistance is overall affetced in emphysema

and it affects more of expiration than of inspiration.


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Vita VIRAJ N. SHAH

3175, JFK Blvd, Apt1306, Philadelphia, PA-19104 • Phone: 267-357-3494 • E-mail:[email protected]

ABOUT MYSELF Team player with expertise in instrumentation, software and algorithm development, statistical and quantitative analysis, six sigma statistics and mathematical modeling OBJECTIVE Zeal to apply my analytical, mathematical and programming skills for developing new systems

SKILLS Software Development: Designed, developed and coordinated software scripts and algorithms Programming Languages: C/C++, VB/VC++ 6.0, MATLAB/MathCAD, Qt Operating Systems: Windows Vista, XP, ME, 2000, 98, 95 Web Technology: HTML, Wikipedia/TWiki Applied Mathematics: Mathematical modeling using Monte Carlo simulation, Black Scholes algorithm, differential equations, regression analysis, ANOVA, probability theory, neural models

Research and Development: Thesis on Lung Model development on VC.net platform to simulate and predict unforeseen conditions; Affine transforms, statistical reteach and Monte Carlo simulation for an Accuracy model EDUCATIONAL QUALIFICATIONS • Masters of Science in Biomedical Engineering, Drexel University, PA Sep’05 – Dec’07

Thesis: Investigate changes in the size of respiratory units (acini) under emphysema in a model of the human lung by computer simulation (GPA 3.63/4.00)

• Bachelor of Science in Biomedical Engineering, Mumbai University, INDIA Sep’01 - May’05 (GPA 3.75/4.00) WORK EXPERIENCE • Co-op at Kulicke & Soffa Industries, Inc, Fort Washington, PA, United States Sep’06 – Sep’07 • Achieved a sub-system accuracy of less than 1.75 micrometer, 3-sigma standard deviation for a

35 micrometer IC chip interconnection by eliminating error sources • Performed reversal technique for the Table Map using Monte Carlo simulations using MATLAB

to achieve self calibration for a wire bonder • Developed Accuracy model using MATLAB and Excel software’s to eliminate error sources at

the scale of a micron • Developed an enterprise Wikipedia for collaboration, knowledge management, project planning

for various locations around the world • Prepared a statistical reteach algorithm by deriving mathematical equations with 3 sigma analyses

in MATLAB to correct the placement error in a wire bonding equipment

• Internship at Philips Medical Systems India Pvt. Ltd, Mumbai, India Jun’04 - Nov’04 • Worked as a Field Service Engineer and installed CathLabs, MRI’s, CT scans, Ultrasound

machines, cardiac monitors and defibrillators. • Performed planned maintenance and troubleshooting for breakdowns and malfunctions


• Accomplished liquid nitrogen refill for 3 Tesla Magnetic Resonance Imaging equipment

• Drexel University, Philadelphia, PA • Research Assistant, Neuroengineering Department Nov’05 - Sep’06 • Designed and developed neural mass models using Runga Kutta techniques on MATLAB for

simulating schizophrenia and brain interconnection techniques

• Teaching Assistant, Bioscience and Biotechnology Department Jan’06 - Jun’06 • Taught various protein quantification assays and protein extraction techniques to a class size

of 20 students • Conducted Lab sessions with safety techniques, tutored students to obtain and analyze data

using Microsoft-Excel package

PROJECT EXPERIENCE • Consultant to prepare Annual Corporate Social Responsibility(CSR) report Jun’07 – Present

Compiled a CSR report which encompasses community development, diversity, marketplace practices, accountability and environmental stewardship for Kulicke & Soffa Industries, Inc

• FDA report to perform risk management and design analysis on medical devices Mar’07 – Jun’07

Prepared a report meeting the FDA 510k, design and safety guidelines for Non-Invasive Insulin Delivery using nano-particles for the treatment of diabetes

• Black Scholes method to analyze futures stock prices Mar’07 – May’07 • Prepared a Visual Basic script in Excel using Black Scholes formula to forecast the prices of

stocks using a Monte Carlo simulation techniques • Used binary tree approach for accounting the option trades

• DNA computers Oct’05 - Dec’06 • Prepared a literature review on traveling salesman problem using DNA computers and

submitted a research paper with the applications and future of DNA computers • Analyzed the functioning of DNA computer with a simple mathematical example

• Electroencephalograph (EEG)recording and infrared transmission Dec’04 - May’05 Designed a system for transmitting EEG signal over infrared and to check the EEG pattern and analyze them using MATLAB

• Institutional Review Board (IRB) Jan’06 - Mar’06 Drafted an IRB for a system with Electrocculography (EOG) for animal and human research protocols

PROFESSIONAL SKILLS Part of Drexel Delegation to United Nations HQ, New York City Aug’07

• Analyzed the Millennium Development Goals (MDG’s) to be achieved by 2015 • Participated in workshops and discussions with speakers from all around the world

Vice President Drexel IEEE Graduate Forum May’06 – May’07

• Conducted workshops, ad hoc events, career fairs, invited prominent speakers and arranged Professional Socials for the Drexel University Graduate Students


EXTRA CURRICULAR • Performed for Drexel Hungama and Drexel Dhinchak dance troops which perform annual

shows for Drexel University • Completed Mountaineering, Camping, Trekking and river rafting activities with Lion Hearts

Adventure Group, Manali, India

01 - Publication - A use friendly Mutliscale lung modeling suite and applications

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