Lecture four The physics of the lungs and breathing

Babylon University
college of dentistry / first stage / medical physics
Lecture four

The physics of the lungs and breathing

Function of the breathing system
The lungs ( pulmonary system ) serve as the supplier of O2 .The blood takes the O2 to the tissues , and removes the CO2 from the tissues , it must come in close contact with the air in the lungs in order to exchange its load of CO2 for a fresh load of O2 . The air we inspire is about 80 % N2 and 20 % O2 . Expired air is about 80 % N2 , 16% O2 and 4% CO2. The lungs perform other physiologic functions :
1- Exchange of O2 and CO2 .
2- Keeping the PH (acidity ) of the blood constant . “When we do work PH increase “CO2 + H2O H2CO3”
3- Play secondary roll in heat exchange and fluid balance of the body by warming the air we breathe in (inspire).
4- Controlling flow of air for talking , coughing , …., etc .
5- Voice production .
6- Removing the dust particles stuck to the moist lining of various airways .
The Airways
The principal air passages into the lungs are shown in Fig. Air normally enters the body through the nose where it is warmed (if necessary) ,filtered , and moisturized . The moist surfaces and the hairs in the nose trap dust particles. During heavy exercise , such as jogging , air is breathed in through the mouth and by passes this filter system .The air then passes through the windpipe (trachea) . The trachea divides in two (bifurcates) to furnish air to each lung through the bronchi. Each bronchus divides and redivides and about 15 more times, the resulting terminal bronchioles supply air to millions of small sacs called alveoli. The alveoli defined , which are like small interconnected bubbles ,are about 0.2 mm in diameter (a sheet of paper is 0.1mm thick) and have walls only 0.4 um thick . They expand and contract during breathing ,they are "where the action is " in the exchange of O2 and CO2.Each alveolus is surrounded by blood so that O2can diffuse from the alveolus into the red blood cells and CO2 can diffuse from the blood into the air in the alveolus.

How Blood and Lungs Interact
The primary purposes of breathing are to bring a fresh supply of O2 to the blood in the lungs and to dispose of the CO2 . Blood is pumped from the heart to the lungs under relatively low pressure. About (1 liter ) of blood supply in the lungs but only 70 ml is in the capillaries of the lungs getting O2 .The transfer of O2 and CO2 into and out of blood is controlled by law of diffusion . Molecules diffuse from region of higher concentration to lower concentration until concentration uniform. A molecule of O2 diffuses faster than CO2 because of its smaller mass.
Two general processes are involved in gas exchange in the lungs :
1- getting the blood to the pulmonary capillary bed ( perfusion )
2- getting the air to the alveolar surfaces ( ventilation ).
If either process fails the blood will not be properly oxygenated.
There are three types of ventilation perfusion areas in the lungs:
1- Area with good ventilation and good perfusion.
2- Area with good ventilation and poor perfusion.
3- Area with poor ventilation and good perfusion.
In a normal lung ,the first type accounts for over 90 % of the total volume .The second occur if the blood flow to part of a lung is blocked by a clot
That causes poor perfusion . In the third type the air passage in the lungs are obstructed
Physics of The Alveoli
The alveoli like millions of small interconnected bubbles they have tendency to get smaller due to surface tension of unique fluid lining . This lining called surfactant . The absence of surfactant in the lungs of some newborn infant is the cause of respiratory distress syndrome ( RDS ) called hyaline membrane disease causes death. To understand the physics of alveoli we have to understand the physics of bubbles . The pressure inside bubble is inversely proportional to radius and directly to surface tension. This relation called ( Laplace s Law) .
P= 4?/R where R radius , ? surface tension
Two forces keep lungs from collapsing :
1- Surface tension between lungs and chest wall .
2- Air pressure inside the lungs.

Partial Pressures of O2 and Co2:
The behavior of the gases (Air exchange by diffusion) obeys to the Dalton’s Law of partial pressures:
To understand the behavior of gases in lungs it is necessary to know Dalton’ s law of partial pressures .Dalton’s law state that if you have a mixture of several gases , each gas make its own contribution to the total pressure as though it were all alone .
The pressure exerted by any one of the gases is known as the partial pressure of that gas , and the total pressure of these gases is the sum of the partial pressures of the mixture gases .
p total = p t 1 + p t2+ p t3 + -----
where p is a partial pressure
Partial Pressure = % (gas)* (atmospheric – partial pressure of water vapor)
In the lung at 37Co & 100 % relative humidity, the partial pressure of water vapor = 47mm Hg, atmospheric pressure.= 760mm Hg
The alveolar airs contain 14 % O2 & 5.6 % Co2.
PO2 = 14/ 100 *(760mmhg – 47 mm hg) ~100 mm hg.
PCo2 = 5.6/ 100* (760mm hg – 47 mm hg) ~ 40mm hg.
Henry Law: It’s state the solubility of gases in liquids “The amount of gas which a liquid will dissolve directly proportional to the partial pressure of the gas”.
O2 is not very soluble in blood or water. Its diffuses faster than a molecule of Co2 because of its Smaller mass & higher Po2.
C O2 Is larger than that O2 – molecule, which actually slow the rate of diffusion, because of low PCo2 & larger mass .
On other hand, the Co2 is ? 25 times more soluble in liquids than the O2, so that the net effect is that the Co2 diffuses about 20 times more rapidly in aqueous liquids than does O2 .
Combination of O2 with Hb (Hemoglobin):
Because of the low solubility of O2 in the blood most of the O2 combine
with Hb in the blood red cells to be carried to the body cells.
The Hb leaving the lungs ? 97% saturate with O2 at PO2 = 100 mm Hg.
O2 dissociate from Hb and diffuse into the cells because of their low PO2
environment.

The dissociation of O2 from Hb is dependent on:
1- PCo2 in the cells.
2- The pH .
3- The temperature .
4- PO2 of the tissue (cells).
* Under resting condition the venous blood return to the heart with
75% of its load of O2 because it is not needed by the tissues:
* During exercise , PCo2 , pH, and temperature are all increased which permit Hb to give most of its O2 .
* In addition, the body can increase the blood flow three times, working
muscles, which results in O2 supply of 10 times more than they consume
at rest.

CO Poisoning (Carbon monoxide):
1- CO molecules attach with Hb nearly 250 times more tightly than O2.
2- Do not easily dissociate in the tissue.
3- Occupy places in Hb normally used to transport O2.
4- CO inhibits the release of O2 from Hb
So even a small amount CO can seriously reduce the O2 to the tissue.
The Physics of Exchanging of Gas between the Lungs and the Blood
The transfer of O2 and CO2 into and out of the blood is controlled by the
physical law of diffusion .All molecules are continually in motion. In gases and liquids , and to certain extent even in solids , the molecules do not remain in one direction .Molecules of a particular type diffuse from region of higher concentration to a region of lower concentration until the concentration is uniform . In the lungs we are concerned with diffusion in both gas and liquids .In the O2 and CO2 exchange in the tissues we are concerned only with diffusion in liquids .The molecules in a gas at room temperature move at about the speed of sound . Each molecule collides about 10¹? times each second with neighboring molecules .
The distance D of molecule will travel from its origin after N collisions is
D= ?? N
Where ? is the mean free path.
? is defined as the average distance between collision .
in air ? =10 ? 7 m
in tissue ? = 10 ? ¹¹ m
Example
What is the typical value of D in air and in tissue for an O2 molecule after 1 sec if N= 10¹? in air and in tissue N = 10¹² ?
In air D = 10? 7 (10¹?)½ =10?² m
In tissue D = 10?¹¹ ( 10¹² )½ = 10- 5 m
Diffusion depends on the speed of the molecules , the speed of molecules increases with temperature . Since N is proportional to the diffusion time ? t .
N ? ?t
D ? ? ?t
?t ? D ²
In the lungs the distance to be traveled in air usually a small fraction of a millimeter ,and diffusion takes place in a fraction of a second .The diffusion of O2 and CO2 in tissue is about 10,000 times slower than it is in air , but the tissue thickness of the molecules must diffuse through in the lungs is very small (0.4?m) and diffusion through the alveolar wall takes place in much less than 1 sec .
Measurement of lung volume
The lung has various volumes and capacities. The volume of the lung
versus time (i.e. the air flow) can be measured by the spirometer which
record it on a graph. These volumes and capacities can be summarized as
follows (which is shown by the graph):

Fig: shows the various volume and capacities of the lungs
1. Tidal volume at rest:
It is the volume of air inhaled with each breath during normal breathing at rest (~ 500 cm3). During heavy exercise the tidal volume is considerably large.
2. Inspiratroy reserve volume:
It is the additional air taken at the end of inspiration, which is possible with some effort to further fill the lungs with air.
3. Expiratory reserve volume:
It is the additional expired air, which can be forced out of the lungs at the end of normal expiration.
4. Functional residual capacity (FRC):
It is the air remaining in the lungs after a normal respiration where the stale air mixes with the fresh air of the next breath.
5. Vital capacity:
The volume of air exhaled when the breath is as deeply as possible and then exhaled as much as possible.
6. Residual volume:
It is the amount of air stale in lungs after vital capacity, which is ~1lit for adult.
- الحجم المدي الجاري T.V " Tidal Volume "
- الحجم الاحتياطي الشهيقي IRV " Inspiratory Reserve Volume "
- الحجم الاحتياطي الزفيري ERV " Expiratory Reserve Volume "
- السعة الحيوية VC " Vital Capacity "
- الحجم المتبقي RV " Residual Volume "
- السعة الرئوية الكلية TLC " Total Lung Capacity "
جهاز قياس التنفس Spirometry
السعات والحجوم التنفسية والرئوية.
بالنسبة للحجوم التنفسية الرئوية :فهي كالتالي:
-1الحجم المدّي:TV : Tidal Volume : يعبّر عن حجم الهواء الذي يُؤخذ أو يُطرح في كل نفس ويعادل (500)مل
-2الحجم الاحتياطي الشهيقي : IRV :Inspiratory Reserve Volume :
يعبّر عن الحجم الأعظم الإضافي من الهواء الذي يُمكن للإنسان ان يستنشقه بشكل قسري بعد شهيق (طبيعي). ويعادل (3000) مل.
-3الحجم الاحتياطي الزفيري :ERV:Exspiratory Reserve Volume
يعبر عن حجم الهواء الأعظم الذي يمكن للإنسان إخراجه بشكل قسري بعد زفير سوي.
ويعادل (1100)مل.
-4الحجم المتبقي:RV :Residual Volume
وهو الهواء الذي يبقى في الرئتين حتى بعد حصول الزفير الأعظم القسري (لايمكن إخراجه و وبالتالي لا يمكن قياسه بطريقة مباشرة). يعادل (1200)مل.
أما بالنسبة للسعات الرئوية : فهي كالتالي:
-1السعة الشهيقية : IC: Inspiratory Capacity:
تعبر عن حجم الهواء الأعظم الذي يمكن استنشاقه ببذل جهد قسري, بعد زفير سوي .
ويعادل 3500 مل. (عبارة عن الحجم المدي + الحجم الاحتياطي الشهيقي) (TV+IRV)(500+3000).
2 -السعة الحيوية : VS :Vital Capacity:
تعبر عن حجم الهواء الأعظم الذي يمكن إخراجه بزفير جهدي ,بعد شهيق جهدي:
ويعادل 4600 مل (عبارة عن الحجم المدي + الحجم الاحتياطي الشهيقي +الحجم الاحتياطي الزفيري) (TV+IRV+ERV)(500+3000+1100).
-3السعة الوظيفية : FRC: Functional Residual Capacity :
يعبر عن حجم الهواء المتبقي في الرئتين بعد زفير سوي ولا يمكن قياسه بطريقة مباشرة.
يعادل 2300 مل (عبارة عن الحجم المدي + الحجم الاحتياطي الزفيري) (TV+ERV).
-4السعة الرئوية الكلية : TLC :Total Lung Capacity :
حجم الهواء الموجود في الرئتين بعد شهيق جهدي أعظم.
ويعادل 5800 مل (عبارة عن الحجم المدي + الحجم المدخر الشهيقي + الحجم المدخر الزفيري + الحجم المتبقي )
(TV+IRV+ERV+RV)(500+3000+1100+1200).
تتم قياس الحجوم والسعات كافة بطريقة مباشرة بواسطة جهاز SpiroMeter .

HW
Calculate the number of O2 molecules absorbed from a typical breath of (500) cm3 . Assume the O2 in the air is reduced from ( 20% to 16% ) as measured at the mouth.
HW
If there are (3*108 ) alveoli in a lung with a functional residual capacity of (2.5) liters, calculate the average volume of an alveolus.
HW
If the thickness of the alveolar walls doubled by what factor would the diffusion time for O2 to reach the blood change ?
HW
In crowded area, the atmospheric pressure is (447) mmHg . Find the P O2 , and PN2 that people in this village inhale.
HW
A persons lung volumes were measured and the following results were obtained : vital capacity ,( 5) liters :residual volume, (1.0) liter and expiratory reserve volume ,(1.5) liters . Find the functional residual capacity.
HW
A person inspired maximally and then began breathing from an expandable bag containing (2) liters of (40%) helium gas .After a few breaths , the helium concentration in the bag was( 10%) . What was this persons total lung capacity?
HW
The compliance of a normal adult lung is about ( 0.2) liter /cm H2O .What is the compliance in m3/Nm-2?
HW
If Rg = (3) cm H2O/(liter/sec) , what air flow rate V would occur at an expiratory pressure of (100) mmHg ?