Pulmonary Equations Flashcards
Boyles Law
P1V1 = P2V2 (pressure gradient that drives gas flow)
Charles Law
V1/V2 = T1/T2
Dalton’s Law
P total = P gas (x)
DSA:
Px = (Pb - Pw) x F
Pb: barometric pressure
Pw: water vapor pressure (74mmHg)
F values: O2 = 21% ; N2 = 79%
Henry’s Law
Cx = kPx ; Pgas (in fluid) = [gas] / solubility
C: content of dissolved gas proportion to partial pressure
k: solubility constant
P: partial pressure
Example: If arterial blood PCO2 = 40mmHg + k (solubility constant) = .06mL CO2/dL blood/mmHg
C CO2 = .06 x 40 = 2.4mL/dL
Transpulmonary pressure (PL)
PL = PA - PPL
PA: intrapulmonary pressure
PL: intra pleural pressure
Across chest wall (PW)
PW = PPL - PBS
PPL: intra pleural pressure
PBS: pressure at body surface
Pressure across respiratory system (PRS)
PRS = PA - PBS
PA: intrapulmonary pressure
PBS: pressure at body surface
Transairway pressure (PTA)
PTA = PAW - PPL
PAW: air way pressure
PPL: intra pleural pressure
Transpulmonary pressure
Pneumothorax Example
PL = PA - PPL
PA: intrapulmonary pressure
PPL: intra pleural pressure
2 ways to to re-inflate lung clinically:
PPL = 0 ; PA = +5 ; PL = +5 - 0 = +5 (add + pressure in air way)
PPL = -5 ; PA = 0 ; PL = 0 - (-5) = +5 (recreate (-) intrapleural pressure)
End of Exhalation
Transpulmonary pressure
PA - PPL = 0 - (-5) = +5 cm H2O
During Inspiration
Transpulmonary pressure
PA - PPL = -2 - (-8) = +6 cm H2O
Lung Volumes during inspiration/expiration
End of inhalation: Lung volume = FRC + Vt
Start of Exhalation: Lung volume = FRC
FRC: functional residual capacity
Vt: tidal volume
Vital Capacity (VC)
VC = IRV + Vt + ERV ; VC = IC + ERV
IRV: inspiratory reserve volume (normal: 3000mL)
Vt: tidal volume (normal: 500mL)
ERV: expiratory reserve volume (normal: 1000mL)
IC: inspiratory capacity
Example: VC = 3000 + 500 + 1000 = 4500mL (normal)
Total lung capacity (TLC)
TLC = VC + RV ; TLC = IC + FRC ; TLC = Vt + ERV + IRV + RV
VC: vital capacity (normal: 4500mL)
RV: residual volume (normal: 1200mL)
IC: inspiratory capacity (normal: 3500mL)
FRC: functional residual capacity (normal: 2200mL)
Example: TLC = 4500 + 1200 = 5700mL (normal)
Functional residual capacity (FRC)
FRC = ERV + RV
ERV: expiratory residual volume (normal: 1000mL)
RV: residual volume (normal: 1200mL)
Example: FRC = 1000 + 1200 = 2200mL (normal)
RV/TLC’s
Normal < .25
Emphysema (increased RV)
Fibrosis (decreased TLC)
Pathology > .25
Compliance
C = ∆V / ∆P (units: mL/ cm H2O)
reflection of distensibility, measure of elastic properties of lung (higher compliance = easier to stretch)
Recoil
R= 1/C
tendency of an object to oppose stretch (lung)
High compliance = less recoil; low compliance = more recoil
La Place’s Law
P = 2T / r
P: net pressure in gas filled sphere
T: surrounding surface tension
r: radius of sphere
Respiratory system compliance (Crs)
Crs = 1/Cl + 1/Ccw
Cl: compliance of lung
Ccw: compliance of chest wall
Airflow through tube due to a pressure difference between 2 ends of tube
AF = ∆P / R
AF: airflow
R: resistance to AF
∆P: difference between barometric pressure (Pb) at open mouth and pressure at alveolus (PA): ∆P= Pb - PA
Resistance (laminar)
R = ∆P / flow (units: cm H2O/L/sec)
R = 8 L n / π r^4
Laminar flow / Turbulent flow
Re (Reynolds # < 1000) = laminar ; P = flow rate x R
Re (Reynolds #> 2000) = turbulent ; P ∝ (flow rate)^2
Reynolds number
Re = 2rvd / n
r: radius
n: viscosity
v: velocity
d: diameter
Airway Resistance
In parallel…
1/R total = 1/R1 + 1/R2 + 1/R3…
Work of breathing (W)
W = P x ΔV
Metabolic Acidosis
Primary disorder: increased production of H+ by tissues
Compensatory response: hyperventilation expires CO2
[H+] increased; pH decreased
pCO2 decreased; HCO3- decreased
Metabolic Alkalosis
Causes: prolonged vomiting, potassium deficiency
Primary disorder: excessive loss of H+ and ovum depletion
[H+] decreased; pH increased
pCO2 increased; HCO3- increased
Respiratory Acidosis
Causes: choking, bronco-pneumonia, acute exacerbation of asthma, chronic obstructive airways disease
Primary disorder: insufficient expiration of CO2 from lungs
[H+] increased; pH decreased
pCO2 increased; HCO3- increased
Respiratory Alkalosis
Causes: hysterical over breathing, mechanical over ventilation, hypoxia
Primary disorder: excessive expiration of CO2 by hyperventilation
[H+] decreased; pH increased
pCO2 decreased; HCO3- decreased
Alveolar Gas Equation
PAO2 = PIO2 - PaCO2 / R
R= .8
Normal Lung Volume Values
Vt (Tidal volume) = 500mL
IRV (inspiratory reserve volume) = 3000mL
ERV (expiratory reserve volume = 1000mL
RV (residual volume) = 1200mL
Inspiratory capacity (IC)
IC = Vt + IRV
IC = 500mL + 3000mL = 3500 mL (normal value)
Clinical Spirometry
simple lung function test (Forced vital capacity)
most informative; measured directly from spirogram
FVC: total air exhaled during forced exhalation;
TLC spirometry test: patient forcibly exhales from TLC level
Does not measure RV (RV + TLC) ; FEV1 / FVC = 80% (normal); obstruction of airway = 47%
FEV1: forced expiratory volume in 1 second
Alveolar pressure (PA)
PA = P tp + P pl
P tp: transpulmonary pressure
P pl: pleural pressure
Force expiratory volume (FEF) OR mid-maximal expiratory flow (MMEF)
25-75% of vital capacity (VC)
FVC maneuver (healthy person vs. person w/ asthma)
Healthy person:
FEV1 = 3.41 ; FVC = 3.81 ; 3.41/3.81 = .86
Person w/ asthma:
FEV1 = 2.1 ; FVC = 3.7 ; 2.1/3.7 = .57
Interpreting FVC maneuver
RD: restrictive disease (fibrosis) ; OD: obstructive disease (COPD)
RD: VC decreased; TLC decreased; RV decreased; FEV1/FVC normal or increased; FEF normal
OD: VC normal or decreased; TLC normal or increased; RV increased; FEV1/FVC decreased; FEF decreased
Inert gas dilution and nitrogen washout technique
measures FRC
V1C1 = (V1 + Vfrc) x C2
Plethysmography
measures lung volumes and FRC ; based on Boyle’s law
Diffusion capacity test (DLCO)
measure CO diffusion capacity; decreased w/ thickening of barrier interstitial or alveolar edema (fibrosis) ; decreases surface area for gas exchange (emphysema, tumor) ; decreased uptake by RBCs (anemia) ; V/Q mismatch
Lung Capacity test (Plethysmography & Helium dilution methods and nitrogen washout)
measures amount of air that you breathe in and out (Vt) and max amount of air you can breath in and out (VC)
Flow meter
measures airway resistance (Raw) and lung compliance (CL); uses esophageal balloon (Ppl)
Normal Raw: 1-3cm H2O/Lsec
Healthy normal tidal breathing:
C = ΔV/ Ppl
CL (static) about equal to CL (dynamic) = .150 - .250 L/cm H2O
Pulmonary Vascular resistance (PVR)
R = ΔP / F
Ventilation perfusion ratio (V/Q) / Healthy Lung parameters
Normal healthy lung:
V/Q: .8
PaO2 = 100mmHg
PaCO2 = 40mmHg
Arterial pH = 7.4
Hypoxemia PaO2 / Hypoventilation PaCO2
PaO2 < 80mmHg
PaCO2 > 45mmHg
Anatomical Shunt (R to L)
PAO2 - PaO2 = AaDO2 = 15mmHg
AaDO2: alveolar-arterial oxygen gradient
Henderson Hasselbach equation
-pH = pK + log [HCO3-] / (.03 x PCO2)
Fick’s Law
D = ΔP x area / thickness
O2 dissolved in blood plasma
VO2 = 5000ml/min x .3mL O2/100mL = 15mLO2/min
Avg. 70kg human consumes 250mLO2/min at rest
Hemoglobin O2 capacity
in RBC about 15g/100mL blood, 1.35mL O2/g Hb
Max O2 bound to Hb = Hb O2 capacity x Hb content
1.35mLO2/gHb x 15gHb/dL blood = ~20.3 mLO2/dL blood
Hemoglobin saturation
%SO2 = (O2 bound to Hb / Hb O2 capacity) x100
%SO2 = 0% PO2 = 0mmHg
%SO2 = 25% PO2 = 15mmHg
%SO2 = 50% PO2 = 25 mmHg
%SO2 = 75% PO2 = 40mmHg
%SO2 = 100% PO2 = 100mmHg
%SO2 = 100% PO2 = 500mmHg (hyperoxia)
Blood Flow
BF = HR x SV
Positive allosteric effectors of HB (P50 reduced; left shift)
↑ pH ↓ PCO2 ↓ 2,3 BPG ↓ Temperature ↑ HbF ↑ CO ↑ MetHb
Negative allosteric effectors of HB (P50 increased; right shift)
↓ pH ↑ PCO2 ↑ 2,3 BPG ↑ Temperature ↑ Altitude
Bohr effect (right shift)
At lung alveoli, O2 binding releases H+ due to high pO2, O2 binding to Hb releases H+
At tissue capillary beds, increased [H+], decreased pH, oxyHb acquires H+ which enhances release of O2 for aerobic metabolism
CO2 transportation
gaseous and dissolved CO2 in plasma
Carbamino compounds: Hb-NH-COO- + CO2
Bicarbonate (HCO3-)
CO2 + H2O → H2CO3 → H+ + HCO3-
Haldane effect
when O2 binds Hb, CO2 released
w/o Haldane CO2Δ = 52-50 = 2 volume %
w/ Haldane CO2Δ = 52-48 = 4 volume %
↑ %SO2 = right shift
↓ %SO2 = left shift
Partial pressure of lung gases at 37°C (body temp)
100°C Wvp = 760mmHg
0°C = 5mmHg
PH2O = 47mmHg
air-lungs interface:
PTotal = 760 - 47 =713mmHg (reduces partial pressure of all gases at lung surface)
PN2 = 713 x .79 = 563.3 PO2 = 713 x .21 = 149.7 PCO2 = 713 x .0004 = .28
Minute ventilation (Ve)
Ve = Vt x f
Vt: tidal volume (500mL/breath)
f: flow rate (15 breaths/min*)
500 x 15 = 7500 ml/min*
*for avg. 70kg male
Alveolar Ventilation (Va)
Va = Vt - Vd x f
Vd: anatomic dead space (150mL for 150lb male)
Vt: 500mL
f: 15 breaths/min
Va = (500 - 150) x 15 = 5250 mL/min exchanged in alveoli
Alveolar Ventilation (after surgery)
Vt: 200mL/breath
Vd: anatomic dead space (150mL for 150lb male)
f: 40 breaths/min
Ve: 8000mL/min
Va = (200 - 150) x 40 = 2000 mL/min
Normal: 5250mL/min
Determinants of alveolar PA O2
PAO2 = 102 mmHg (normal steady state)
PAO2 = [O2] entering - [O2] leaving
O2 entering determined by: PIO2 and Va
PAO2 directly proportional to PIO2 and Va
Alveolar gas equation (PO2)
PAO2 = PIO2 - (PACO2 / R)
R = respiratory gas quotient (VCO2/VO2) If fuel is: Carbohydrate, R = 1 Fat, R = .7 Normal, R = .8
Alveolar gas equation (PCO2)
PACO2 = VCO2 / Va
Normal: 40mmHg
PACO2 = [CO2] entering - [CO2] leaving
PACO2 inversely proportional to Va
O2 content
(Hb g/dL x 1.34) x SaO2 +. (PaO2 x .003)
