Lungs Model III

1
Lungs Model III

• Hoppensteadt-Peskin Lung Simulator

2
Scope of the Simulator

• It appears that simulator is for O2 transport
  simulation only.
• Some serious reduction may be needed if we want
  to apply simulator to gases that have linear
  solubility in blood (such as modification of the
  function cphi(ca,cv,r) program).
• Simulator shows O2 related concentrations as
  function of the various ri ratios. Plotting of
  such variables as functions of altitude, or
  parameters that characterize anemia, exercise
  etc, requires some modification (adding of for
  loops, etc).

3
Groups of Alveoli

• Program uses the index i1,,n to indicate groups
  of alveoli with different ventilation-perfusion
  ri ratio. For example, if n is set to 1, it means
  that all alveoli have the same r value.
• A better way of doing it (without changing n that
  by default is set to 100), is via the beta
  parameter.

4
The Beta Parameter

• Beta resides in the setup_lung.m file.
• When beta0, the ventilation-perfusion ratio is
  constant throughout the lungs.
• When beta1, the alveoli ratios ri are totally
  uncorrelated random numbers.
• Any value of beta between 1 and 0 relates
  directly to the correlation coefficient of the
  100 ri values.
• Its of interest to run every simulation for at
  least 3 values of beta 0,0.5 and 1.

5
Single Alveolus vs Whole Organism parameters

• Names of specific alveoli-group i parameters (out
  of n groups) are all elements of vectors of size
  n.
• This includes the vectors Q, VA, ca, PA, Pa, cA
  etc (as seen in the file named outchecklung.m.
• Global (whole organism) parameters M (and
  eventually cv), cI (and related variables cref,
  cstar etc) to be explained.

6
H function (related to the Hb-O2 dissociation
curve) - 1

• Hill curve with power n3. If one wants to
  change that to the more accurate n2.5, need to
  replace the 1/3 power (in function cphi()) to
  2/5, but then there may be a need to modify P as
  well!

7
H function (related to the Hb-O2 dissociation
curve) - 2
P in the program is taken to be 25 mmHg, which
is the partial pressure of O2 at which Hb is
half-saturated. That is, when P25 mmHg, only
two out of four active sites of Hb are occupied,
on the average. If we decrease power from 3 to
2.5, P may need to be increased somewhat (may be
to 40 mmHg). Lets not do all that.

• .

8
H function (related to the Hb-O2 dissociation
curve) - 3

• The constant c is the theoretical concentration
  of O2 bound to Hb at infinite partial pressure of
  O2. That is when Hb is 100 saturated.
• Program takes cstar to be equal to four times the
  concentration of Hb in the blood, which is almost
  the same as O2 concentration in inspired air, at
  sea level.

9
H function (related to the Hb-O2 dissociation
curve) - 4

• In setup_lung.m the constant cref, which is the
  reference oxygen concentration (in moles/liter)
  is computed as cref0.2/(22.4(310/273)).
• Then program sets cIcref and cstarcref.
• Anemia or polycythemia can be modeled via
  changing cstar (up or down, respectively)

10
H function (related to the Hb-O2 dissociation
curve) - 5

• We can model sudden exposure to high altitude via
  lowering of cI, with respect to cref, or model
  inhalation of oxygen rich air, via increase of
  cI.
• If one stays long enough in high altitude, then
  eventually cstar changes and becomes larger than
  cref.

11
Equations to be solved for each alveoli group

• For n groups, with 4 unknowns in each, we have 4n
  equations with 4n unknowns, grouped into n
  disjoint groups of 4 equations.
• The global constants cI and cv are considered
  given.
• Equations are scaled, so that concentrations are
  in moles/liter (rather than molecules/liter), and
  thats why we have RT, and not KT.

12
Numerical Solution of the H() equation

• Function cacarterial(cv,r) solves the H equation
  numerically, via the method of bisections.
• Method of bisections Search for a sign change in
  intervals that shrink by factors of 2.
• See book (section 2.7, formula 2.7.9) Move all
  terms to one side of the equation, and substitute
  values for the unknown. Look for sign change.

13
Rate of Oxygen Consumption M

• File setup_lung.m nominally lets M 0.25 cref
  5.6 (in moles/liter).
• One can now simulate various changes in M, which
  is more intuitive than changing cv. For each
  value of M, the value of cv can be found, by
  cvsolve.m

14
Running the unmodified lung.m produces three
unedited figures -1

• Figure 1 is for VA vs Q for each alveoli group.
• Above figure is for beta0.5. Try beta0 or 1.

15
Running the unmodified lung.m produces three
unedited figures -2

• Figure 2 is for cacblood vs r, and (below
  that) cAcair vs r. (It is unclear, what the
  horizontal green and blue dots are).

16
Running the unmodified lung.m produces three
unedited figures -3

• Figure 3 if for partial pressures as functions
  of r Look at the Pressures vector in the
  outchecklung.m file (and study Matlabs plot
  color code

17
In summary

• Need to modify the files to allow for more
  meaningful curves such as, pressures and
  concentrations as functions of the altitude (if
  cI is somehow calibrated against h, the
  elevation).
• All plots require better editing axes names,
  legend and annotations.