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inhalation-model's Introduction

Introduction:

This contribution contains the MoBi implementation of a mechanistic physiologically-based pharmacokinetic inhalation model that brings together lung anatomy, particle deposition, particle dissolution, and mucociliary clearance from previous work and connects it to a two-compartment model.

In this model, the lung is separated into the extrathoracic region and 24 lung generations (or sections) that each consist of concentric layers: epithelial lining fluid, epithelium, and subepithelium. The model allows for absorption of particles in the lung as well as oral absorption of particles in the extrathoracic region.

Using MoBi and the ospsuite R package, the user enters parameters describing the physicochemical properties of the molecule, the micro-constants pertaining to the two-compartment model, oral and lung bioavailabilities, particle size distribution, and dose.

Simulation of the model returns:

  • amount or concentration of drug at each compartment and at each generation of the lung over the time of the simulation,
  • amount or concentration of drug at each compartment of the two-compartment model as well as the extrathoracic region.

This repository is organized as follows:

File name Description
Inhalation_model_user_guide.pdf Includes:
1. Introduction to the model and model details
2. A description of the model implementation in Mobi
3. Step-by-step tutorial of a basic inhalation simulation
Inhalation_model_structure_evaluation.pdf Slide deck demonstrating the use of the inhalation model to capture the observed behaviour of four molecules of varying solubilities.
inhalation_model_two_compt_1_bin.mbp3 MoBi project template containing the inhalation model connected to a two-compartment model
populate_model.R R script that is used to calculate deposition fractions based on empirical equations (Yu & Diu, 1982)
custom_deposition.R R script that is used to specify the deposition fractions directly
configure_inhalation_parameters.R Template to guide the use of the populate_model.R and custom_deposition.R files. It is currently configured for the ciprofloxacin which is used in the tutorial within the user guide
ParticleBin_1.pkml Template for a single particle bin. This file can be used to add additional particle bins in the case of a polydisperse formulation
Standard_Molecule.pkml Template for a generic molecule building block. This file is used to load the parameter "Solubility in epithelial lining fluid"
stass_2017_ciprofloxacin_inhaled.pkml Building block that contains Stass et al (2017) data used in the tutorial within the user guide

References

[1] Boger, E., & Fridén, M. (2019). Physiologically based pharmacokinetic/pharmacodynamic modeling accurately predicts the better bronchodilatory effect of inhaled versus oral salbutamol dosage forms. Journal of aerosol medicine and pulmonary drug delivery, 32(1), 1-12.

[2] Boger, E., & Wigström, O. (2018). A partial differential equation approach to inhalation physiologically based pharmacokinetic modeling. CPT: pharmacometrics & systems pharmacology, 7(10), 638-646.

[3] Stass, H., Nagelschmitz, J., Kappeler, D., Sommerer, K., Kietzig, C., & Weimann, B. (2017). Ciprofloxacin dry powder for inhalation in patients with non-cystic fibrosis bronchiectasis or chronic obstructive pulmonary disease, and in healthy volunteers. Journal of aerosol medicine and pulmonary drug delivery, 30(1), 53-63.

[4] Weibel, E. R., Cournand, A. F., & Richards, D. W. (1963). Morphometry of the human lung (Vol. 1). Berlin: Springer.

[5] Willmann, S., Thelen, K., Becker, C., Dressman, J. B., & Lippert, J. (2010). Mechanism-based prediction of particle size-dependent dissolution and absorption: cilostazol pharmacokinetics in dogs. European journal of pharmaceutics and biopharmaceutics, 76(1), 83-94.

[6] Yu, C. P., & Diu, C. K. (1982). A comparative study of aerosol deposition in different lung models. American Industrial Hygiene Association Journal, 43(1), 54-65.

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inhalation-model's Issues

mass transfer from subepithelium compartment to blood formula correction

Dear Moriah:
I have corrected the following to accord with Borger's paper.
So in order for mass to transfer from Subepi to the system,
mass transfer rate = Q_CO*(R*A_sub/V_sub/Kp_u - A_blood/V_blood)

rather than

mass transfer rate =Q_CO*(R*A_sub/V_sub/K_p_u_lung - A_blood/V_blood)

Kp_u is the tissue-to-plasma partition coefficient of lung.

I have added a new parameter in the Lung compartment and run one simulation on my laptop, it should be doing fine. (but please check as well!)
inhalation_model_two_compt_withkp.zip

Calculation of the volumes and drug concentrations in epithelial lining fluid, epithelium, and subepithelium

Dear Moriah,

I came across your great work for the MoBi implementation of the inhalation model published by Boger, E et al., and I had some questions about this inhalation model in MoBi.

I am a bit confused about the calculation of volumes and drug concentrations for the epithelial lining fluid (ELF), epithelium, and subepithelium in different generations. I took the 20th generation as an example. The calculations of the volume and drug concentration for ELF are shown as follows in your MoBi implementation.

Parameter: Inhaled ciprofloxacin|Organism|Lung|AlveolarRegion|Generation_20|EpithelialLiningFluid|Volume
IsFixed: False
Value: 7.47568204220349E-11 [l]
Formula: Lpih_ELF*(D-h_ELF)
L: Inhaled ciprofloxacin|Organism|Lung|AlveolarRegion|Generation_20|Airway length(0.0085 [dm])
h_ELF: Inhaled ciprofloxacin|Organism|Lung|AlveolarRegion|Generation_20|EpithelialLiningFluid|Height of epithelial lining fluid(7E-07 [dm])
D: Inhaled ciprofloxacin|Organism|Lung|AlveolarRegion|Generation_20|Airway diameter(0.004 [dm])
L: ..|..|Airway length
h_ELF: ..|Height of epithelial lining fluid
D: ..|..|Airway diameter

Parameter: Inhaled ciprofloxacin|Organism|Lung|AlveolarRegion|Generation_20|EpithelialLiningFluid|Ciprofloxacin|Concentration
IsFixed: False
Value: 0 [µmol/l]
Formula: V>0 ? M/V : 0
M: Inhaled ciprofloxacin|Organism|Lung|AlveolarRegion|Generation_20|EpithelialLiningFluid|Ciprofloxacin(0 [µmol])
V: Inhaled ciprofloxacin|Organism|Lung|AlveolarRegion|Generation_20|EpithelialLiningFluid|Volume(7.47568204220349E-11 [l])

The calculated volume for ELF is 7.47568204220349E-11 L, and I think this is the volume for only one airway in this generation. For the 20th generation, there are 524,288 airways in total, so the total volume for ELF in this generation should be 7.47568204220349E-11 L multiplied by 524,288, right? If this is ture, the drug concentration should be determined as the amount of drug in ELF in the 20th generation devided by total volume of ELF in the 20th generation. However, it seems that you used the volume of ELF in one airway for the calculation of drug concentration? And drug amout in ELF defined in the model looks like the total amount in all airways for this generation.

Following to my aforementioned confusion, the total volume for ELF, epithelium, and subepithelium in all generations is quite small (0.0588 L based on my caclutation, see belows for the details). This is much smaller than the acutal lung volume (0.57 L=0.0076* 70 kg* 1.0 g/cm3). My question is if I want to calculate the drug concentrations separately in the total lungs, in the tracheobronchial region (generations 1-16), and in the alveolar region (generations 17-24), I do not know how to use the appropriate volume values.

Generation | ELF (L) | epithelium (L) | subepithelium | Airways | Total volume in each  generation
1 | 5.45E-05 | 2.99E-04 | 2.58E-03 | 1 | 2.93E-03
2 | 1.47E-05 | 7.37E-05 | 7.06E-04 | 2 | 1.59E-03
3 | 3.98E-06 | 2.01E-05 | 1.97E-04 | 4 | 8.83E-04
4 | 1.07E-06 | 5.44E-06 | 5.51E-05 | 8 | 4.93E-04
5 | 1.44E-06 | 7.33E-06 | 7.61E-05 | 16 | 1.36E-03
6 | 9.42E-07 | 4.81E-06 | 5.17E-05 | 32 | 1.84E-03
7 | 6.32E-07 | 3.25E-06 | 3.62E-05 | 64 | 2.57E-03
8 | 4.40E-07 | 2.27E-06 | 2.63E-05 | 128 | 3.72E-03
9 | 2.98E-07 | 1.55E-06 | 1.89E-05 | 256 | 5.31E-03
10 | 1.14E-07 | 2.91E-07 | 3.98E-07 | 512 | 4.11E-04
11 | 8.18E-08 | 2.08E-07 | 2.86E-07 | 1024 | 5.90E-04
12 | 5.80E-08 | 1.48E-07 | 2.05E-07 | 2048 | 8.42E-04
13 | 4.27E-08 | 1.10E-07 | 1.52E-07 | 4096 | 1.25E-03
14 | 3.02E-08 | 7.78E-08 | 1.09E-07 | 8192 | 1.78E-03
15 | 2.32E-08 | 5.99E-08 | 8.42E-08 | 16384 | 2.74E-03
16 | 1.79E-08 | 4.63E-08 | 6.55E-08 | 32768 | 4.25E-03
17 | 1.58E-10 | 8.16E-10 | 5.00E-09 | 65536 | 3.91E-04
18 | 1.22E-10 | 6.32E-10 | 3.87E-09 | 131072 | 6.06E-04
19 | 9.45E-11 | 4.88E-10 | 2.99E-09 | 262144 | 9.37E-04
20 | 7.48E-11 | 3.86E-10 | 2.37E-09 | 524288 | 1.48E-03
21 | 5.93E-11 | 3.06E-10 | 1.88E-09 | 1048576 | 2.35E-03
22 | 4.88E-11 | 2.52E-10 | 1.55E-09 | 2097152 | 3.87E-03
23 | 3.85E-11 | 1.99E-10 | 1.22E-09 | 4194304 | 6.11E-03
24 | 3.31E-11 | 1.71E-10 | 1.05E-09 | 8388608 | 1.05E-02

Thanks in advanced.

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