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«Date:_ Approved: _ David F. Katz, Supervisor _ Stefan Zauscher _ George A. Truskey _ Fan Yuan _ Kim A. Woodrow Dissertation submitted in partial ...»

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Mechanistic Models of Anti-HIV Microbicide Drug Delivery

by

Yajing Gao

Department of Biomedical Engineering

Duke University

Date:_______________________

Approved:

___________________________

David F. Katz, Supervisor

___________________________

Stefan Zauscher

___________________________

George A. Truskey

___________________________

Fan Yuan

___________________________

Kim A. Woodrow

Dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Biomedical Engineering in the Graduate School of Duke University 2016 i v

ABSTRACT

Mechanistic Models of Anti-HIV Microbicide Drug Delivery by Yajing Gao Department of Biomedical Engineering Duke University Date:_______________________

Approved:

___________________________

David F. Katz, Supervisor ___________________________

Stefan Zauscher ___________________________

George A. Truskey ___________________________

Fan Yuan ___________________________

Kim A. Woodrow An

Abstract

of a dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Biomedical Engineering in the Graduate School of Duke University 2016 i v Copyright by Yajing Gao 2016 Abstract A new modality for preventing HIV transmission is emerging in the form of topical microbicides. Some clinical trials have shown some promising results of these methods of protection while other trials have failed to show efficacy. Due to the relatively novel nature of microbicide drug transport, a rigorous, deterministic analysis of that transport can help improve the design of microbicide vehicles and understand results from clinical trials. This type of analysis can aid microbicide product design by helping understand and organize the determinants of drug transport and the potential efficacies of candidate microbicide products.

Microbicide drug transport is modeled as a diffusion process with convection and reaction effects in appropriate compartments. This is applied here to vaginal gels and rings and a rectal enema, all delivering the microbicide drug Tenofovir. Although the focus here is on Tenofovir, the methods established in this dissertation can readily be adapted to other drugs, given knowledge of their physical and chemical properties, such as the diffusion coefficient, partition coefficient, and reaction kinetics. Other dosage forms such as tablets and fiber meshes can also be modeled using the perspective and methods developed here.

The analyses here include convective details of intravaginal flows by both ambient fluid and spreading gels with different rheological properties and applied

–  –  –

in different compartments. The results are Tenofovir concentration distributions in time and space for a variety of microbicide products and conditions. The Tenofovir concentrations in the vaginal and rectal mucosal stroma are converted, via a coupled reaction equation, to concentrations of Tenofovir diphosphate, which is the active form of the drug that functions as a reverse transcriptase inhibitor against HIV. Key model outputs are related to concentrations measured in experimental pharmacokinetic (PK) studies, e.g. concentrations in biopsies and blood. A new measure of microbicide prophylactic functionality, the Percent Protected, is calculated. This is the time dependent volume of the entire stroma (and thus fraction of host cells therein) in which Tenofovir diphosphate concentrations equal or exceed a target prophylactic value, e.g.

an EC50.

Results show the prophylactic potentials of the studied microbicide vehicles against HIV infections. Key design parameters for each are addressed in application of the models. For a vaginal gel, fast spreading at small volume is more effective than slower spreading at high volume. Vaginal rings are shown to be most effective if inserted and retained as close to the fornix as possible. Because of the long half-life of Tenofovir diphosphate, temporary removal of the vaginal ring (after achieving steady state) for up to 24h does not appreciably diminish Percent Protected. However, full steady state (for the entire stromal volume) is not achieved until several days after ring

–  –  –

surface area of coated mucosa and whether the interiors of rectal crypts are filled with the enema fluid. For the enema 100% Percent Protected is achieved much more rapidly than for vaginal products, primarily because of the much thinner epithelial layer of the mucosa. For example, 100% Percent Protected can be achieved with a one minute enema application, and 15 minute wait time.

Results of these models have good agreement with experimental pharmacokinetic data, in animals and clinical trials. They also improve upon traditional, empirical PK modeling, and this is illustrated here. Our deterministic approach can inform design of sampling in clinical trials by indicating time periods during which significant changes in drug concentrations occur in different compartments. More fundamentally, the work here helps delineate the determinants of microbicide drug delivery. This information can be the key to improved, rational design of microbicide products and their dosage regimens.





–  –  –

Abstract

List of Tables

List of Figures

Acknowledgements

1. Introduction

1.1 Topical Microbicides and Modeling

1.2 Clinical Trials and Microbicide Delivery Vehicles

1.3 Active Pharmaceutical Ingredient in Microbicides

1.3.1 Tenofovir as Microbicide

1.4 Vaginal Geometry

1.5 Pharmacokinetic Models

1.5.1 Comparison between Classic and Mechanistic PK Model

1.5.2 Multivariate Optimization in Parameter Space (MOPS) Approach

1.6 Diffusion and Transport Theory

1.7 Numerical Methods

2. Mass Transport of Drug in the Vaginal Mucosa

2.1 Introduction

2.2 Materials and Methods

2.2.1 Geometry of the Model

2.2.2 Governing Equations for Gel, Epithelium, and Stroma

–  –  –

2.2.4 Conservation of Mass Equation for Tenofovir in Blood

2.2.5 Parameters in the Model

2.2.6 Numerical Solution of the Equations

2.3 Results

2.3.1 Drug Concentration Profile at Different Times

2.3.2 Average Concentrations in Compartments vs. Time

2.3.3 Pharmacokinetic Summary Measures

2.3.4 Results for Daily Dosing and BAT24 Dosing

2.3.5 Effects of Variations in Epithelial Thickness

2.3.6 Interpreting Biopsy Concentration

2.3.7 Perturbation of Model Parameters

2.3.7.1 Variation in Tissue Diffusion Coefficient

2.3.7.2 Variation in Partition Coefficient

2.3.7.3 Variation in Dilution Constant

2.3.7.4 Variation in Stroma Blood Transfer Constant

2.4 Discussion

2.5 Conclusion

3. Gel Spreading in the Vagina

3.1 Introduction

3.2 Materials and Methods

3.2.1 Constitutive Equations

–  –  –

3.3 Results

3.3.1 Power Law Fluid

3.3.2 Herschel-Bulkley Fluid

3.3.3 Carreau-like Fluid

3.3.4 Fitting Rheological Parameters

3.3.5 Rheology of Gel Aging

3.3.6 Comparison with Compliant Wall Model

3.4 Discussion

3.5 Conclusion

4. Combining Gel Spreading and Drug Transport

4.1 Introduction

4.2 Materials and Methods

4.2.1 Geometry of the Model

4.2.2 Rheology of Test Gels

4.2.3 Governing Equations for Drug Transport

4.2.4 Boundary and Initial Conditions

4.2.5 Parameters in the Model

4.3 Results

4.3.1 Spreading in Large and Small Vagina

4.3.2 Heat Map of Concentration Distribution

4.3.3 Volume-averaged Concentration in Multiple Compartments vs. Time.......... 115

–  –  –

4.3.5 Plots of Combined Percent Protected and Gel Coating

4.3.6 Sensitivity of Model Parameters

4.4 Discussion

4.5 Conclusion

5. Model of Intravaginal Rings

5.1 Introduction

5.2 Materials and Methods

5.2.1 Geometry of the Model

5.2.2 Governing Equations and Boundary Conditions

5.2.2.1 Fluid Mechanics Model

5.2.2.2 Sagittal Plane Model

5.2.2.3 Coronal Plane Model

5.2.3 Parameters in the Model

5.3 Results

5.3.1 Heat Plot of Concentration in Sagittal Plane Model

5.3.2 Heat Plot of Concentration in Coronal Plane Model

5.3.3 Average Concentration in each Compartment

5.3.4 Percent Protected after Ring Insertion and Removal

5.3.5 Percent Protected with Parameter Variations

5.4 Discussion

5.5 Conclusion

–  –  –

6.1 Introduction

6.2 Materials and Methods

6.2.1 Geometry of the Model

6.2.2 Governing Equations

6.2.3 Boundary and Initial Conditions

6.2.4 Parameters in the Model

6.2.5 Numerical Solution of Governing Equations

6.3 Results

6.3.1 Heat Map of Typical Solution

6.3.2 Effects of Variable Enema Retention Time

6.3.3 Effects of Crypt Size

6.3.4 Effects of Advective Fluid Flow

6.3.5 Concentration Profiles as a Function of Depth

6.3.6 TFV-DP Concentration in Stromal Host Cells

6.3.7 Simulated TFV and TFV-DP Concentrations in Biopsies

6.4 Discussion

6.5 Conclusion

7. Conclusions

7.1 Summary

7.2 Future Directions

Appendix A: Fluid Flow in a Rectal Cylindrical Geometry

–  –  –

References

Biography

–  –  –

Table 2: Summary pharmacokinetic parameters from the model with comparison to Schwartz et al data in parentheses

Table 3: Summary PK parameters in epithelium and stroma with varying epithelial thickness

Table 4: Rheological parameters of three test gels

Table 5: Parameters in gel spreading and drug transport model

Table 6: Effects of the 6 parameters on log-linear model for coefficient variation. Unit for concentration is fmol/mg. Values are multiplicative factor for any variable that is part of the Comparison column, the baseline factor is 1

Table 7: Parameters in the Tenofovir ring model

Table 8: Percent of stroma protected with varying drug release rate per day (row) and vaginal fluid production per day (column), the last column has a thicker epithelium(*).

Values are for EC50 of 5000 fmol/mg (left) and 500 fmol/mg (right) at steady state. Bolded cell is the baseline condition.

Table 9: Parameters in the enema model

–  –  –

Figure 2: Molecular structure of Tenofovir diphosphate.

Figure 3: Vaginal geometry with introitus to the left and cervix to the right. The blue bolus is a gel with squeezing force indicated by arrows.

Figure 4: Diagram of classic PK model (left) and mechanistic PK model (right). The model is a simple two compartment one. It could characterize drug transport from a gel layer into a homogeneous tissue specimen.

Figure 5: Classic PK (empirical) model fitted to mechanistic PK (deterministic) model in the tissue for a two compartment problem

Figure 6: Graphical representation of MOPS approach, each line is possible solution at different time point, the red dot is the optimal solution.

Figure 7: Comparison between a residual and MOPS fit to the empirical model with the deterministic model

Figure 8: Drawing of the vaginal mucosa with gel layer, epithelium, and stroma. Line of symmetry is indicated on top

Figure 9: Concentration profiles of Tenofovir in gel and tissue at 2, 4, 8, and 24 hours... 48 Figure 10: Average concentration over time for each compartment

Figure 11: Concentration in stroma with daily dosing, coitus is at time zero

Figure 12: Concentration in stroma with BAT24 dosing, coitus is at time zero................. 52 Figure 13: Concentration in compartments with varying epithelial thickness.................. 54 Figure 14: Ratio of stromal concentration to biopsy with varying epithelial and biopsy thickness

Figure 15: Concentration in compartments with varying tissue diffusion

Figure 16: Concentration in compartments with varying partition coefficient.................. 59

–  –  –

Figure 18: Concentration in compartments with varying stroma blood transfer constant

Figure 19: Illustration of squeezing by two plates of a gel in channel geometry with applied force F

Figure 20: Coated area of a pluronic gel

Figure 21: Viscosity vs. shear rate for a typical gel on log-log scale

Figure 22: Rheology of a fresh and 12 months aged 3002 gel

Figure 23: Gel spreading for fresh and aged gel at 2 mL and 4 mL

Figure 24: Height profiles at different times for the compliant wall model

Figure 25: Area coated ratio between compliant and rigid wall model

Figure 26: Geometry of gel spreading and drug transport. Top is an exaggerated picture of the model and the bottom is a rectilinear approximation

Figure 27: Four different cases of gel flow dependent on the initial position of inserted gel, where it can either leak and/or flow in one direction only

Figure 28: Péclet number of gel spreading and diffusion

Figure 29: Fraction of area coated and volume leaked for a large sized vagina.............. 111 Figure 30: Fraction of area coated and volume leaked for a small sized vagina............. 112 Figure 31: Concentration distribution for TFV and TFV-DP on the log scale.................. 114 Figure 32: Volume averaged TFV concentration in gel, epithelium, and blood.............. 116 Figure 33: Volume averaged concentrations of TFV-DP in stroma

Figure 34: Percent Protected of the stroma. Rows are gels DG1, DG2, and DG3. The columns are different EC50 values of 5, 50, and 500 fmol/mg



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