Embedded Files
Objectives: This project was attempted in February and March of 2020, ideally I would have tested the design in a wet lab setting, but all labs were shut down due to the COVID-19 pandemic. This report focuses on the Engineering Design Process as well as Mathematical and Computational Models
Clinical Need
Hypertension, commonly known as high blood pressure, is a condition in which the pressure of blood against the walls of the arteries is high for too long. Normal blood pressure is considered to be under 120/80 mmHg (systolic/diastolic), although elevated systolic blood pressure can be between 120-129 mmHg. Stage 1 hypertension is categorized as having a blood pressure of 130-139 mmHg systolic pressure and 80-89 mmHg diastolic blood pressure. Stage 2 Hypertension is having over 140/90 mmHg (systolic/diastolic) (Facts About Hypertension | cdc.gov). Hypertension increases the risk of cardiovascular disease. Nearly half of the adults in the United States have some form of hypertension, and only half of those with hypertension have it under control (Estimated Hypertension Prevalence, Treatment, and Control Among US Adults). If diagnosed early, lifestyle modifications can decrease hypertension and the diseases it can lead to; however, many cases need pharmacological therapy to help control blood pressure.
Current Treatments & Design Ideas
Recommended drugs for hypertension treatment include diuretics, beta-blockers, angiotensin-converting enzyme inhibitors (ACEI), angiotensin receptor blockers (ARBs), and calcium channel blockers (CCBs) (Hypertension Management: An Update). Beta-blockers, like propranolol, are used as first-line medications for patients recovering from post-myocardial infarctions (MI), also known as heart attacks. Non-selective beta-blockers manage hypertension post-MI by acting as an adrenaline-blocking agent in blood vessels (Systemic delivery of β-blockers via transdermal route for hypertension). However, propranolol falls short compared to other drugs due to the high variability in metabolism when taken orally. This makes it a perfect drug to be administered transdermally through a patch.
There are several transdermal patches for both selective and non-selective beta-blockers. Atenolol, a selective beta-blocker, has adverse side effects when administered orally frequently. A group developed a transdermal patch with atenolol and glibenclamide using various polymeric blends. The polymers included were hydroxypropyl methylcellulose (HPMC), Poly vinyl pyrrolidone (PVP) and Carbopol (CP) (Preparation, in-vitro and in-vivo characterization of transdermal patch containing glibenclamide and atenolol: a combinational approach.). This transdermal therapeutic system (TTS) resulted in zero-order kinetics, a useful metric for drug delivery. Timolol, a non-selective beta-blocker, was found to have enhanced transdermal delivery using electroporation (Transdermal delivery of timolol by electroporation through human skin.). A benefit of electroporation is that it also allows controlled quantity of the drug delivered by varying certain parameters like voltage, duration, and frequency of electrical pulses. Propranolol (PP), the non-selective beta-blocker, when used with certain enhancers (e.g. terpenes and alkanes) that increase lipophilicity and paired with hydrochloride (HCl) to increase hydrophilicity, can have optimal flux through the skin (https://www.ncbi.nlm.nih.gov/pubmed/2013847). In addition, having PVP and HPMC was found to increase the release rate of PP-HCl. Using the information from similar transdermal delivery systems, using PP-HCl with terpene enhancers as the molecule released from a patch with PVP and HPMC should have an optimal release rate and flux through the skin.
Design Constraints
Cost: Should meet or be lower than the existing price of the drug Propranolol.
Usability: To reduce the patient compliance factor, the patch should be long-lasting.
Appearance: The patch should be small and available in various “skin-tone” colors.
Durability: Since the patch will be placed on the body for a prolonged period of time, it should be waterproof, have strong adhesive properties and be resistant to mechanical factors (rubbing, stretching, etc.) The packaging it comes in should also protect the patch from environmental wear and tear.
Design Specifications
Patch Size: 10 x 6 x 1 mm (60 )
Patch Duration: Worn for seven days
Cost: Approximately $8.40-$10.66 (Hypertension Management: An Update)
Molecule Size: Less than 500 Daltons (https://www.researchgate.net/publication/12478012_The_500_Dalton_rule_for_the_skin_penetration_of_chemical_compounds_and_drugs)
Molecule Properties: Hydrophilic with Lipophilic enhancers like terpenes
Drug Properties:
Toxic Dosages: Life-threatening (1-2.5 g), Fatal (2-3 g, Blood-Plasma concentration of 2.2 mg.
Effective Dosage: 30-320 mg in general, 80-240 mg for hypertension, blood plasma concentration between 60 and 0.1 mg/L
Age Considerations: Half-life is 11 hours in elderly (62-79 years old), 5 hours in younger (25-33 years old) (Propranolol hydrochloride)
Design Overview and Sketch
The design of the patch will follow the structure of a reservoir transdermal patch. The schematic below details the different parts of the patch. Most reservoir transdermal patches have a polymer layer made of PVP and HPMC that controls the rate at which the drug is delivered to the body. This layer will also include terpenes. These are natural compounds that can be used to enhance the permeability of other molecules through the skin layer. The anti-hypertensive drug being used in the reservoir is Propranolol. This is a type of non-selective β blocker. The molecular weight of this drug is 259.34 g/mol which makes it small enough to be able to diffuse through the skin (Propranolol hydrochloride). In addition, the nature of this drug is lipophilic, which also makes it a good candidate to diffuse across the skin.
Figure 1: This is a schematic of the proposed design. Descriptions of each number are as follows:
1: This would be the outside layer of the transdermal patch. It will be made out of a metallic plastic laminate which will be drug impermeable.
2: This is the reservoir for where the drug will be stored. In it are molecules of Propranolol.
3: This is the polymer layer that will control the rate of drug delivery and will be made out of PVP and HPMC along with a terpene to enhance the permeability of Propranolol.
4: This is the adhesive layer.
Mathematical Model
As a disclaimer, this is an extremely simplified model and just gives a starting point for future computational and experimental models.
We begin by defining a coordinate system for our patch. I have chosen to look at the patch as a rectangle and to assume diffusion only into the skin, or in the z-direction, which makes the x and y directions impermeable (figure 3). This will make our system a time-dependent diffusion equation in one dimension.
Figure 2 (Left): z and x coordinates are marked on the sketch for reference.
This derivation relies on Fick's second law, but in order to understand Fick's second law, you must understand Fick's first law. Fick's first law describes the phenomenon that particles move from areas of higher concentration to areas of lower concentration. The number of a certain molecule moving through a given area over a certain amount of time is called flux.
The equation for this diffusion in one dimension using the drawing to the right is J (flux) = -Dab * dCa / dz. The flux of particle A in the z-direction, or to the right in the diagram, is equal to the Diffusion coefficient of a in b times the change in the concentration of particle A with respect to the z-direction. A really great video to learn the basics of how this equation is derived can be found here.
Figure 4 (Right): Molecule A diffusing into molecule B.
Figure 3: z and x coordinates system pertaining to the patch, shows impermeability in the y-direction.
Fick's second law predicts how diffusion will cause the concentration to change with respect to time. A quick derivation of Fick's second law is shown below.
Figure 5: Flux through a cube at x and x+ delta x, used for derivation of Fick's second law
This is the equation that will need to be solved to give the mathematical model for the patch. This equation is derived using the continuity equation. The solution is shown below.
This equation was solved by writing it in dimensionless parameters and then using the separation of variables to solve. The concept here is that materials move from higher concentrations to lower concentrations. It is assumed that the concentration of the drug at the time that it is placed on a patient’s skin is very low. The concentration of the drug in the patch is much greater and therefore diffuses into the skin. The graph to the left demonstrates the proof of this concept: the concentration difference between the surface and the patch is very great at t = 0. As t increases the difference between the two becomes far less, slowing the rate of diffusion. This mathematical model is oversimplified, as it does not account for what will happen as the drug is carried away from the site and into the body. This would increase the rate of diffusion since the concentration will be kept relatively low at the site. This will need to be accounted for in order to ensure that the appropriate amount of drug is diffusing into the body. Ideally, we would need to find a method to keep the rate of the diffusion constant, but this will require much more complex mathematical modeling and computational simulation.
Figure 6: Graph of the difference in concentration between the surface of the skin and the patch over time. As time increases, the difference in concentration between the surface of the skin and the patch decreases, demonstrating that the drug has diffused into the skin. C0 is the initial concentration of the drug at the skin surface. C1 is the initial concentration of the drug in the patch. C is the concentration of drugs in the patch. The concentration of drugs in the patch becomes closer to that of the skin over time as the drug diffuses into the skin.
Computational Model
To model our drug delivery system we used COMSOL modeling software. As with any modeling, assumptions were made to simplify the model, and ideas of how to improve the model will be addressed.
The model was modeled in units of meters, in reality, the units would be cm, but in this case, modeling in meters allowed for a nicer display.
The patch is hypothetically a 1 by 0.6 cm rectangle with a depth of 0.1 cm. A time-dependent study that displayed the transport of a diluted species was used. The diffusion coefficient was 1*e^-7 m^2/sec. An initial concentration of 0.02 mol/m^3 was placed at the top of the patch. The combination of the diffusion coefficient and initial concentration allowed the drug to diffuse steadily over time but prevented it from diffusing too rapidly or too slowly. The study was run for 6000 seconds, or 100 minutes. The model made several assumptions: that the concentration of drug was initially just at one surface, the concentration was zero everywhere else, and that the patch can rely completely on diffusion to function. Future improvements will test different concentrations, adding a permeable skin layer with a convective flow (blood flow) to the model, and gathering data for concentration over time in the skin layer. Also considering factors such as temperature, bodily fluids presence, and loss of adhesive will be important. Models will never be able to fully predict a system but can help to avoid future mistakes and give a hypothetical dataset prior to real experiments.
Figure 7: Diffusion of the drug at time = 0 seconds
Figure 8: Diffusion of the drug at time = 1500 seconds
Figure 9: Diffusion of the drug at time = 6000 seconds
Experimental Plan (Prior to COVID-19)
There are many design aspects to be considered with a transdermal patch. We will attempt to isolate two. The first is the rate of delivery of the drug in the reservoir in vitro and the other is expanding it to see how the patch functions in vivo, specifically the effect it would have on human skin. For the in vitro experimental testing, we want to see what is the optimum setup to correctly dose the patients using the patch. Our design proposes the use of terpenes to make the skin surface more permeable to propranolol. The aspect that we would modify is the type of terpene we are using to enhance the permeability of the drug in question. The three different terpenes that will be used along with controls for the experiment can be found in the table below. The 1,8-cineole terpene will be used as the positive control. This has been used as a marker terpene for propranolol and compared to the negative control, there should be enhanced permeability and a faster rate of drug delivery. The permeability of the skin to propranolol will be mirrored in the rate of drug diffusion from the patch into the body. The way that we would be able to test the amount of drug being delivered would be to use an agar model. The transdermal patch would be placed on top of a block of agar. This block of agar would model the part of the body that the patch would be placed on. The drug in the reservoir would be dyed so that over time as it diffused into the agar block, we could visually see it over the course of a week. The agar would be imaged over time (once every 24 hours) so that we can see whether the patch is delivering the appropriate daily dose which would be in the 80-240 mg range as it is for hypertension. This would be done by using ImageJ to quantify the amount of the dyed drug in the block of agar at 24 hour periods. This will also tell us what the daily dose the patch administers is and this value can be compared to the daily recommended therapeutic dose.
To summarize, the 1,8-cineole marker terpene added would act as the positive control test condition and no terpene added at all would act as the negative control. The 1,4-cineole terpene added, 1, (+)-limonene terpene added, and the 8, (-)-fenchone terpene added are the testing conditions that were settled on for this experiment.
The second level of experimental analysis we would want to do is see how the patch and the various terpene modifications react with the skin. The next step would be to take the patches with the terpene modifications and test them on animal subjects. This would show if the addition of the terpenes have any negative effects on the skin. This would include looking to see for redness, irritation or swelling on the skin surface. The two factors that would decide on the best design would be no adverse effects of the addition of the terpenes and the correct rate of delivery. Of all of the design modifications, we expect that the 1,4-cineole terpene will yield the best results. (Systemic delivery of β-blockers via transdermal route for hypertension).
Sources
“Facts About Hypertension.” Centers for Disease Control and Prevention, Centers for Disease Control and Prevention, 25 Feb. 2020, www.cdc.gov/bloodpressure/facts.htm.
Cdc. “Hypertension Prevalence in the U.S.: Million Hearts®.” Centers for Disease Control and Prevention, 5 Feb. 2020, millionhearts.hhs.gov/data-reports/hypertension-prevalence.html.
Nguyen, Quang et al. “Hypertension management: an update.” American health & drug benefits vol. 3,1 (2010): 47-56.
Ahad, Abdul, et al. “Systemic Delivery of β-Blockers via Transdermal Route for Hypertension.” Saudi Pharmaceutical Journal, vol. 23, no. 6, 2015, pp. 587–602., doi:10.1016/j.jsps.2013.12.019.
Anitha et al. “Preparation, in-vitro and in-vivo characterization of transdermal patch containing glibenclamide and atenolol: a combinational approach” Pak. J. Pharm. Sci., 24 (2011), pp. 155-163
Denet, Anne-Rose, and Véronique Préat. “Transdermal Delivery of Timolol by Electroporation through Human Skin.” Journal of Controlled Release, vol. 88, no. 2, 2003, pp. 253–262., doi:10.1016/s0168-3659(03)00010-5.
Hori, Mltsuhiko, et al. “Enhancement of Propranolol Hydrochloride and Diazepam Skin Absorption In Vitro: Effect of Enhancer Lipophilicity.” Journal of Pharmaceutical Sciences, vol. 80, no. 1, 1991, pp. 32–35., doi:10.1002/jps.2600800109.
Page updated
Google Sites
Report abuse