A mechanics model for injectable microsystems in drug delivery
Introduction
Localized drug delivery to biological tissues/organs for treatment, cure, and/or therapeutic stimulation represents a desirable alternative to systemic delivery with the potential to decrease severe side effects from drugs in unwanted regions of the body (Kayl and Meyers, 2006; Partridge et al., 2001; Rosenblum et al., 2018; Senapati et al., 2018) and increase the drug's effectiveness (Kumar and Pillai, 2018; Stearns et al., 2019; Tng et al., 2012). The rapid and ongoing development of microelectronics and microfluidics for bioelectronic medicine offers possibilities to manipulate small drug volumes (i.e., nanoliters – microliters) in compact and precise ways for chemical/biomedical analysis and clinical applications (Ashraf et al., 2011; Beebe et al., 2002; Cobo et al., 2015; Meng and Hoang, 2012; Nguyen et al., 2002; Stewart et al., 2018; Suzuki and Yoneyama, 2003). Bioelectronics featuring electrochemical actuation for fluidic control rely on gas formation from a reversible chemical reaction (e.g., water electrolysis) as the driving force to pump the drug inside the device reservoirs into the target location (e.g., brain, nerves, eyes) (Neagu et al., 2000, 1996; Stanczyk et al., 2000). Electrochemical actuation offers low heat generation during operation – as compared to thermally-actuated pumps like in (Jeong et al., 2015; Noh et al., 2018; Qazi et al., 2019) – and can be realized by a simple mechanical design shown in Fig. 1A where an electrolyte reservoir – where gas formation occurs – and a drug reservoir are separated by a flexible polymer membrane which deforms to pump the drug (Neagu et al., 2000; Zhang et al., 2019b, 2019a). As electrical current is applied to the electrodes in direct contact with the electrolyte, an electrochemical reaction initiates in the electrolyte chamber as shown in Fig. 1E and the pressure inside the chamber increases – due to gas formation – to deform the flexible membrane and deliver the drug as shown in Fig 1A. The electrolyte reservoir is filled with electrolyte such that there is no initial volume of gas in the chamber.
To realize the localized drug delivery, partially implantable wireless bioelectronic devices have been proposed for behavioral neuroscience studies as an alternative to hard, bulky, and tethered devices (Fan et al., 2011; Qazi et al., 2020; Rezaei et al., 2019; Seidl et al., 2010) because they offer unrestricted animal movement, lightweight designs, refillable ports, and programmable drug flowrates (Cobo et al., 2014; Zhang et al., 2019a, 2019b). Devices with the same actuation principle have been used for localized drug delivery in the brain tissue (Sheybani et al., 2015; Zhang et al., 2019a), and peripheral nerves (Zhang et al., 2019b), for cancer therapeutics (Cobo et al., 2016; Gensler et al., 2012, Gensler et al., 2010), transdermal insulin delivery (Kabata et al., 2008; Ziaie et al., 2004), intraocular delivery (Li et al., 2008, Li et al., 2010), and remain competitive candidates for future development of soft, implantable biodegradable devices for clinical research to directly target and treat affected tissues/organs and avoid unnecessary exposure of drugs in off-target body locations (Chen et al., 2021; Tng et al., 2012).
To design and optimize the bioelectric device and control the drug delivery process, analytical models – based on the theoretical gas generation rate of the electrochemical reaction – have been proposed (Lee et al., 2010) but neglect the flexible membrane geometry and elasticity and the flow resistance from the microfluidic channels limiting the control of the delivery to the electrical current. Fig. 1 shows the 12 parameters – related to the different subsystems of the device: flexible membrane (Fig. 1B and 1C), microfluidics (Fig. 1D), and electrochemical reservoir (Fig. 1E) – that influence the drug delivery process. The list includes initial pressure in the biological tissue , microchannel cross-section , and length , drug viscosity , flexible membrane thickness and radius , Young's modulus , Poisson ratio , and stress-strain curve , the temperature of the electrolyte solution , and the electrical current that is supplied to the electrodes. Recently, a scaling law of delivery that combines all the parameters into three non-dimensional parameters related to the initial gas volume in the electrolyte chamber, the initial environmental pressure in the animal's target tissue/organ, and the microfluidic resistance was established (Avila et al., 2021) with analytical solutions, derived from singular perturbation method (Kumar, 2011), for the drug delivery time and volume/flowrate temporal profiles when the non-dimensional microfluidic resistance is negligible or small.
For neuroscience studies targeting/modulating certain regions of the brain, bioelectronic devices with small microchannel cross-sections – in the length scale of the brain anatomy (e.g., diameter of neurons in the caudate nucleus: 7.5 - 32.5 μm) (Adinolfi and Pappas, 1968) – are preferred to increase the drug delivery accuracy and target cells in the intended brain region. Small microchannel cross-sections result in larger microfluidic resistance and a new analytical model is required to obtain the delivery parameters (e.g., delivery time) since the assumption of small non-dimensional microfluidic resistance in the prior solution (Avila et al., 2021) is no longer appropriate.
A new analytic solution of the drug delivery time for large microfluidic resistance is obtained in this article, which is validated by the numerical results for small and large deformation. The focus is on the volume temporal profile and drug delivery time for large microfluidic resistance. For rapid drug delivery, the initial gas volume inside the reservoir is taken as zero (i.e., the electrolyte reservoir in Fig. 1A is full).
The organization of this article is as follows. First, the Marlow hyperelastic strain energy potential, which is based on the uniaxial stress-strain curve obtained from experiments for any (hyper)elastic materials, is used for the flexible membrane in Section 2. The mechanics analysis of the flexible membrane is then described and classified in Section 3 for small and large pressures for two polymers membranes with different stress-strain behavior. It is followed by the mechanics analysis of drug delivery to yield not only a scaling law of key drug delivery parameters but also the analytic solution in Section 4, which is validated by numerical results for large microfluidic resistance in Section 5. Section 6 discusses the parameters affecting the non-normalized, dimensional delivery time, and presents a design of bioelectronic device for an application to revert an opioid overdose.
Section snippets
Marlow hyperelastic model
The mechanical properties of the flexible membrane polymer materials depend on factors related to the polymer chemistry, manufacturing process, temperature, level of deformation, among others. The strain energy potential proposed by Marlow (Marlow, 2003) can be used to model approximately incompressible isotropic hyperelastic materials under the assumption that the material response only depends on the first invariant and can be determined from the uniaxial tension test. The Marlow strain
Mechanics of the flexible polymer membrane
Figs. 1B and 1C show the schematic for bending- and stretching-dominated deformations, respectively, where denotes the maximum membrane deflection. Their main difference is the slope of deflection at the edge of the membrane () remains zero for the bending-dominated deformation (small deformation) in Fig. 1B but becomes non-zero when the deformation is stretching-dominated (large deformation) in Fig. 1C. For a flexible membrane of radius , thickness , and pressures and on its two
Mechanics of drug delivery
For the bioelectronic device presented in Fig. 1, three different subsystems in the bioelectronic device contribute to the drug delivery process: electrochemical (electrolyte + electrodes), solids (flexible membrane), and fluids (microchannels). In the electrochemical subsystem, hydrogen and oxygen gas generated during the chemical reaction can be modeled based on the ideal gas law aswhere P is the pressure, V is volume change inside the electrolyte reservoir, R is the ideal gas constant,
Results
For drug delivery applications with injectable electrochemical devices, one critical result is the (normalized) total time to deliver the drug dosage, which is affected by the two non-dimensional parameters and . For example, proposed future devices to deliver hundreds of microliters of drug in humans can be designed – based on the proposed implantable microsystems used in small animals – with the parameters shown in Table 1, which yield .
Influence of and , limitations of
Discussions
The normalized drug delivery time depends only on two non-dimensional parameters ( and ). Minimization of the (not normalized) drug delivery time is discussed in this Section, particularly in the case of reversing an opioid overdose.
Conclusions
In summary, this works presents the analytical model for injectable bioelectronic devices during drug delivery and shows that the normalized drug delivery time is based only on two non-dimensional parameters: the normalized environmental pressure and microfluidic resistance. The analytic model, detailed analysis, and results are important to optimal design of injectable microsystems for localized drug delivery studies.
CRediT authorship contributor statement
Raudel Avila – Conceptualization, Methodology, Validation, Formal Analysis, Investigation, Writing – Original Draft, Writing – Review & Editing, Visualization.
Yixin Wu – Conceptualization, Validation, Investigation, Data Curation, Writing – Review & Editing.
John A. Rogers – Conceptualization, Resources, Writing – Review & Editing, Supervision.
Yonggang Huang – Conceptualization, Methodology, Validation, Formal Analysis, Investigation, Resources, Writing – Original Draft, Writing – Review &
Data availability statement
The data sets generated and supporting the findings of this article are obtainable from the corresponding author upon reasonable request. The authors attest that all data for this study are included in the paper.
Declaration of Competing Interest
The authors declare no conflict of interest.
Acknowledgment
R.A. acknowledges support from the National Science Foundation Graduate Research Fellowship (NSF Grant No. 1842165) and Ford Foundation Predoctoral Fellowship.
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