The Emergence of Microneedle-Based Smart Sensor/Drug-Delivery Patches: A Scaling Theory Defines the Tradeoff between the Response Time and the Limits of Detection ^†

Abstract

Smart, ultra-scaled, always-on wearable, and implantable (WI) sensors are an exciting frontier in personalized medicine. These sensors integrate sensing and actuation capabilities, enabling real-time analyte detection for on-demand drug delivery, akin to a biological organ. The microneedle (MN)-based patch serves as a critical novel interface element in this system. It is inexpensive, minimally invasive, and safe, showing promise in glycemic management and insulin therapy in laboratory and animal studies. However, the current design of MNs relies primarily on empirical approaches, with significant challenges. These challenges include potential diffusion delays that may impede time-critical drug intervention and an iterative design process lacking a clear understanding of the tradeoff between the response time and the limits of detection. In this paper, we introduce the first predictive framework for MN sensors, based on physical scaling laws and biomimetic concepts. Our framework is supported by experimental and numerical validations, establishing analytical scaling relationships that capture the fundamental workings of hollow and porous-swellable MN sensors. It quantifies essential performance metrics like the ’response time (RT)’ and the ’limit of detection (LOD)’ while assessing the tradeoffs associated with various geometrical and physical parameters of the MN technology. As a result, our model provides a universal framework for interpreting/integrating the experimental findings reported by laboratories worldwide. By leveraging this predictive framework, researchers can advance the development and optimization of MN sensors, leading to improved performance and expanded applications in the field of wearable and implantable technologies.

1. Introduction

Smart healthcare, powered by ultra-scaled, and always-on digital electronics and wearable and implantable (WI) sensors, marks an exciting frontier in modern medicine. Technological advancements, including microfabrication, miniaturization, portability, low power, and cost-effectiveness, have shifted testing sites from traditional laboratories to “under or on skin” platforms [1,2,3,4].

Traditional devices developed for laboratory-based measurements face inherent limitations [5]: expensive tests, limited access in poorer communities, obtaining a single data point per test, and significant delays related to sample collection, laboratory reports, and therapy. Despite promoting point-of-care (POC) diagnostics as a complementary approach, these limitations persist, hindering independent and continuous monitoring of chronic diseases like diabetes and blood pressure. For them, indeed, highly trained technicians and self-disciplined patients are still required to run measurements or deliver drugs as needed, impeding accurate timely interventions.

A promising solution to these healthcare needs lies in closed-loop WI systems, integrating smart-sensing-controller–therapeutic interaction, as shown in Figure 1a. This revolutionary paradigm combines accurate sensing modalities with power transfer technology, data communication infrastructure, and machine learning algorithms, enhancing theragnostics. Skin-worn tattoos, patches, and textiles with wearable and implantable technology, along with actuating systems like brain and muscle stimulators or drug injectors, enable uninterrupted monitoring and immediate on-demand corrective therapies.

Microneedle (MN)-based patches, shown in Figure 1b, are part of WI systems, offering minimally-invasive analyte monitoring and drug delivery over several weeks [6,7]. These patches with short microneedles (a few hundred micrometers) can absorb analyte molecules or deliver drugs into the dermis. Compared to traditional hypodermic needles, MNs are less invasive and less painful due to fewer pain receptors in the dermis [8,9]. Moreover, the interstitial fluid (ISF) within the dermis contains valuable biomarkers like glucose, lactate, sodium ions, and others [10,11].

The combination of disease diagnostics and drug delivery makes MN platforms ideal for closed-loop applications such as glycemic management and insulin therapy [12,13,14]. In traditional ‘open-loop’ operations, a patient performs glucose measurements and insulin pump therapy. In contrast, a smart MN patch integrates autonomous glucose measurement, data transmission to a controller algorithm, and autonomous therapeutic insulin delivery, forming a more efficient ‘closed-loop’ system.

2. Challenges and Limitations of MN Technology

The number of publications in MN-related areas has been growing exponentially over the past 20 years, with more than 80% of these publications focusing on experimental systems and fabrication protocols [15]. Despite significant progress in the field, the current design and optimization of MN systems involve costly and time-consuming iterative design of experiments. Researchers have explored a range of MN technologies, such as porous, swellable, and dissolvable platforms, alongside traditional hollow MNs, to achieve continuous monitoring with minimized sensor response delay and maximize the extracted concentration. Numerical analysis tools, such as finite element methods with COMSOL Multiphysics software, have limitations in efficiently exploring the vast design space associated with MN geometry and material parameters. The lack of universal scaling functions derived from numerical simulations makes it challenging to transfer insights from one design to another, hindering the systematic design and optimization of MN-based systems.

While a theory for therapeutic drug delivery has been developed [16], a comprehensive physics-based model for sensing optimization mediated by MNs is still missing. Without such a theory, it is difficult, if not impossible, to minimize the response time and maximize the extracted analyte concentration (limit of detection, LOD) for an optimized and efficient closed-loop system.

To address this gap, our work focuses on developing a generalized physics-based model for the in vivo operation of hollow, porous, and swellable (P−S) MN-based patches. Through validation against numerical simulations and experimental data, our theory establishes the foundation for the MN-related framework and provides strategies for designing and optimizing MN systems within the closed-loop theragnostic scenario. Moreover, the generality of the MN scaling theory makes it applicable to a broader range of applications, including electrochemical or optical sensors, enzymatic or nonenzymatic processes, in vitro and in vivo measurements, sensing, and actuation mechanisms.

3. A Scaling Theory of the Response Time and the Limit of Detection

3.1. Specific Design Challenges

• Wearable sensing devices require continuous and effective operation, necessitating real-time tracking of analyte concentrations. However, integrating MNs into wearable patches poses challenges due to analyte diffusion from the interstitial fluid (ISF) to the sensing site. This diffusion causes inherent delays in the sensor response (response time) and reduces the detectable analyte concentration (LOD) (Figure 2a), hindering an immediate closed-loop therapeutic response.
• Integrating fluid-absorbing MNs into electrochemical enzyme-based patches for on-site analysis adds complexity. Decoupling the impact of individual MN and enzymatic parameters on overall sensor performance proves to be a challenging task.
• Unlike hollow MNs, which absorb ISF across their tip aperture, P−S MNs enhance ISF absorption across their lateral surface, leading to a significant reduction in the response time and increased extracted analyte concentration (Figure 2). However, a theory comparing different MN technologies and quantifying this enhancement is currently missing.

3.2. Theoretical Framework of Hollow Microneedles

First, we derive a generalized framework to quantify the geometry-dependent response delay and LOD observed in hollow-type MN sensors. Here, the MNs are integrated in an enzymatic wearable patch with the sensing site (electrode) on the upper end of the patch, as shown in Figure 2a. We model the analyte extraction across MN tip and base as ion uptake by bacteria and gas flow across leaves the stomata [17] and molecule transport along MN length as the spreading resistance of a point contact [18]. It can be shown that the overall response time ${\mathrm{t}}_{\mathrm{tot}}$ is the sum of individual contributions from the MN, patch, and enzymatic reaction:

$$\begin{array}{c}\hfill {\mathrm{t}}_{\mathrm{tot}}={\mathrm{t}}_{\mathrm{MN}}+{\mathrm{t}}_{\mathrm{PATCH}}+{\mathrm{t}}_{\mathrm{EZ}},\end{array}$$

(1)

where ${\mathrm{t}}_{\mathrm{MN}}\mathrm{and}{\mathrm{t}}_{\mathrm{PATCH}}$ are the turn-on delay times of analyte transport through the MN and sensor patch, and ${\mathrm{t}}_{\mathrm{EZ}}$ is the effective time resulting from the diffusion and reaction in the enzyme layer, shown in Figure 2a. To quantify the time components, we approximate each sensor domain as a diffusive resistor R $[\mathrm{s}·{\mathrm{m}}^{-3}]$ and multiply it by the corresponding transported ISF volume V [19]. To generalize the theory, we express the geometry-dependent components of (1), namely ${\mathrm{l}}_{\mathrm{n}},{\mathrm{s}}_{\mathrm{base}},{\mathrm{s}}_{\mathrm{tip}},{\mathrm{s}}_{\mathrm{i}}$, in terms of scaled variables, ${\mathrm{r}}_{\mathrm{T}}=\frac{{\mathrm{l}}_{\mathrm{n}}}{{\mathrm{s}}_{\mathrm{tip}}},{\mathrm{r}}_{\mathrm{B}}=\frac{{\mathrm{l}}_{\mathrm{n}}}{{\mathrm{s}}_{\mathrm{base}}},{\mathrm{r}}_{\mathrm{i}}=\frac{{\mathrm{l}}_{\mathrm{n}}}{{\mathrm{s}}_{\mathrm{i}}}$, where ${\mathrm{l}}_{\mathrm{n}},{\mathrm{s}}_{\mathrm{tip}},{\mathrm{s}}_{\mathrm{base}}$ are the MN length, half width of MN tip, and base apertures, respectively, ${\mathrm{s}}_{\mathrm{i}}$ is the MN inter-base distance:

$$\begin{array}{c}\hfill {\mathrm{t}}_{\mathrm{MN}}={\mathrm{R}}_{\mathrm{base}}{\mathrm{V}}_{\mathrm{base}}+{\mathrm{R}}_{\mathrm{n}}{\mathrm{V}}_{\mathrm{n}}+{\mathrm{R}}_{\mathrm{tip}}{\mathrm{V}}_{\mathrm{tip}}=\mathrm{f}({\mathrm{r}}_{\mathrm{T}},{\mathrm{r}}_{\mathrm{B}},{\mathrm{r}}_{\mathrm{i}},{\mathrm{D}}_{\mathrm{body}},{\mathrm{D}}_{\mathrm{n}},{\mathrm{D}}_{\mathrm{patch}}),\end{array}$$

(2)

$$\begin{array}{c}\hfill {\mathrm{t}}_{\mathrm{PATCH}}={\mathrm{R}}_{\mathrm{patch}}{\mathrm{V}}_{\mathrm{patch}}=\mathrm{f}({\mathrm{x}}_{\mathrm{patch}},{\mathrm{D}}_{\mathrm{patch}}),\end{array}$$

(3)

$$\begin{array}{c}\hfill {\mathrm{t}}_{\mathrm{EZ}}=\mathrm{diffusion}-\mathrm{limited}({\mathrm{t}}_{\mathrm{MN}},{\mathrm{t}}_{\mathrm{PATCH}})\mathrm{vs}\mathrm{reaction}-\mathrm{limited}\left(\mathrm{reaction}\mathrm{rates}\right).\end{array}$$

(4)

Here, ${\mathrm{x}}_{\mathrm{patch}}$ is the patch thickness, ${\mathrm{D}}_{\mathrm{body}},{\mathrm{D}}_{\mathrm{n}},{\mathrm{D}}_{\mathrm{patch}}$ are the analyte effective diffusivity in the dermis, MN, and patch, respectively. The parameter ${\mathrm{t}}_{\mathrm{EZ}}$ results from the competition of the analyte supply from the dermis (transport-limited) and enzyme kinetics (reaction rates).

Second, we quantify the averaged analyte concentration extracted in the patch (${\mathrm{G}}_{\mathrm{patch}}$), given a fixed concentration in the dermis ${\mathrm{G}}_{\mathrm{R}}$, see Figure 2a. Regardless of the transduction mechanism (colorimetric, electrochemical, etc.), the accumulated ${\mathrm{G}}_{\mathrm{patch}}$ is a critical parameter related to the minimum signal level set by the noise limit (LOD); since the ${\mathrm{G}}_{\mathrm{patch}}$ may degrade below the noise limit along the diffusive path to the sensing site, the sensor may not register the analyte fluctuations in the skin and, thus, fail to deliver the appropriate amount of drug. To determine ${\mathrm{G}}_{\mathrm{patch}}$, we assume steady state conditions and apply flux continuity among the enzyme, patch, and MN [19]:

$$\begin{array}{c}\hfill \frac{{\mathrm{G}}_{\mathrm{patch}}}{{\mathrm{G}}_{\mathrm{R}}}\propto \frac{{\mathrm{R}}_{\mathrm{ez}}+\frac{{\mathrm{R}}_{\mathrm{patch}}}{2}}{{\mathrm{R}}_{\mathrm{base}}+{\mathrm{R}}_{\mathrm{n}}+{\mathrm{R}}_{\mathrm{tip}}}.\end{array}$$

(5)

3.3. Theoretical Enhancement of Porous and Swellable Microneedles

For a faster closed-loop sensing and therapy, several approaches have been experimentally proposed, including the integration of P−S MNs in wearable patches [6,7,20,21]. Here, we derive a universal scaling relationship for P−S MNs and quantify their flux enhancement against hollow MNs. Ideally, given an arbitrary MN technology, the absorbing flux across the MN base aperture should be maximized for superior performance; a higher flux would absorb a higher analyte concentration in a shorter time to satisfy timely monitoring restrictions and minimum signal-to-noise ratio levels.

Although the theory can be generalized for an arbitrary geometry, we assume a cylindrical, homogeneous, isotropic MN, as shown in Figure 2b. First, we apply a flux balance in a slice of the MN at a distance x from the base:

$$\begin{array}{c}\hfill {\Phi }_{\mathrm{in},\mathrm{x}+\Delta \mathrm{x}}{\mathrm{A}}_{\mathrm{c}}-{\Phi }_{\mathrm{in},\mathrm{x}}{\mathrm{A}}_{\mathrm{c}}+{\Phi }_{\mathrm{out},\mathrm{x}}{\mathrm{A}}_{\mathrm{s}}=0,\end{array}$$

(6)

where the concentration-dependent flux Φ is the gradient of analyte concentration, and ${\mathrm{A}}_{\mathrm{c}}\mathrm{and}{\mathrm{A}}_{\mathrm{s}}$ are the crossectional and lateral surface areas of the slice. The steady state solution of (6) gives the analyte profile ${\mathrm{G}}_{\mathrm{x}}$ within the MN, assuming a fully absorbing MN base aperture (${\mathrm{G}}_{\mathrm{x}=0}=0$), see Figure 2b:

$$\begin{array}{c}\hfill \frac{{\mathrm{G}}_{\mathrm{x}}}{{\mathrm{G}}_{\mathrm{R}}}=1-\frac{cosh\left(\mathrm{m}({\mathrm{l}}_{\mathrm{n}}-\mathrm{x})\right)+\mathrm{H}sinh\left(\mathrm{m}({\mathrm{l}}_{\mathrm{n}}-\mathrm{x})\right)}{cosh\left({\mathrm{ml}}_{\mathrm{n}}\right)+\mathrm{H}sinh\left({\mathrm{ml}}_{\mathrm{n}}\right)},\end{array}$$

(7)

where $\mathrm{s}$ is the MN radius, $\mathrm{m}\equiv \sqrt{\frac{2{\mathrm{h}}_{\mathrm{T}}}{\mathrm{s}{\mathrm{D}}_{\mathrm{n}}}}$, with ${\mathrm{h}}_{\mathrm{T}}$ being an empirical geometry-dependent coefficient regulating the analyte transfer between the MN and dermis, and $\mathrm{H}=\frac{{\mathrm{h}}_{\mathrm{T}}}{\mathrm{m}{\mathrm{D}}_{\mathrm{n}}}$.

Second, to evaluate the extraction efficiency of a P−S MN (${\Gamma }_{\mathrm{PS}}$), we normalize the flux at the base of MN aperture ($\Phi \propto {\mathrm{D}}_{\mathrm{n}}\frac{{\mathrm{dG}}_{\mathrm{x}}}{\mathrm{dx}}$ at $\mathrm{x}=0$):

$$\begin{array}{c}\hfill {\Gamma }_{\mathrm{PS}}={\mathrm{r}}_{\mathrm{h}}\frac{sinh\left({\mathrm{r}}_{\mathrm{h}}\right)+\frac{1}{2}{\mathrm{r}}_{\mathrm{g}}{\mathrm{r}}_{\mathrm{h}}cosh\left({\mathrm{r}}_{\mathrm{h}}\right)}{cosh\left({\mathrm{r}}_{\mathrm{h}}\right)+\frac{1}{2}{\mathrm{r}}_{\mathrm{g}}{\mathrm{r}}_{\mathrm{h}}sinh\left({\mathrm{r}}_{\mathrm{h}}\right)},\end{array}$$

(8)

where

$$\begin{array}{c}\hfill {\mathrm{r}}_{\mathrm{h}}={\mathrm{ml}}_{\mathrm{n}}\equiv \sqrt{{\mathrm{h}}_{\mathrm{T}}/\left(\frac{{\mathrm{sD}}_{\mathrm{n}}}{2{\mathrm{l}}_{\mathrm{n}}^2}\right)},\end{array}$$

(9)

$$\begin{array}{c}\hfill {\mathrm{r}}_{\mathrm{g}}\equiv \frac{\mathrm{s}}{{\mathrm{l}}_{\mathrm{n}}}.\end{array}$$

(10)

Here, the parameter ${\mathrm{r}}_{\mathrm{h}}$ encapsulates the geometric and physical properties of MN and the surrounding environment, thereby dictating the P−S ability to absorb analytes from the dermis. To compare the performance of the P−S and hollow technologies, we derive a similar relationship for hollow MNs at the base aperture of the MN:

$$\begin{array}{c}\hfill {\Gamma }_{\mathrm{H}}\approx \frac{1}{1+\frac{{\mathrm{D}}_{\mathrm{n}}}{{\mathrm{D}}_{\mathrm{body}}}{\mathrm{r}}_{\mathrm{g}}}.\end{array}$$

(11)

The ratio ${\Gamma }_{\mathrm{PS}}/{\Gamma }_{\mathrm{H}}$ shows the theoretical enhancement in extracting the flux between the P−S MNs and hollow MNs.

4. Results

4.1. Impact on the Response Time and the Limit of Detection

Validated against COMSOL-based simulations, Figure 3a shows the impact of ${\mathrm{l}}_{\mathrm{n}}$ on the response time (left, (1)) and the limit of detection (right, (5)) for a hollow MN-based patch. As expected, the theory predicts a tens of minutes to tens of hours lag time affecting the sensing operation of MN-based patches, depending on the sensor design. The diffusion time across the patch (${\mathrm{t}}_{\mathrm{PATCH}}$, (3)) and the enzyme-related delay (${\mathrm{t}}_{\mathrm{EZ}}$, (4)) set the critical limit of the performance. Overall, a longer MN would increase the transport time, degrading the closed-loop efficiency and suppressing the absorbed analyte concentration. Although not reported, a similar approach can be applied to predict the impact of other geometric and physical properties (MN apertures, MN material, and patch thickness) on sensor performance.

4.2. Enhancement and Limitations for Porous and Swellable Microneedles

Figure 3b shows the impact of ${\mathrm{l}}_{\mathrm{n}}$ on the enhancement factor between P−S and hollow MNs ((8), (11), left) and on the tradeoff between the extracted flux and mechanical constraints for a P−S MN (right). Unlike a hollow MN, a P−S MN benefits from a longer MN, because of the enhanced surface area absorbing biofluid, see Figure 3a (right). The enhancement factor introduced by ${\mathrm{l}}_{\mathrm{n}}$ is between 3 and 4; yet, by varying other geometric and physical variables (MN radius, diffusivity, etc.), it can achieve a factor of 6. Despite the significant benefits in performance, P−S MNs suffer from a weaker mechanical strength, limiting their skin insertion. Figure 3b shows that the tradeoff between the performance and mechanical constraints defines a ‘window design’ for P−S MNs. To successfully insert the MNs, a margin of mechanical safety (${\mathrm{F}}_{\mathrm{ins},\max }<{\mathrm{F}}_{\mathrm{buck}}$, buckling limit higher than the maximum force supported by the MN) should be guaranteed, see [22]. While a longer MN maximizes the extracting flux Φ, it may cause mechanical failure (${\mathrm{F}}_{\mathrm{ins},\max }>{\mathrm{F}}_{\mathrm{buck}}$); therefore, there exists an optimized length satisfying both performance and mechanics at ${\mathrm{F}}_{\mathrm{ins},\max }={\mathrm{F}}_{\mathrm{buck}}$.

5. Conclusions

We have developed a generalized theoretical framework for hollow and P−S MNs integrated into wearable patches as part of a comprehensive predictive model for personalized, autonomous, and independent theragnostics. Our theory quantifies sensor performance, including the response time and extracted analyte concentration, based on the geometric and physical properties of the sensor. We also identified the fundamental limitations of hollow MNs and predicted an enhancement factor introduced by P−S MNs, albeit with a tradeoff of weaker mechanical strength.

The model can be generalized to analyze novel MN technologies for an improved response time. For instance, the integration of sensing sites (electrodes) within MNs accelerates the detection by reducing the transport time [23]. Despite the potential degradation due to biofouling, the approaches involving functionalized MN surfaces reduce the response time by directly exposing sensing sites to analyte fluctuations in the dermis [24].

For a comprehensive analysis, the model should incorporate considerations of mechanical failure, inflammation, and biocompatibility-related concerns of MNs. More generally, by including a sensing-to-therapy algorithm and a theory for drug delivery, we would be able to provide a comprehensive framework for a systematic optimization of MN-based systems.