Pharmacokinetics‐Based Design of Subcutaneous Controlled Release Systems for Biologics

ABSTRACT

Protein therapeutics have emerged as an exceedingly promising treatment modality in recent times but are predominantly given as intravenous administration. Transitioning to subcutaneous (SC) administration of these therapies could significantly enhance patient convenience by enabling at‐home administration, thereby potentially reducing the overall cost of treatment. Approaches that enable sustained delivery of subcutaneously administered biologics offer further advantages in terms of less frequent dosing and better patient compliance. Controlled release technologies, such as hydrogels and subcutaneous implantable technologies, present exciting solutions by enabling the gradual release of biologics from the delivery system. Despite their substantial potential, significant hurdles remain in appropriately applying and integrating these technologies with the ongoing development of complex biologic‐based therapies. We evaluate the potential impact of subcutaneously delivered controlled release systems on the downstream pharmacokinetics (PK) of several FDA‐approved biologics by employing rigorous mathematical analysis and predictive PK simulations. By leveraging linear time‐invariant (LTI) systems theory, we provide a robust framework for understanding and optimizing the release dynamics of these technologies. We demonstrate simple quantitative metrics and approaches that can inform the design and implementation of controlled release technologies. The findings highlight key opportunity areas to reduce dosing frequency, stabilize concentration profiles, and synergize the codelivery of biologics, calling for collaboration between drug delivery and PK scientists to create the most convenient, optimized, and effective precision therapies.

Summary.

• What is the current knowledge on the topic?

  • ○
    Controlled release technologies offer benefits for subcutaneous administration of biologics, enhancing patient convenience and compliance. However, integration of these technologies with biologic therapies is not routinely implemented in early drug development due to the unknown consequences of their impact on pharmacokinetic, pharmacodynamic profiles and treatment outcomes.
• What question did this study address?

  • ○
    Our approach investigated the impact of subcutaneous controlled release system design features on dose, dosing regimens and PK profiles of several FDA‐approved biologic drugs.
• What does this study add to our knowledge?

  • ○
    The proposed approach highlights the use of quantitative metrics and design strategies, highlighting key opportunities to reduce dosing frequency, stabilize drug concentrations, and optimize the co‐delivery of biologics. It demonstrates the feasibility of using PK modeling in early design to guide the development of controlled release systems.
• How might this change drug discovery, development, and/or therapeutics?

  • ○
    The methodology proposed in this work promotes an early collaboration between drug delivery and PK scientists, paving the way for more complex biologic therapies and enabling more convenient, effective, and safe treatments for patients.

1. Introduction

Biologics such as monoclonal antibodies and fusion proteins have swiftly evolved as a cornerstone in modern medicine. Unlike small molecule drugs, the unique molecular structure, relatively large size of biologics and their susceptibility for degradation in the gastrointestinal tract typically preclude oral administration [1]. Thus, biologics are predominantly given as intravenous (IV) injections although some products do provide the option of subcutaneous (SC) injection as an alternative route of drug delivery. While IV administration allows precise control of drug delivery directly into the blood, it necessitates long visits to healthcare facilities, leading to a significant burden on patients and healthcare systems. In addition to this, people in remote areas and developing nations often do not have access to the clinics making it further difficult for them to receive treatment of biologics that are predominantly given as IV administration. SC injections are either administered at a clinic or can be self‐administered. In recent years, many biologics have been designed for SC administration because of this benefit and improved patient compliance [2]. Even so, some SC dosed biologics often require frequent dosing, resulting in a high patient burden and gaps in care or no access to treatment for some patients [2, 3].

Biologics exhibit distinct pharmacokinetic (PK) properties that necessitate a nuanced understanding during the course of drug development. The unique PK properties of each biologic drug are often greatly influenced by its molecular and target properties. Small proteins are often non‐specifically cleared rapidly from blood compared antibodies that exhibit extended half‐lives because of FcRn recycling mediated by the Fc region [1]. The majority of biologics exhibit target‐mediated drug disposition (TMDD), wherein the interaction of the drug with the specific target affects the PK [1]. This phenomenon can lead to nonlinear behavior post SC absorption and clearance at low doses, further complicating dosing regimens. Additionally, the toxicities associated with biologic drugs are driven by peak concentrations (C _max), presenting challenges in achieving therapeutic levels without reaching toxic thresholds [4, 5]. Unique approaches such as complex step‐up dosing schedules have been designed to try to overcome these challenges for some products [6]. Changes in these PK properties can greatly affect the downstream pharmacodynamics and must be intentionally designed for each specific therapy. With the rise of potent new modalities such as immunocytokines, T‐cell bispecifics, antibody drug conjugates, further control of biologic PK could provide improved therapies for patients, beyond what is possible with traditional dosing strategies.

Starting in the 1960s, material and drug delivery scientists began to design implantable or injectable materials that could be placed into the body (such as in the SC space) to slowly release drugs of interest [7]. Ever since controlled release technologies, such as hydrogels (both injectable and implantable), have emerged as promising solutions [8, 9, 10, 11, 12]. Aqueous in nature and often composed of polymeric networks forming a nanometer‐scale mesh, hydrogels enable slow diffusion of biologic drugs, facilitating a gradual release into the systemic circulation, and demonstrating the potential to prolong the half‐lives of biologic drugs and sustain more steady concentration profiles [13]. Additionally, many cutting‐edge SC implantable technologies involving spray‐dried antibodies and polymers have been developed [14, 15, 16, 17]. These novel systems ensure that antibodies can solubilize, remain biologically active, and slowly release from the implant. Scientists are working tirelessly to make the implantation and removal process as painless and fast as possible. It is also crucial that any injected or implanted controlled release system does not cause immune responses or fibrotic capsule formation [7, 18]. Although many sophisticated technologies have been developed, little attention is applied to optimize downstream PK during the design of controlled release systems. At present, the design of most controlled release systems is primarily focused on achieving the slowest possible release of biologic from the system, often without the support of clearly defined PK objectives. There exists a significant gap in quantitative knowledge and design criteria for engineering controlled release technologies that can effectively regulate the downstream PK of specific biologics of interest.

While controlled release technologies present exciting opportunities to improve patient outcomes, there remain challenges in translation between the design of these controlled release technologies and their desired downstream effects on the PK of biologics. It is still not completely understood how one should specifically design a controlled release system around a given therapy and what PK parameters are relevant to consider in their design. It is also unclear which biologics may be most benefited by having controlled release systems. In the current paradigm, controlled release technologies and biologic drugs are commonly developed separately, and only combined at late stages when a need arises. Unifying these strategies and thoughts at the early drug development stage has the potential to offer superior and optimized drug products for patients.

In this work we focus on subcutaneous controlled release systems and their design related to the pharmacokinetics of biologics. We show using mathematical analysis that controlled release technologies can affect the downstream pharmacokinetics of biologics in certain scenarios dependent on the drug of interest and the controlled release technology's specific parameters. We demonstrate through case studies using pharmacokinetic simulations with several FDA‐approved biologics that controlled release technologies have the potential to reduce the dosing frequency of fast‐clearing biologics, to reduce toxicity of potent molecules by maintaining more steady concentration profiles, to extend the exposure of biologic drugs exhibiting TMDD, and to synergize the co‐delivery of biologics in combinations. This work can serve as a design framework for the development of future controlled release technologies for biologics.

2. Methods

2.1. Pharmacokinetic Model to Evaluate the Downstream Pharmacokinetics of Biologics From Subcutaneous Controlled Release Technologies

Controlled release systems can be modeled as a compartment that releases drug into the subcutaneous space using a controlled release rate constant (Figure 1A) [12, 19, 20, 21, 22]. First‐order release is assumed in this work (Table S1), but other forms of release, such as zero‐order release, can also be relevant [20]. The release rate constant, termed k _cr, predominantly ranges from 0.001 to 0.1 day⁻¹ (Supplementary Discussion 1, Table S1) [9, 10, 13, 19, 23]. The controlled release compartment can be linked to other pharmacokinetic models (Supplemenrary Discussion 2), but we focus on a typical two compartment model with SC absorption [24, 25, 26].

FIGURE 1.

Two compartment model with subcutaneous absorption and an additional controlled release compartment. (A) Model schematic showing the dose is administered within the controlled release compartment, and a first‐order rate constant governs the kinetics connecting the controlled release compartment to the SC compartment. In cases including target‐mediated drug disposition of the biologic, an additional specific clearance term can be added to the model from the central compartment, shown here as Michaelis–Menten (MM) kinetics (noted in gray). (B) Two compartment simulations of etanercept with a single administration of 1 mg/kg dose with varying controlled release rates (k _cr). IV and SC dosing are shown as controls. When k _cr > 0.205 day⁻¹ (dotted lines), the terminal slope equals −0.205, and the half‐life (HL) is 3.4 days. When k _cr < 0.205 day⁻¹ (solid lines), the terminal slope equals −k _cr, and the half‐life (HL) is equivalent to $\frac{\mathit{ln}\left(2\right)}{k_{\text{cr}}}$. The method was validated by fitting the terminal slopes shown here.

The rate of change of the drug in the controlled release compartment, A _cr , can be described as,

$$\frac{d{A}_{\text{cr}}\left(t\right)}{\mathit{dt}}=-k_{\text{cr}}·A_{\text{cr}}\left(t\right)$$ (1)

Here we assume that no drug is left or lost in the controlled release compartment. The rate of change of the drug in the subcutaneous compartment, A _sc is given by,

$$\frac{d{A}_{\text{sc}}\left(t\right)}{\mathit{dt}}=k_{\text{cr}}·A_{\text{cr}}\left(t\right)-k_{\text{abs}}·A_{\text{sc}}\left(t\right)$$ (2)

where k _abs is the rate of subcutaneous absorption.

The rate of change in the central compartment, A _c, can be described as,

$$\begin{array}{c}\frac{d{A}_{\text{c}}\left(t\right)}{\mathit{dt}}=F·k_{\text{abs}}·A_{\text{sc}}\left(t\right)-\left(\frac{\mathit{CL}}{V_{\text{c}}}+\frac{Q}{V_{\text{c}}}\right)·A_{\text{c}}\left(t\right)+\frac{Q}{V_{\text{p}}}·A_{\text{p}}\left(t\right)\hfill \end{array}$$ (3)

where CL is the non‐specific clearance, Q represents the intercompartmental flow rate, and V _c and V _p represent the volumes of the central and peripheral compartments, respectively. The subcutaneous bioavailability fraction, F, can be multiplied directly to k _abs as shown [19, 27].

Finally, the rate of change in the peripheral compartment, A _p can be described as,

$$\frac{d{A}_{\text{p}}\left(t\right)}{\mathit{dt}}=\frac{Q}{V_{\text{c}}}·A_{\text{c}}\left(t\right)-\frac{Q}{V_{\text{p}}}·A_{\text{p}}\left(t\right)$$ (4)

This system of ODEs is a linear time‐invariant (LTI) system.

2.2. A Mathematical Framework to Aid in the Design of Controlled Release Technologies

We describe an analytical framework inspired by systems theory to assess how controlled release technologies may alter the pharmacokinetic half‐lives of biologics. We formalize our multi‐compartment pharmacokinetic model as a linear time‐invariant (LTI) system. Conventional pharmacokinetic approaches primarily focus on direct comparisons of rate constants of absorption and elimination in determining the rate‐limiting step of exposure. This is often influenced by the shape of the PK profile and can lead to bias for systems that exhibit flip‐flop pharmacokinetics [28]. In contrast to this, this LTI‐based framework provides the basis to holistically and mechanistically compare half‐life behavior of any complex pharmacokinetic system, irrespective of flip‐flop kinetics. By leveraging the mathematical tools intrinsic to LTI systems, such as eigenvalue analysis, we extract a robust understanding of the rate‐limiting steps on PK. The most relevant half‐life for the downstream pharmacokinetics will depend on the relative eigenvalue magnitudes [29]. The least negative eigenvalue will dominate the half‐life. This approach not only simplifies the complexity of multi‐compartment models, but also sets the stage for studies involving nonlinear or time varying systems.

For the 2 compartment model described in Figure 1A, we denote the state vector as x(t) = [A _cr(t), A _sc(t), A _c(t), A _p(t)] ^T . The system matrix A and the input initial condition matrix B can be written as,

or

$$A = \left[\begin{array}{cccc}-k_{cr}\hfill & 0& 0& 0\\ k_{cr}& -k_{abs}& 0& 0\\ 0& F*k_{abs}& -(a+b)& c\\ 0& 0& b& -c\end{array}\right]$$

where

$$a=\frac{\text{CL}}{V_{\text{c}}}$$

$$b=\frac{Q}{V_{\text{c}}}$$

$$c=\frac{Q}{V_{\text{p}}}$$

and

$$B=\left[\begin{array}{c}{A}_{cr}\left(0\right)\\ 0\\ 0\\ 0\end{array}\right]$$

So, the system of equations can be written as,

$$\frac{d}{\mathit{dt}}x\left(t\right)=A·x\left(t\right).$$ (5)

The eigenvalues ${\lambda }_{1,2,3,4}$ of the block‐diagonal matrix $A$ are then given by,

$${\lambda }_{1,2}=\frac{-\left(a+b+c\right)\pm \sqrt{{\left(a+b+c\right)}^2-4·a·c}}{2}$$ (6)

$${\lambda }_3=-k_{\text{abs}}$$ (7)

$${\lambda }_4=-k_{\text{cr}}$$ (8)

Here, λ ₁ and λ ₂ represent the eigenvalues governed by non‐specific clearance. λ ₃ represents the eigenvalue governed by absorption, and λ ₄ represents the eigenvalue governed by the controlled release rate.

For stable LTI systems, the reciprocal of the magnitude of the largest real part of the eigenvalues $\frac{1}{{\lambda }_{\text{max}}}$, is associated with the characteristic time constant of the system [29]. This time constant approximates how quickly the system responds to changes and reaches equilibrium. More precisely, the quantity $\frac{\ln \left(2\right)}{{\lambda }_{\mathit{max}}}$ is the steady‐state half‐life of the system. The negativity of the eigenvalues implies asymptotic stability, which is expected for a biologically plausible model [29]. In Equation (6), λ ₂  < λ ₁ for all biologics, so λ ₂ will never dominate the half‐life. Only in certain scenarios, λ₃  > λ ₁, meaning the subcutaneous absorption rate constant dictates the dominant half‐life, leading to flip‐flop pharmacokinetics [28]. This approach can be applied to other compartmental models (Supplementary Discussion 2). Since the parameters other than k _cr are commonly estimated during development through PK studies, drug delivery and PK scientists can now directly engineer the controlled release depot to release at a rate that will effectively prolong the biologic drug's half‐life (Equation 9). For a controlled release system to have an effect on the half‐life of a biologic,

$$k_{\text{cr}}<\left|\mathit{max}\left({\lambda }_1,{\lambda }_3\right)\right|.$$ (9)

While our mathematical framework focuses on first‐order release kinetics due to its widespread applicability and compatibility, it is important to consider other release mechanisms, such as zero‐order release. Unlike first‐order kinetics, zero‐order release does not yield distinct eigenvalues that affect the system's half‐life behavior. Instead, zero‐order release maintains a constant systemic concentration for a period of time, leading to a different transient pharmacokinetic profile, then the drug elimination would follow the same half‐life as either the subcutaneous (SC) or intravenous (IV) administration.

2.3. PK Model Parameters

Population PK model parameters were collected from cited population pharmacokinetic studies for each biologic using the population estimates with baseline covariates. All studies involved FDA‐approved drugs and were subcutaneously dosed, so reported subcutaneous parameters were used for simulations. Parameters used in case studies are listed in Tables S2 and S3. The controlled release rate constant, k _cr, was assumed to range from 0.001 day⁻¹ to 0.1 day⁻¹ based on current literature (Supplemenrtary Discussion 1, Table S1). The doses for controlled release were limited to < 1 g doses based on current literature [30].

2.4. PK Simulations

Simulations utilized the full system of ODEs that describe the corresponding pharmacokinetic compartment model. Simulations were performed using the Simbiology Model Builder and Model Analyzer applications within Matlab (Version 2023A). An example simbiology model file is included as a Supporting Information. Generation of plots and the resulting quantification of pharmacokinetic parameters were performed using Prism (Version 9).

3. Results

3.1. Applications of Linear Time‐Invariant Systems Theory for Pharmacokinetics‐Based Design of Controlled Release Systems

We apply our analysis based on LTI systems theory to diverse FDA‐approved subcutaneously delivered biologics and gain understanding regarding what controlled release rates are needed to provide significant value in optimizing the downstream pharmacokinetics (Table 1). Certain biologic drugs, such as peptides and smaller proteins, have highly negative eigenvalues (fast pharmacokinetics), and the half‐life timescale could potentially be altered with a controlled delivery system. Antibodies typically have prolonged pharmacokinetics compared to smaller proteins [1], so they would require k _cr < = 0.01 day⁻¹ for a controlled release system to prolong the half‐life.

TABLE 1.

Summary of FDA‐approved commonly known subcutaneously delivered biologic drugs and relevant timescale parameters from published population‐pharmacokinetic studies. These timescale parameters can be used as a framework to design a controlled release system that can effectively alter the dominant half‐life of the biologic drug based on our analysis. λ ₂ is not included here since λ ₂  < λ ₁ in all cases. Only maintenance doses are shown here for the primary indications of the biologics. For controlled release approaches to impact the PK, k _cr must be less than |max(λ ₁, λ ₃)|.

Biologic drug	Class	Dose	Dosing interval	Pop PK model	λ1	λ3	Half‐life (days)
Trastuzumab	Monoclonal Antibody	600 mg	Q3W	2 comp [24] with MM	−0.0174	−0.404	39.8
Tocilizumab	Monoclonal Antibody	162 mg	Q2W	2 comp [25] with MM	−0.0260	−0.230	26.7
Peginterferon alpha‐2a	Pegylated Cytokine	180 ug	QW	1 comp [31]	−0.145	−0.672	4.79
Adalimumab	Monoclonal Antibody	40 mg	Q2W	2 comp [26]	−0.0641	−0.259	10.8
Semaglutide	GLP‐1 Agonist Peptide	0.25–1 mg	QW	1 comp [32]	−0.092	−0.686	7.53
Somatropin	Protein	0.5 mg/kg	QW	1 comp [33]	−21.0	−2.93	0.236
Enfuvirtide	Peptide	90 mg	BID	1 comp [31]	−5.36	−2.71	0.256
Gonal‐F	Hormone	75 IU	QD	2 comp [34]	−0.369	−3.84	1.88
Dupilumab	Monoclonal Antibody	300 mg	Q2W	2 comp [35] with MM	−0.0279	−0.254	24.8
Pertuzumab	Monoclonal Antibody	600 mg	Q3W	2 comp [36]	−0.0292	−0.338	23.7
Darbepoetin Alfa	Erythropoietin	0.45–2.25 mg/kg	Q2W‐Q4W	2 comp [37]	−0.262	−0.508	2.65
Infliximab	Monoclonal Antibody	120 mg	Q2W	2 comp [38]	−0.0651	−0.273	10.6
Etanercept	Fusion Protein	25–50 mg	BIW‐QW	2 comp [39]	−0.205	−0.588	3.38

We examine the SC PK of etanercept, a TNF inhibitor used to treat arthritis [39]. The maximum eigenvalue for etanercept PK is equal to −0.205 day⁻¹ (Table 1), so a controlled release system with k _cr < 0.205 day⁻¹ would prolong the half‐life compared to conventional SC dosing. We simulate PK profiles of etanercept using a two compartment model with a single dose of 1 mg/kg over 100 days (Figure 1B) [39]. When k _cr > 0.205 day⁻¹, the terminal slope equals −0.205, and the half‐life is a consistent 3.4 days, a regime in which the half‐life is clearance‐dominated. In this regime, the C _max will decrease as k _cr approaches 0.205 day⁻¹. For biologic drugs with C _max‐related toxicities, such as T cell bispecific engagers, a k _cr close to the clearance‐driven eigenvalue may reduce toxicities while maintaining similar exposure and half‐life behavior [6]. When k _cr < 0.205 day⁻¹, the terminal slope equals −k _cr, and the half‐life is equivalent to $\frac{\mathit{ln}\left(2\right)}{k_{\text{cr}}}$, a regime in which the half‐life is controlled release‐dominated. It is also important to note that while the half‐life is prolonged with a small k _cr, the maximum concentration C _max decreases significantly.

3.2. Controlled Release Systems for Reducing the Dosing Frequency of Fast Clearing Protein Therapeutics

A potential benefit of controlled release technologies is the ability to reduce dosing frequency of drugs that traditionally require frequent SC dosing. Etanercept is subcutaneously dosed once to twice per week at a 50 mg dose and has a short half‐life of 3.4 days, governed by λ ₁ (Table 1). Weekly doses of 25 mg are also occasionally given. With its wide therapeutic index (TI) and relatively short half‐life, our analysis suggests that etanercept is a prime candidate to benefit from a controlled release system. The wide TI of etanercept also enables administration of higher doses in a controlled release implantable or injectable system without risk, and its dominant half‐life can be optimally tuned and prolonged with currently existing controlled release technologies (Figure 1B).

In Figure 2, we show simulated concentration profiles of the FDA‐approved SC doses of etanercept based on a two compartment PK model [39]. We propose two controlled release dosing strategies of a 325 mg and a 650 mg dose given every 90 days with a k _cr = 0.01 day⁻¹. Our two proposed controlled release approaches equate to nearly equivalent average steady state concentration, C _{ss , avg}, average steady state maximum concentration, C _{ss , max}, and minimum concentration, C _{ss , trough}, values (Figure 2B–D) compared to the clinically approved SC dose levels. The steady state exposure is thought to be the key driver for etanercept efficacy [40], so C _{ss , avg} is an important design parameter to match to observe similar downstream activity. The proposed dosing regimens require a longer time period for the controlled release strategies to reach steady state, but may be mitigated by more frequent supplemental conventional SC dosing and switching to solely controlled release SC systems thereafter (Figure S1). In Figure S2, we demonstrate how altering the dose, dosing interval and release rate for etanercept will each affect the PK profile with controlled release.

FIGURE 2.

The effect of controlled release on reducing dosing frequency of a fast‐clearing protein, etanercept (A) The pharmacokinetic simulation profile over 400 days of two current subcutaneous doses/regimens (purple), and the simulated profiles of two potential controlled release systems (orange and red). (B) The steady state average concentration C _{ss , avg} of each simulation. (C) The steady‐state C _{ss , max} of each simulation. (D) The steady‐state C _{ss , trough} of each simulation.

The proposed dosing strategies reduce the number of doses the patient must endure from 52 doses per year to 4 doses a year, approximately a 13‐fold reduction in number of administrations per year. A 90 day dosing frequency would offer a great convenience for patients with less visits to clinics, specifically for patients from impoverished locations. This example highlights how our framework can aid in the selection of prime biologics for controlled release approaches.

3.3. Controlled Release Systems for Potent Biologics With a Narrow Safety Window

In contrast to etanercept, many biologics such as immunocytokines, T‐cell bispecifics, antibody drug conjugates are highly potent, and exhibit a narrow therapeutic window, leading to toxicities commonly driven by high C _max or C _avg values [6]. While SC dosing can mitigate some toxicities associated with peak concentrations, controlled release approaches can offer further benefit by minimizing concentration fluctuations. Here, we consider peginterferon alpha‐2a, a pegylated interferon‐alpha [41], which is not commonly prescribed because of its frequent side effects. Peginterferon alpha‐2a is dosed at 180 μg weekly and exhibits a half‐life of approximately 5 days (Table 1). Our analysis using a one compartment SC PK model [41] demonstrates that when the controlled release rate constant k _cr is less than the dominant eigenvalue (−0.145) the effective half‐life can be extended (Figure S3).

Figure 3 shows simulated pharmacokinetic profiles of peginterferon alpha‐2a at the approved clinical SC dose and a hypothetical controlled delivery system [41]. Three proposed controlled release dose levels are administered once every 30 days with k _cr = 0.01 day⁻¹. The controlled release simulations lead to more consistent concentration profiles that exhibit lower C _max, higher C _trough, and tunable C _avg values (Figure 3B–D). The controlled release technology also offers the ability to optimize each of these parameters. A complete understanding of the dose–response toxicity behavior is needed to propose an optimal dosing regimen, but a controlled release approach with a more stable pharmacokinetic profile may lead to reduced toxicities.

FIGURE 3.

The effect of controlled release in tuning the pharmacokinetics of a potent biologic. (A) Pharmacokinetic simulation profiles of currently approved weekly subcutaneous dosing of peginterferon alpha‐2a and proposed controlled release dosing strategies (assessing three dose levels). Steady state profiles are shown (time zero begins at steady state). (B) The steady state average concentration of each simulation. (C) The steady‐state C _{ss , max} of each simulation. (D) The steady‐state C _{ss , trough} of each simulation.

There is also risk of delivering higher doses with controlled release to the patient in the case there is any burst release upon delivery. Burst release (BR) is a phenomenon when some percentage of the drug escapes directly to the subcutaneous space upon implantation or injection [21]. Burst release can contribute to as high as 50% of the total drug dose (Table S1) [12, 21]. To provide insight into how this risk could be understood and addressed for future biologics, burst release of peginterferon alpha‐2a was simulated at various percentages by delivering a percentage of the starting dose directly to the subcutaneous compartment instead of the controlled release compartment (Figure 4A).

FIGURE 4.

The effect of burst release (BR) on the downstream pharmacokinetics of a potent biologic. (A) Compartment diagram illustrating how BR is modeled as split dosing between the controlled release depot compartment and the subcutaneous compartment. The rest of the model structure remained a one compartment PK model. (B) Pharmacokinetic simulation profiles of peginterferon alpha‐2a applying different BR percentages. These simulations use a dose of 700 μg administered every 30 days. Steady state profiles are shown (time zero begins at steady state). The C _max of the maximum tolerated dose of peginterferon alpha‐2a [42] is marked in the thick orange dashed line. The C _max of the standard weekly SC dose of peginterferon alpha‐2a is marked in the red dashed line. (C) The steady state concentration of each simulation. (D) The steady‐state C _{ss , max} of each simulation. (E) The steady‐state C _{ss , trough} of each simulation.

As initial conditions do not affect the eigenvalues of an LTI system (Equations (6), (7), (8)), BR will not affect the steady state half‐life behavior, but it will affect the transient PK behavior. We find that as the BR percentage increases, the transient PK of peginterferon alpha‐2a converges to that of the conventional SC delivery. A 10% burst release still shows a lower steady state C _max and higher C _trough compared to the weekly subcutaneous delivery, but as the BR percentage reaches 50% there is a substantial increase in the steady state C _max and reduction in C _trough (Figure 4C–E). However, in this specific case example, the predicted C _max of the 50% burst release still remains lower than the maximum tolerated dose reported for peginterferon alpha‐2a [42]. Connecting in vitro BR measurements to downstream pharmacokinetic parameters can help design an effective and safe SC controlled release therapy.

3.4. Controlled Release Systems for Antibodies With High Target‐Mediated Drug Disposition

A unique property of biologics is their susceptibility for target‐mediated drug disposition (TMDD), a phenomenon in which drug binding to its pharmacological target (such as cell surface receptor or soluble receptor) can lead to altered PK characteristics, based on target antigen properties [1]. At low doses, antibodies with TMDD exhibit faster overall clearance and shorter half‐lives.

When target‐specific nonlinear clearance is at play, such as in cases of target mediated drug disposition (TMDD) [1], assumptions must be made to linearize the system in order to apply our LTI systems‐based analysis. Supplementary Discussion 2 shows the full derivation for the eigenvalue that takes into account Michaelis–Menten (MM) kinetics, a commonly used model to represent specific clearance [24]. The Michaelis–Menten specific clearance is represented by,

$${\mathit{CL}}_{\mathit{MM}}\left(C\right)=\frac{V_{\text{max}}·C}{K_{\text{m}}+C}$$ (10)

where V _max is the maximum rate of target specific clearance, K _m is the drug concentration at which the rate of target specific clearance is half of V _max, C is the drug concentration. When the concentration is much less than K _m (low doses), the saturable kinetics can be approximated as first‐order linear kinetics (Supplementary Equation 10). The rate of specific clearance becomes directly proportional to the concentration, which effectively turns the Michaelis–Menten equation into a linear equation, and the eigenvalues can be approximated in this limit (Supplementary Discussion 2),

$${\lambda }_{1,2}=\frac{-\left(a+b+c+v\right)\pm \sqrt{{\left(a+b+c+v\right)}^2-4·\left(a·c+c·v\right)}}{2}$$ (11)

where

$$v=\frac{V_{\text{max}}}{K_{\text{m}}·V_c}$$

and V _max and K _m are the Michaelis–Menten parameters. This eigenvalue formula is only relevant in the limit of low concentrations of drug relative to K _m, so it is limited to scenarios where K _m is not a very small value. Our full PK simulations do not apply this assumption and include the nonlinear dynamics, but our steady state half‐life analysis uses these assumptions to inform the dominant eigenvalues. For scenarios where the approximation of K _m> > C, the eigenvalues may not reflect the complete dynamics of the system and the full ODE based model should be simulated.

To conceptually understand how a controlled release system may influence the half‐life in tandem with the effects of TMDD, we focus on trastuzumab, an antibody that is known to exhibit TMDD. Michaelis–Menten (MM) clearance can be applied to account for targetmediated nonlinear clearance of Trastuzumab (Supplementary Discussion 2) [24]. For trastuzumab, when MM clearance is not considered, |λ ₁| = 0.0174 day⁻¹ (Table 1), and when MM parameters are considered, |λ ₁| = 0.0578 day⁻¹ (Equation 11); thus, we would expect that a controlled release rate constant k _cr = 0.01 day⁻¹ should increase the half‐life as TMDD becomes relevant at lower doses. Trastuzumab exhibits TMDD at its current clinical maintenance dosing regimen of 600 mg, Q3W. We simulated potential controlled release systems at 3 dose levels to observe how TMDD affects the resulting PK (Figure 5A). The simulations apply the entire system of ODEs including the nonlinear clearance described with MM kinetics. We include a high SC dose (100 mg/kg) in our simulation as purely an exercise to demonstrate minimal impact of TMDD effect. However, note 100 mg/kg of trastuzumab would not be practically feasible to dose clinically and hence need to consider this as a theoretical example scenario without direct clinical relevance. At 100 mg/kg, the terminal slope is minimally affected by controlled release delivery because the dominant eigenvalues are close in magnitude. As the TMDD becomes more prominent at the lower concentrations (10 mg/kg and 1 mg/kg), the difference in terminal slope and half‐life between subcutaneous dosing and the controlled delivery groups increases further as predicted. At 1 mg/kg and 10 mg/kg, the terminal slope is greatly reduced with controlled release delivery and half‐life is extended. In the terminal region the concentration is below K _m where K _m = 33.9 μg/mL. The dominant eigenvalue is driven by k _cr because TMDD leads to an increase in |λ ₁|. For the 1 mg/kg simulation, all concentrations throughout the simulation are below K _m, so there is an increase in the %AUC of the SC Dose relative to the 10 mg/kg controlled release dose. These findings are also confirmed in the case of tociluzumab (Figure S4) [25]. Figure S5 additionally shows the effect of controlled release dosing of trastuzumab at the clinical maintenance dose at steady‐state.

FIGURE 5.

The effect of controlled release delivery on the downstream pharmacokinetics of trastuzumab across doses. (A) Pharmacokinetic simulation results over 100 days after a single administration of trastuzumab across 3 doses delivered through conventional SC and controlled release systems. Three rate constants for controlled release systems are considered. As the dose is lowered from 100 mg/kg to 1 mg/kg, TMDD further effects the PK as the central concentration reaches values below K _m (33.9 ug/mL). (B) %C _max of the SC dose across doses and k _cr values. (C) %AUC over 100 days of the SC dose across doses and k _cr values.

While our work has focused on the steady‐state half‐life behavior, transient properties, such as C _max will be affected by controlled release delivery approaches as well. Our steady state half‐life analysis does not capture these dynamics, but our simulations illustrate significant effects on the transient properties. It is important to note that if one desired a lower C _max and a comparable AUC (area‐under‐the‐curve), without affecting the half‐life, the k _cr = 0.1 day⁻¹ scenario in this single administration simulation could afford that, lowering the C _max by approximately half and delivering nearly equivalent AUC (Figure 5B,C). This design could be desirable for drugs with C _max related toxicities during initial doses, such as T‐cell engaging bispecific antibodies that trigger CRS at high concentrations [6].

3.5. Controlled Release Systems for Improving Co‐Delivery of Biologic Drug Combinations

Controlled delivery approaches have the potential to align the exposure of co‐delivered biologic drug combinations that otherwise differ in their dosing regimen due to differing elimination rates and half‐lives. For patient compliance, it may be beneficial sometimes to align dosing regimens of co‐delivered drugs. In some cases, we wish to have aligned exposure in order to synergize in their downstream pharmacodynamics [10, 11]. Dosing strategies are designed to maximize synergy of the two drugs [36]. Currently there are limited numbers of approved therapies involving the co‐delivery of biologics.

As a proof‐of‐concept case study, we examine Phesgo, an FDA‐approved therapy that involves the co‐delivery of trastuzumab and pertuzumab (Figure 6). Pertuzumab and trastuzumab bind to different epitopes of human epidermal growth factor receptor 2 (HER2) protein, so they work in synergy when co‐dosed. These two antibodies exhibit different pharmacokinetic behavior [24, 36] as evidenced by the different eigenvalues in our analysis (Table 1). Pertuzumab does not exhibit observable TMDD, while trastuzumab exhibits significant TMDD at approved clinical doses.

FIGURE 6.

The effect of controlled release on the downstream pharmacokinetics of two co‐delivered biologic drugs with different PK behavior. (A) The pharmacokinetic simulation profiles of trastuzumab and pertuzumab (k _cr = 0.01 day⁻¹, equivalent half‐lives). Pertzumab is dosed at 2 mg/kg in the case of controlled release to match the AUC of the SC 1 mg/kg pertuzumab dosing. (B) The pharmacokinetic simulation profiles of trastuzumab and pertuzumab at adjusted doses with SC and with controlled release systems. (C) The C _max of trastuzumab (blue) and pertuzumab (purple) in various delivery scenarios. (D) The AUC over 100 days of trastuzumab (blue) and pertuzumab (purple) in various delivery scenarios.

When these two drugs are delivered at the same dose subcutaneously, they exhibit different pharmacokinetic behavior and half‐lives (Figure 6A). Trastuzumab exhibits a dominant eigenvalue of 0.0578 day⁻¹ (Equation 11), while pertuzumab exhibits a dominant eigenvalue of 0.0292 day⁻¹. These SC‐delivered antibodies exhibit roughly equivalent C _max values, but different half‐lives and AUC values (Figure 6A,C,D). When a controlled release system with a sufficiently small controlled release rate constant is applied (Pertuzumab CR dose increased to match pertuzumab SC AUC), the dominant eigenvalue of these two different biologics becomes equivalent, aligning the terminal slope of the two biologic drugs. When they are delivered with a controlled release system at the adjusted doses, they exhibit more aligned half‐lives (Figure 6A), but still different AUC and C _max values. Even when the trastuzumab dose with SC delivery is increased to 2 mg/kg, the AUC does show improved alignment with pertuzumab, but the C _max values further diverge (Figure 6B–D). Finally, when the trastuzumab dose is adjusted with controlled delivery (Figure 6B), then all the half‐life, AUC and C _max values become nearly equivalent (Figure 6C,D). The illustration of this combination (Phesgo) in our work is intended to demonstrate how we can optimize and align PK properties of two antibodies (of distinct PK properties) co‐delivered in a controlled delivery system for SC administration but not necessarily to suggest clinical implementation of this case study. A thorough diligence of practical utility and clinical implementation feasibility should be investigated before exploring controlled release drug delivery systems for drug combinations.

4. Discussion

In this work, we provide an engineering framework based on linear time‐invariant systems theory that will assist PK and drug delivery scientists in designing effective controlled release systems for biologic drug development. We use SC administered biologics as case examples to demonstrate how specific parameters of controlled release systems should be adjusted for PK optimization for specific biologics to achieve more convenient and effective therapies. Our eigenvalue analysis provides quantitative insights into the necessary rate or timescale for a controlled release system to release a biologic drug for PK optimization. Our approach provides a modular way of effectively designing controlled release systems for drugs with known PK parameters. Future work could apply systems theory to study the transient pharmacokinetic response of different controlled drug delivery approaches.

Through our analysis and simulations, we demonstrate how etanercept can be delivered with an SC controlled drug delivery system to reduce SC dosing frequency (up to a 13× reduction) while providing desired systemic exposure. Etanercept can benefit greatly as a prime candidate for controlled release by applying our analysis. Similar possibilities are possible for several other biologics, such as GLP‐1 peptides where proof‐of‐concept has already been shown preclinically [21]. Controlled release technologies can also provide more stable concentration profiles for drugs that may exhibit toxicities due to large fluctuations in PK behavior. For example, peginterferon alpha‐2a can benefit from a controlled release system that provides desired SC systemic exposure while reducing toxicities.

By analyzing the effects of controlled release systems on the PK of an antibody with TMDD, such as trastuzumab, we demonstrate a stronger impact with controlled drug delivery systems. Our simulations also show the potential for aligning PK for two distinctly behaved drugs via co‐delivery in a controlled release system. For example, Phesgo, co‐delivering trastuzumab and pertuzumab, can have better‐aligned half‐lives, C _max, and AUC values. The case studies explored and candidate biologics presented in this work are solely for the purpose of illustrating our method with real‐world examples and not necessarily make recommendation for developing controlled release systems for these biologics.

While there are many opportunities with controlled release technologies, there remain limitations and challenges before these approaches become standard practice. Our mathematical analysis and predictive PK simulations provide theoretical guidance and quantitative metrics for early‐stage design of controlled release technologies, but experimental validation of in vitro‐in vivo correlation will be needed as the design process progresses. Examples have validated correlations in preclinical studies, but clinical studies are needed to ultimately confirm the potential of these technologies [9, 12, 19].

Formulation limitations play a crucial role in determining the suitability of biologics for controlled release technologies [30]. While controlled release approaches can extend the exposure of biologics, there are significant challenges associated with high concentration doses, particularly within the SC dose volume of 1.5–5 mL [30]. Although hydrogel materials can load up to 300 mg/mL of protein [43], advanced formulation technologies are needed for required dosages without causing aggregation or instability. While a limitation of this work is its primary focus on first‐order release kinetics, our analytical framework provides a robust foundation for understanding and predicting the pharmacokinetics of controlled release systems, and future studies can build on this by incorporating the complexities of other release mechanisms. In addition, we detail various studies that have demonstrated and confirmed the effectiveness and potential of different controlled release technologies in sustaining the delivery of biologics and improving their pharmacokinetic profiles Supplementary Discussion 1, [44, 45, 46, 47, 48, 49, 50].

We hope to demonstrate that in specific scenarios, it may be most effective to begin co‐designing controlled release delivery approaches while developing the biologics. In this way, the biologic itself, the PK, the pharmacodynamics and the efficacy can be appropriately understood and engineered together as one therapy, rather than developing a controlled release technology as an after‐thought. With this work we hope to inspire a change in the industry mindset in this paradigm.

Author Contributions

Abigail K. Grosskopf, Vittal Shivva, and Antonio A. Ginart designed the research. Abigail K. Grosskopf and Vittal Shivva wrote the manuscript. Abigail K. Grosskopf and Antonio A. Ginart performed the research. Abigail K. Grosskopf and Phillip Spinosa analyzed the data. Phillip Spinosa contributed new analytical tools. All authors reviewed the manuscript.

Conflicts of Interest

Abigail K. Grosskopf, Phillip Spinosa, and Vittal Shivva are full‐time employees at Genentech Inc., and hold stocks in the company. The authors declare no conflicts of interest.

Supporting information

Supinfo 1

Supinfo 2