# In Vitro-In Vivo Correlation for the Degradation of Tetra-PEG Hydrogel Microspheres with Tunable β-Eliminative Crosslink Cleavage Rates

Authors: Jeff Henise; Shaun D. Fontaine; Brian R. Hearn; Samuel J. Pfaff; Eric L. Schneider; Julia Malato; Donghui Wang; Byron Hann; Gary W. Ashley; Daniel V. Santi
Journal: International Journal of Polymer Science
 (2019)

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## Abstract

The degradation of Tetra-PEG hydrogels containingβ-eliminative crosslinks has been studied in order to provide an in vitro-in vivo correlation for the use of these hydrogels in our chemically controlled drug delivery system. We measured time-dependent gel mass loss and ultrasound volume changes of 13 subcutaneously implanted Tetra-PEG hydrogel microspheres having degradation times ranging from ~3 to 250 days. Applying a previously developed model of Tetra-PEG hydrogel degradation, the mass changes correlate well with the in vitro rates of crosslink cleavage and hydrogel degelation. These results allow prediction of in vivo biodegradation properties of these hydrogels based on readily obtained in vitro rates, despite having degradation times that span 2 orders of magnitude. These results support the optimization of drug-releasing hydrogels and their development into long-acting therapeutics. The use of ultrasound volume measurements further provides a noninvasive technique for monitoring hydrogel degradation in the subcutaneous space.


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## Body

## 1. Introduction

We have developed a chemically controlled drug delivery system in which a drug is covalently attached via a carbamate to a polymeric hydrogel carrier using a self-cleavingβ-eliminative linker (L1); a similar β-eliminative linker (L2) with a slower cleavage rate is installed into each crosslink of the polymer to trigger gel degradation after drug release (Figure 1). Upon subcutaneous injection, the drug is slowly released into the systemic circulation, and subsequently, the gel biodegrades into small fragments that are eliminated.Figure 1
Depiction of chemically controlled drug release and subsequent degradation of a Tetra-PEG hydrogel withβ-eliminative crosslinks.Figure2 depicts the chemistry that drives linker cleavage for both drug release and gel biodegradation. Here, the linker is attached to a drug or polymer chain (carrier) via a carbamate group (Figure 2, 1). Two carbons removed from the carbamate leaving group is an acidic carbon–hydrogen bond (C–H) which also contains an electron-withdrawing “modulator” (Mod) group that controls the pKa of the C–H bond. Upon proton removal to give 2 (in Figure 2), a rapid β-elimination occurs, cleaving the linker-carbamate bond and releasing the free drug. The rate of drug release is proportional to the acidity of the proton, which is, in large part, controlled by the electron-withdrawing ability of the pKa modulator. The rate of linker cleavage is also retarded as the basicity of the amine in the carbamate increases [1] or by substitution of deuterium for hydrogen in the acidic C–H bond to obtain a primary kinetic isotope effect [2].Figure 2
β-Elimination mechanism of linker cleavage.The polymeric carrier we use is the well-studied, near-homogeneous Tetra-PEG hydrogel [3] that can be administered by subcutaneous (SC) in situ gelation [1, 4] or, preferably, by SC injection of uniform ~40 μm-diameter microspheres through a small-bore needle [5].Most long-acting drug delivery systems involve encapsulation of a drug in a polymer that contains ester or other hydrolysable crosslinks, as exemplified by PLGA delivery systems. Here drug release and polymer degradation/erosion occur concurrently. In the present system, the rates of drug release,kL1, and hydrogel degradation, kL2, are independent and can be balanced so that the drug is released before the gel undergoes significant degradation/erosion. Otherwise, excessive fragments of gel will be solubilized that are covalently bound to the drug; although the drug will ultimately be released, such transient fragments should be minimized. Nonetheless, polymer degradation should be as fast as practical, so the gel does not remain in an in vivo compartment as an inert substance for unnecessary periods. This goal requires coordination and balancing of the rates of hydrogel degradation and drug release; we have suggested from computational approaches that the ratio of rates kL2/kL1 of ~3 may be a desirable balance for most such subcutaneous implants [6].While thein vivo kL1 can be determined by pharmacokinetic studies of the released drug, the in vivo rate of gel degradation kL2 is more difficult to assess. Temporal profiles describing mass loss or erosion of SC-implanted gels have conventionally been measured by analysis of the remaining implanted material in excised tissue from animals over time. Such studies have usually been performed by analysis of one implant per animal after euthanasia, necessitating multiple animals for each profile. Recently, efforts have shifted to the use of biomedical imaging to noninvasively monitor in vivo changes accompanying degradation of implants—notably MRI and various ultrasound (US) methodologies that can be translated across species [7]. However, these approaches measure several concurrent changes, including mass loss and gel swelling or shrinkage. Regardless of the methodology used, in vitro models have thus far been poor predictors of in vivo gel degradation.In the present work, we first established an approach to assess the mass loss of degradableβ-eliminative Tetra-PEG hydrogel microspheres subcutaneously (SC) implanted into rats. Temporal monitoring of volume changes were likewise determined using 3D ultrasound computer tomography (USCT) measurements of the implant cavity volumes. Then, we used these methods to determine degradation profiles of Tetra-PEG hydrogel microspheres having in vivo degradation times ranging from ~3 to 250 days. We fit the in vivo mass loss profiles to our mechanistic model for Tetra-PEG hydrogel degradation [6], relating them to the in vitro rates of microsphere degelation. These equations allowed translation of easy-to-obtain in vitro data to predict in vivo biodegradation rates, thus providing in vitro-in vivo correlations (IVIVC). Finally, we established a correlation between hydrogel degradation and implant volume at the injection site as measured by ultrasound which allows for noninvasive monitoring.


## 2. Materials and Methods

### 2.1. Synthesis and Crosslink Structure of Hydrogels

The fabrication of our Tetra-PEG hydrogel drug delivery system has been described [4, 5] and is detailed in Supplementary Material. Two general types of hydrogels were prepared, one where the cleavable crosslinker is attached to the α-group of lysine and the other where the crosslinker is attached to the ε-group of lysine (Figure 3). The hydrogels in Figure 3 were prepared by combining a 20 kDa 4-armed PEG-(cyclooctyne)4 (4) with a 20 kDa 4-armed PEG-(azido-linker-lysine)4 where the crosslinker (L2) is attached to either the α- (5) or ε-amine (6) of the lysine to give the corresponding α- (7) or ε- (8) triazolyl-crosslinked hydrogels. The free lysine amino groups of the hydrogels were then modified with 0.2 equivalents of 5(6)-carboxyfluorescein to serve as a probe for degradation, and the excess amines were capped by acetylation with acetyl N-hydroxysuccinimide. For comparison, hydrogel materials were prepared both as bulk-gel cones and as microspheres.Figure 3
Formation of Tetra-PEG hydrogels with cleavable crosslinks connected to theα- or ε-amine of a lysine residue that forms part of the crosslink. The R groups in hydrogels 7 and 8 show the position where a cleavable linker can be attached to tether a releasable drug or, in the case of this work, where fluorescein has been attached to facilitate detection of gel components by fluorescence upon gel degradation.


### 2.2. Measurement ofIn Vitro Gel Properties

Values for the crosslinker cleavage half-life (t1/2,L2invitro) for α-amine crosslinks (7) were measured by observing the decomposition of MeO-PEG-linker-carbamoyl-[5-(aminoacetamido)fluorescein] as previously reported [1], while those for ε-linked crosslinks (8) were measured using PEGylated Nα-(2,4-dinitrophenyl)-Nε-(carbamoyl-linker)-lysine as previously reported [1]. The in vitro degradation or time to reverse degelation (tRG) of the hydrogels was determined by placing fluorescein-labeled hydrogels, as cones or as microspheres, into buffer at 37°C and following the dissolution of gel components by absorbance at 495 nm (Supplementary Material). The tRG is determined as the time of intersection of the steepest part of the in vitro solubilization curve with the horizontal line representing total solubilization (Figure 4).Figure 4
In vitro solubilization (degelation) curves of Tetra-PEG hydrogels with crosslinks of different cleavage rates showing tRG values (Table S1). Crosslink cleavage rate modulators are shown in the legend of the figure. The tRG values were determined as an average of four replicates under accelerated conditions of pH 8.4, 9.0, or 9.4 at 37°C and converted to pH 7.4 values as described [11].


### 2.3.In Vivo Gel Erosion and Volume Changes

For each gel, subcutaneous injections of fluorescein-labeled microspheres (100μL) were made at various times into 8 sites spaced evenly over the shaved back of rats (Figure 5(a)). Three replicate animals were used for each gel. The time interval between injections was calculated as approximately 3×tRGinvitro/8, so that the eight injections were spaced in time to cover the expected period for complete degradation [6]. In this manner, the earliest injections had the longest residence time in the animal and the latest injections had the shortest residence time. After an animal had received seven injections (Figure 5(b)), and the first injection could no longer be detected by palpation, the animal was administered the final injection, at time equal to approximately 3×tRGinvitro, then was euthanized. Each injection site was analyzed for implant volume by 3D ultrasound computer tomography (USCT), and then the tissue surrounding the injection sites was removed using a 12 mm punch biopsy for measurements of the remaining gel by digestion of tissue followed by fluorescein detection. These methods are described in detail in Supplementary Material.Figure 5
Injections of microspheres in the rat. (a) Temporal sequence of eight injections of microspheres in the rat spaced in intervals of approximately3×tRGinvitro/8; C is an untreated control site for background fluorescence determination. (b) Photograph of tattoo-marked SC injection sites labeled 1, 3, 5, and 7 at termination of the experiment where 1 is the oldest injection with almost completely degraded microspheres and 7 is the newest injection with fully intact microspheres. Tattoo circles are approximately 12 mm in diameter.
(a)
(b)


## 2.1. Synthesis and Crosslink Structure of Hydrogels

The fabrication of our Tetra-PEG hydrogel drug delivery system has been described [4, 5] and is detailed in Supplementary Material. Two general types of hydrogels were prepared, one where the cleavable crosslinker is attached to the α-group of lysine and the other where the crosslinker is attached to the ε-group of lysine (Figure 3). The hydrogels in Figure 3 were prepared by combining a 20 kDa 4-armed PEG-(cyclooctyne)4 (4) with a 20 kDa 4-armed PEG-(azido-linker-lysine)4 where the crosslinker (L2) is attached to either the α- (5) or ε-amine (6) of the lysine to give the corresponding α- (7) or ε- (8) triazolyl-crosslinked hydrogels. The free lysine amino groups of the hydrogels were then modified with 0.2 equivalents of 5(6)-carboxyfluorescein to serve as a probe for degradation, and the excess amines were capped by acetylation with acetyl N-hydroxysuccinimide. For comparison, hydrogel materials were prepared both as bulk-gel cones and as microspheres.Figure 3
Formation of Tetra-PEG hydrogels with cleavable crosslinks connected to theα- or ε-amine of a lysine residue that forms part of the crosslink. The R groups in hydrogels 7 and 8 show the position where a cleavable linker can be attached to tether a releasable drug or, in the case of this work, where fluorescein has been attached to facilitate detection of gel components by fluorescence upon gel degradation.


## 2.2. Measurement ofIn Vitro Gel Properties

Values for the crosslinker cleavage half-life (t1/2,L2invitro) for α-amine crosslinks (7) were measured by observing the decomposition of MeO-PEG-linker-carbamoyl-[5-(aminoacetamido)fluorescein] as previously reported [1], while those for ε-linked crosslinks (8) were measured using PEGylated Nα-(2,4-dinitrophenyl)-Nε-(carbamoyl-linker)-lysine as previously reported [1]. The in vitro degradation or time to reverse degelation (tRG) of the hydrogels was determined by placing fluorescein-labeled hydrogels, as cones or as microspheres, into buffer at 37°C and following the dissolution of gel components by absorbance at 495 nm (Supplementary Material). The tRG is determined as the time of intersection of the steepest part of the in vitro solubilization curve with the horizontal line representing total solubilization (Figure 4).Figure 4
In vitro solubilization (degelation) curves of Tetra-PEG hydrogels with crosslinks of different cleavage rates showing tRG values (Table S1). Crosslink cleavage rate modulators are shown in the legend of the figure. The tRG values were determined as an average of four replicates under accelerated conditions of pH 8.4, 9.0, or 9.4 at 37°C and converted to pH 7.4 values as described [11].


## 2.3.In Vivo Gel Erosion and Volume Changes

For each gel, subcutaneous injections of fluorescein-labeled microspheres (100μL) were made at various times into 8 sites spaced evenly over the shaved back of rats (Figure 5(a)). Three replicate animals were used for each gel. The time interval between injections was calculated as approximately 3×tRGinvitro/8, so that the eight injections were spaced in time to cover the expected period for complete degradation [6]. In this manner, the earliest injections had the longest residence time in the animal and the latest injections had the shortest residence time. After an animal had received seven injections (Figure 5(b)), and the first injection could no longer be detected by palpation, the animal was administered the final injection, at time equal to approximately 3×tRGinvitro, then was euthanized. Each injection site was analyzed for implant volume by 3D ultrasound computer tomography (USCT), and then the tissue surrounding the injection sites was removed using a 12 mm punch biopsy for measurements of the remaining gel by digestion of tissue followed by fluorescein detection. These methods are described in detail in Supplementary Material.Figure 5
Injections of microspheres in the rat. (a) Temporal sequence of eight injections of microspheres in the rat spaced in intervals of approximately3×tRGinvitro/8; C is an untreated control site for background fluorescence determination. (b) Photograph of tattoo-marked SC injection sites labeled 1, 3, 5, and 7 at termination of the experiment where 1 is the oldest injection with almost completely degraded microspheres and 7 is the newest injection with fully intact microspheres. Tattoo circles are approximately 12 mm in diameter.
(a)
(b)


## 3. Results and Discussion

### 3.1. Synthesis and Crosslink Structure of Hydrogels

While the rate of cleavage of ourβ-eliminative linkers is primarily controlled by the structure of the modulator group as discussed above, this rate can be fine-tuned using various structural parameters, including the nature of the releasable amine group to which the linker is attached (e.g., the α- or ε-amino group of lysine) and the use of a deuterium atom in place of the acidic hydrogen atom shown in Figure 2 to slow the cleavage via a kinetic isotope effect [1, 2]. Using this information, a series of 13 Tetra-PEG hydrogels was prepared, covering a range of in vitro degelation times from 12 to 2750 hours (Supplementary Material (available here)).


### 3.2. Correlation between Linker Cleavage Rate andIn Vitro Time to Reverse Degelation (tRG)

ThetRG is the time at which the initially intact crosslinks are reduced to a critically low fraction and the gel becomes completely soluble. For Tetra-PEG hydrogels, the tRG is dependent upon the half-life of crosslink bond cleavage (t1/2,L2) and the quality of the gel (f) as defined by the number of unformed crosslinks present in the initial gel as shown below [6, 8]:
(1)tRG=t1/2,L2⋅ln1−f/0.39ln2,f=1–0.39⋅2tRG/t1/2,L2.Conversely, ift1/2,L2invitro is known from kinetic measurements of the crosslinking group, and tRGinvitro is known from in vitro degelation measurements, the gel quality factor f can be calculated as shown. Supplementary Material, Table S1, provides the tRG, t1/2,L2invitro, and f values of all hydrogels used in this study. Calculation of the quality factors revealed that the hydrogels fell into one of two groups, a major group (Table S1, D-M) having f~0.20±0.08 and a small group (Table S1, A-C) having f~0.45±0.02. The difference in these groups was traced to the quality of the starting commercial PEG-tetraamines used to synthesize the gels. Groups D-M were prepared using a PEG-tetraamine having 98% of expected amine end groups, while groups A-C were prepared using a PEG-tetraamine having only 82% of expected amine end groups. Thus, gels A-C contained a far greater fraction of unformed crosslinks in the initial gels.Within experimental error, thetRG of 100 μL single-molecule bulk-gel cones are the same as for the ~4×10−5 μL microspheres (Table S1), showing that degradation rates of gels are volume independent. Also, since the surface area to volume ratio of microspheres are ~100-fold higher than the cones, the data show that linker cleavage rates are homogeneous throughout the gels, making tRG independent of gel particle size.As predicted, attachment of the crosslinker to the more basicε-amine rather than α-amine groups of Lys slows both the β-elimination reaction and the tRG of gels by ~2-fold [1]. Likewise, an α-deuterated linker with Mod=MeSO2− or -CN shows an α-deuterium isotope effect that slows both the β-elimination and the tRG of gels by ~2.5- to 3.5-fold, respectively [2].


### 3.3.In Vivo Gel Erosion and Volume Changes

Each hydrogel microsphere material was injected into the subcutaneous space of rats in a sequence temporally spaced according to the expected degelation time, as described in Materials and Methods, in order to get a time course ofin vivo degelation (Figure 5(a)). The resultant circular to slightly elliptical protuberances from the 100 μL injections were initially ~10 mm (L) × ~8 mm (W) × ~3 mm (h). With time, the protuberances decreased in size, appeared to flatten, and then disappeared (Figure 5(b)).Measurements of the hydrogel components remaining in each injection site were made by excision of tissue containing the microspheres and detection of fluorescein by fluorescence following digestion of the tissue as described in Material and Methods. During degradation of the hydrogel, cleavage of the crosslinks results in formation of oligomeric pieces of gel of various sizes; if the oligomer is sufficiently small, it will be eliminated from the subcutaneous space through the systemic or lymphatic circulation. The mass of gel remaining at the injection site will equal the original mass minus the mass of released small fragments. This analysis measures the remaining mass of intact microspheres as well as any large soluble fragments that have not diffused beyond the perimeter of the sampled tissue.According to our mechanistic model for Tetra-PEG hydrogels [6], the probability (PN,t) that an oligomeric gel fragment composed of N monomers is released from the gel at time t is given as
(2)PN,t=∑QNLDptN−1+Lqt2N+2−2L+D,pt=1−f∗exp−k2t,qt=1−pt,where k2 is the first-order rate constant for crosslink cleavage (k2=ln2/t1/2,L2), f is the gel quality factor (equation (1)), and QNLD is a statistical factor describing the number of oligomers of size N having a topology described by L and D that contain a given monomer as detailed in [6]. If we set an upper limit of Nmax for the size of gel fragments that can be efficiently eliminated from the SC space, the fraction of the total gel released at time t is thus given by the sum of the probabilities of release for N≤Nmax, and the mass of remaining hydrogel (Gelt/Gel0) can be calculated as
(3)GeltGel0=1−∑N=1,Nmax∑QNLDptN−1+Lqt2N+2−2L+D.According to this model, the degradation behavior of the hydrogel should be determined solely by the rate of cleavage of crosslink bonds (k2) and the gel quality factor f. According to our model, then, any Tetra-PEG hydrogel having quality factor f should exhibit the same time course for mass of gel remaining at the injection site when the time axis is normalized as t/tRGinvitro.For analysis, the fluorescence remaining at the injection site at timet (Ft) was normalized to the value at t=0 (Ft/F0) and is equal to Gelt/Gel0 (equation (3)). The time of the measurements was also normalized to tRG (t/tRGinvitro) for a given material. Data sets from materials of equivalent quality factor f were then overlaid (Figure 6(a)). This revealed that the loss of gel mass from the injection site followed identical behavior for all gel materials having equivalent quality factors despite having residence times that varied by an order of magnitude and that the initial quality of the gel has a profound impact on the in vivo degradation behavior. Regardless of the quality factor, the best-fit values for t1/2,L2invivo were uniformly longer than expected by a factor of 1.36 based on the values (t1/2,L2invitro) measured in vitro at 37°C, suggesting that the in vivo tRG is ~1.36 times the measured in vitro rate. This is consistent with the reported lower subcutaneous temperature in rats relative to the core temperature of 37°C [9]. Using the previously reported temperature dependence for linker cleavage [1], this suggests that the temperature in the rat subcutaneous space is approximately 34°C.Figure 6
Loss of gel components as a function oftRG. (a) Fractional fluorescence (Ft/F0) remaining at the injection site as a normalized function of t/tRGinvitro for 13 different hydrogel microspheres having tRG values ranging from 12 to 2750 hours and f=0.21 (black square) or f=0.45 (red circle). The data were grouped into clusters having a median of t/tRGinvitro±0.2, and vertical lines show the mean±standard deviation of the measured parameter within each cluster. Theoretical curves were calculated according to equation 3 where Nmax=6 and t1/2,L2=1.36·tRGinvitro. (b) Fit of the clustered ultrasound volumes of materials E-M (Table S1) to equation 4 using V0=83.5 mm3 and Q=1.5. Error bars represent the standard deviation of the clustered volume data.
(a)
(b)The amount of hydrogel remaining at the subcutaneous injection site over time is thus directly predictable based on our previously developed mechanistic model of Tetra-PEG hydrogel degradation, requiring knowledge only of theirin vitro tRG values and linker cleavage rates.As tissue biopsy is not a desirable means of studying hydrogel residence in a clinical setting, we measured the volume occupied by hydrogel implants by 3D ultrasound computer tomography (USCT), a painless, noninvasive technique readily translated to other animals and humans. Figure7 shows that immediately after injection of microspheres, a cross-section of the cavity formed in the SC space is as an elliptical structure readily identified by its unique sonographic features. Initially, the implanted hydrogel displays contrasting echogenic elements which over time transforms to an echolucent space that decreases in volume until it is undetectable. The volumes occupied by the microspheres were determined by integration of the implant area from 2D ultrasound image stacks obtained at constant depth and evenly spaced intervals (0.5 mm) along the length of the implant to give a 3D model of the implant (Figure 7(b)). Plots of cavity volume vs. time were constructed for each gel studied (Figure S1).Figure 7
Ultrasound analysis of implants. (a) 2D images of microsphere implants, with the degradation crosslink modulator -CN (ε-Lys), showing the widest cross-section at 0, 1700, and 5880 hours post injection, and the time relative to in vitro reverse degelation time (t/tRGinvitro). Scale bars=2 mm. (b) 3D USCT renderings showing the volumes of the implants shown in (a).The volume change over time was more complex than that for the loss of hydrogel components described above due to the swelling behavior of the hydrogels as they degrade and the force applied by the surrounding tissues [10]. As crosslinks are broken, the gel structure becomes less dense and the gel occupies a larger equilibrium volume up until the point that mass loss from the gel is sufficient to overcome the decrease in density. It is further expected that there will be some pressure applied by the surrounding tissues to counter increases in gel volume due to this swelling. Given this added complexity, only hydrogels having equivalent quality factors (f=0.2) were included in the volume analysis. Data points between materials were combined into the same groups of equivalent t/tRGinvitro±0.2 described above for the fluorescence data. The average initial cavity volumes in all animals of groups E-M (Table S1) resulting from 100 μL injections were 84±15 mm3, probably reflecting compression of the suspension and rapid absorption of the liquid buffer surrounding the microspheres. After an initial period, gel swelling became evident with the average volume increasing to 104±36 mm3 at a time equal to the in vivo tRG (i.e., 1.36 times the in vitro tRG as discussed above), after which the volume decreased to zero at 3-4 times the in vitro tRG. The time required for the cavity to collapse was thus the same as the time at which gel components were completely lost (Figure 6).In the absence of an analytical model for the change of hydrogel density during degradation, the ultrasound-determined volumes of the gels were empirically fit to a double-sigmoid curve (equation (4)) using parameters for initial volume V0 and a swelling factor Q that describes the volume increase due to loss of gel density during degradation.
(4)Vt=V01−Q1+t/tRGinvitro3+Q1+t/tRGinvitro6.As for the fluorescence data described above, the cavity volumes measured by ultrasound predictably correlate with thein vitro properties of the hydrogels, allowing for the use of noninvasive ultrasound techniques to monitor the status of hydrogels in the subcutaneous space.The primary objectives of this work were to characterize thein vivo degradation rates of Tetra-PEG hydrogel microspheres containing tunable β-eliminative crosslinks and to construct an in vitro-in vivo correlation (IVIVC) that would allow prediction of in vivo degradation from data obtained in vitro. Using microspheres with in vivo degradation times of ~3 to 250 days, we measured the loss of gel mass over time from the injection site and demonstrated that the in vivo degradation behavior is well-described by the mechanistic model of Reid et al. [6]. Thus, the in vivo degradation behavior of our β-eliminatively linked Tetra-PEG hydrogels is predictable based only on the in vitro linker cleavage rate (kL2invitro) and hydrogel degelation time (tRGinvitro). Importantly, the relationship held for 13 different gels spanning a tRGinvitro range of 12 to 2750 hours and should be useful for predicting in vivo properties of yet-unmade gels. In a secondary objective, we demonstrated that changes in volume of the subcutaneous microsphere depots as measured by ultrasound imaging are an effective, noninvasive, and painless surrogate for following in vivo degradation of our hydrogels.Approaches for measuring actual mass loss accompanying gel degradation usually involve isolation (excision) and quantitation of remaining material in animal implants over time. Early serial studies usually used one implant per animal and suffered from the need for numerous animals and interanimal variation. Here, the experimental design used longitudinal subcutaneous injections of the polymer at eight locations on a rat over the expectedin vivo lifetime; then, after the first-injected polymer had disappeared by visualization/palpation, the animals were euthanized and the gels in all injection sites were analyzed. The earliest injections had the longest residence time in the animal, and the latest injections had the shortest residence time. Hence, a single animal provided the full temporal analysis of in vivo gel degradation, and intra-animal variation was avoided.The constant gel mass over varying long periods prior to the onset of degelation shows that the microspheres do not migrate from the initial site of deposition. Thus, in case the microsphere-drug conjugates require removal, they can be completely excised by a simple punch biopsy.


## 3.1. Synthesis and Crosslink Structure of Hydrogels

While the rate of cleavage of ourβ-eliminative linkers is primarily controlled by the structure of the modulator group as discussed above, this rate can be fine-tuned using various structural parameters, including the nature of the releasable amine group to which the linker is attached (e.g., the α- or ε-amino group of lysine) and the use of a deuterium atom in place of the acidic hydrogen atom shown in Figure 2 to slow the cleavage via a kinetic isotope effect [1, 2]. Using this information, a series of 13 Tetra-PEG hydrogels was prepared, covering a range of in vitro degelation times from 12 to 2750 hours (Supplementary Material (available here)).


## 3.2. Correlation between Linker Cleavage Rate andIn Vitro Time to Reverse Degelation (tRG)

ThetRG is the time at which the initially intact crosslinks are reduced to a critically low fraction and the gel becomes completely soluble. For Tetra-PEG hydrogels, the tRG is dependent upon the half-life of crosslink bond cleavage (t1/2,L2) and the quality of the gel (f) as defined by the number of unformed crosslinks present in the initial gel as shown below [6, 8]:
(1)tRG=t1/2,L2⋅ln1−f/0.39ln2,f=1–0.39⋅2tRG/t1/2,L2.Conversely, ift1/2,L2invitro is known from kinetic measurements of the crosslinking group, and tRGinvitro is known from in vitro degelation measurements, the gel quality factor f can be calculated as shown. Supplementary Material, Table S1, provides the tRG, t1/2,L2invitro, and f values of all hydrogels used in this study. Calculation of the quality factors revealed that the hydrogels fell into one of two groups, a major group (Table S1, D-M) having f~0.20±0.08 and a small group (Table S1, A-C) having f~0.45±0.02. The difference in these groups was traced to the quality of the starting commercial PEG-tetraamines used to synthesize the gels. Groups D-M were prepared using a PEG-tetraamine having 98% of expected amine end groups, while groups A-C were prepared using a PEG-tetraamine having only 82% of expected amine end groups. Thus, gels A-C contained a far greater fraction of unformed crosslinks in the initial gels.Within experimental error, thetRG of 100 μL single-molecule bulk-gel cones are the same as for the ~4×10−5 μL microspheres (Table S1), showing that degradation rates of gels are volume independent. Also, since the surface area to volume ratio of microspheres are ~100-fold higher than the cones, the data show that linker cleavage rates are homogeneous throughout the gels, making tRG independent of gel particle size.As predicted, attachment of the crosslinker to the more basicε-amine rather than α-amine groups of Lys slows both the β-elimination reaction and the tRG of gels by ~2-fold [1]. Likewise, an α-deuterated linker with Mod=MeSO2− or -CN shows an α-deuterium isotope effect that slows both the β-elimination and the tRG of gels by ~2.5- to 3.5-fold, respectively [2].


## 3.3.In Vivo Gel Erosion and Volume Changes

Each hydrogel microsphere material was injected into the subcutaneous space of rats in a sequence temporally spaced according to the expected degelation time, as described in Materials and Methods, in order to get a time course ofin vivo degelation (Figure 5(a)). The resultant circular to slightly elliptical protuberances from the 100 μL injections were initially ~10 mm (L) × ~8 mm (W) × ~3 mm (h). With time, the protuberances decreased in size, appeared to flatten, and then disappeared (Figure 5(b)).Measurements of the hydrogel components remaining in each injection site were made by excision of tissue containing the microspheres and detection of fluorescein by fluorescence following digestion of the tissue as described in Material and Methods. During degradation of the hydrogel, cleavage of the crosslinks results in formation of oligomeric pieces of gel of various sizes; if the oligomer is sufficiently small, it will be eliminated from the subcutaneous space through the systemic or lymphatic circulation. The mass of gel remaining at the injection site will equal the original mass minus the mass of released small fragments. This analysis measures the remaining mass of intact microspheres as well as any large soluble fragments that have not diffused beyond the perimeter of the sampled tissue.According to our mechanistic model for Tetra-PEG hydrogels [6], the probability (PN,t) that an oligomeric gel fragment composed of N monomers is released from the gel at time t is given as
(2)PN,t=∑QNLDptN−1+Lqt2N+2−2L+D,pt=1−f∗exp−k2t,qt=1−pt,where k2 is the first-order rate constant for crosslink cleavage (k2=ln2/t1/2,L2), f is the gel quality factor (equation (1)), and QNLD is a statistical factor describing the number of oligomers of size N having a topology described by L and D that contain a given monomer as detailed in [6]. If we set an upper limit of Nmax for the size of gel fragments that can be efficiently eliminated from the SC space, the fraction of the total gel released at time t is thus given by the sum of the probabilities of release for N≤Nmax, and the mass of remaining hydrogel (Gelt/Gel0) can be calculated as
(3)GeltGel0=1−∑N=1,Nmax∑QNLDptN−1+Lqt2N+2−2L+D.According to this model, the degradation behavior of the hydrogel should be determined solely by the rate of cleavage of crosslink bonds (k2) and the gel quality factor f. According to our model, then, any Tetra-PEG hydrogel having quality factor f should exhibit the same time course for mass of gel remaining at the injection site when the time axis is normalized as t/tRGinvitro.For analysis, the fluorescence remaining at the injection site at timet (Ft) was normalized to the value at t=0 (Ft/F0) and is equal to Gelt/Gel0 (equation (3)). The time of the measurements was also normalized to tRG (t/tRGinvitro) for a given material. Data sets from materials of equivalent quality factor f were then overlaid (Figure 6(a)). This revealed that the loss of gel mass from the injection site followed identical behavior for all gel materials having equivalent quality factors despite having residence times that varied by an order of magnitude and that the initial quality of the gel has a profound impact on the in vivo degradation behavior. Regardless of the quality factor, the best-fit values for t1/2,L2invivo were uniformly longer than expected by a factor of 1.36 based on the values (t1/2,L2invitro) measured in vitro at 37°C, suggesting that the in vivo tRG is ~1.36 times the measured in vitro rate. This is consistent with the reported lower subcutaneous temperature in rats relative to the core temperature of 37°C [9]. Using the previously reported temperature dependence for linker cleavage [1], this suggests that the temperature in the rat subcutaneous space is approximately 34°C.Figure 6
Loss of gel components as a function oftRG. (a) Fractional fluorescence (Ft/F0) remaining at the injection site as a normalized function of t/tRGinvitro for 13 different hydrogel microspheres having tRG values ranging from 12 to 2750 hours and f=0.21 (black square) or f=0.45 (red circle). The data were grouped into clusters having a median of t/tRGinvitro±0.2, and vertical lines show the mean±standard deviation of the measured parameter within each cluster. Theoretical curves were calculated according to equation 3 where Nmax=6 and t1/2,L2=1.36·tRGinvitro. (b) Fit of the clustered ultrasound volumes of materials E-M (Table S1) to equation 4 using V0=83.5 mm3 and Q=1.5. Error bars represent the standard deviation of the clustered volume data.
(a)
(b)The amount of hydrogel remaining at the subcutaneous injection site over time is thus directly predictable based on our previously developed mechanistic model of Tetra-PEG hydrogel degradation, requiring knowledge only of theirin vitro tRG values and linker cleavage rates.As tissue biopsy is not a desirable means of studying hydrogel residence in a clinical setting, we measured the volume occupied by hydrogel implants by 3D ultrasound computer tomography (USCT), a painless, noninvasive technique readily translated to other animals and humans. Figure7 shows that immediately after injection of microspheres, a cross-section of the cavity formed in the SC space is as an elliptical structure readily identified by its unique sonographic features. Initially, the implanted hydrogel displays contrasting echogenic elements which over time transforms to an echolucent space that decreases in volume until it is undetectable. The volumes occupied by the microspheres were determined by integration of the implant area from 2D ultrasound image stacks obtained at constant depth and evenly spaced intervals (0.5 mm) along the length of the implant to give a 3D model of the implant (Figure 7(b)). Plots of cavity volume vs. time were constructed for each gel studied (Figure S1).Figure 7
Ultrasound analysis of implants. (a) 2D images of microsphere implants, with the degradation crosslink modulator -CN (ε-Lys), showing the widest cross-section at 0, 1700, and 5880 hours post injection, and the time relative to in vitro reverse degelation time (t/tRGinvitro). Scale bars=2 mm. (b) 3D USCT renderings showing the volumes of the implants shown in (a).The volume change over time was more complex than that for the loss of hydrogel components described above due to the swelling behavior of the hydrogels as they degrade and the force applied by the surrounding tissues [10]. As crosslinks are broken, the gel structure becomes less dense and the gel occupies a larger equilibrium volume up until the point that mass loss from the gel is sufficient to overcome the decrease in density. It is further expected that there will be some pressure applied by the surrounding tissues to counter increases in gel volume due to this swelling. Given this added complexity, only hydrogels having equivalent quality factors (f=0.2) were included in the volume analysis. Data points between materials were combined into the same groups of equivalent t/tRGinvitro±0.2 described above for the fluorescence data. The average initial cavity volumes in all animals of groups E-M (Table S1) resulting from 100 μL injections were 84±15 mm3, probably reflecting compression of the suspension and rapid absorption of the liquid buffer surrounding the microspheres. After an initial period, gel swelling became evident with the average volume increasing to 104±36 mm3 at a time equal to the in vivo tRG (i.e., 1.36 times the in vitro tRG as discussed above), after which the volume decreased to zero at 3-4 times the in vitro tRG. The time required for the cavity to collapse was thus the same as the time at which gel components were completely lost (Figure 6).In the absence of an analytical model for the change of hydrogel density during degradation, the ultrasound-determined volumes of the gels were empirically fit to a double-sigmoid curve (equation (4)) using parameters for initial volume V0 and a swelling factor Q that describes the volume increase due to loss of gel density during degradation.
(4)Vt=V01−Q1+t/tRGinvitro3+Q1+t/tRGinvitro6.As for the fluorescence data described above, the cavity volumes measured by ultrasound predictably correlate with thein vitro properties of the hydrogels, allowing for the use of noninvasive ultrasound techniques to monitor the status of hydrogels in the subcutaneous space.The primary objectives of this work were to characterize thein vivo degradation rates of Tetra-PEG hydrogel microspheres containing tunable β-eliminative crosslinks and to construct an in vitro-in vivo correlation (IVIVC) that would allow prediction of in vivo degradation from data obtained in vitro. Using microspheres with in vivo degradation times of ~3 to 250 days, we measured the loss of gel mass over time from the injection site and demonstrated that the in vivo degradation behavior is well-described by the mechanistic model of Reid et al. [6]. Thus, the in vivo degradation behavior of our β-eliminatively linked Tetra-PEG hydrogels is predictable based only on the in vitro linker cleavage rate (kL2invitro) and hydrogel degelation time (tRGinvitro). Importantly, the relationship held for 13 different gels spanning a tRGinvitro range of 12 to 2750 hours and should be useful for predicting in vivo properties of yet-unmade gels. In a secondary objective, we demonstrated that changes in volume of the subcutaneous microsphere depots as measured by ultrasound imaging are an effective, noninvasive, and painless surrogate for following in vivo degradation of our hydrogels.Approaches for measuring actual mass loss accompanying gel degradation usually involve isolation (excision) and quantitation of remaining material in animal implants over time. Early serial studies usually used one implant per animal and suffered from the need for numerous animals and interanimal variation. Here, the experimental design used longitudinal subcutaneous injections of the polymer at eight locations on a rat over the expectedin vivo lifetime; then, after the first-injected polymer had disappeared by visualization/palpation, the animals were euthanized and the gels in all injection sites were analyzed. The earliest injections had the longest residence time in the animal, and the latest injections had the shortest residence time. Hence, a single animal provided the full temporal analysis of in vivo gel degradation, and intra-animal variation was avoided.The constant gel mass over varying long periods prior to the onset of degelation shows that the microspheres do not migrate from the initial site of deposition. Thus, in case the microsphere-drug conjugates require removal, they can be completely excised by a simple punch biopsy.


## 4. Conclusions

In summary, we have characterized thein vivo degradation behaviors of Tetra-PEG hydrogel microspheres containing tunable β-eliminative crosslinks. Using Tetra-PEG hydrogel microspheres with in vivo degradation times of up to almost one year, we measured the time-dependent loss of gel substance from the injection site and the changes in volume of the injected microsphere depots in the subcutaneous compartment of rats. The in vivo loss of hydrogel from the injection site is completely predictable based on a mechanistic model and depends only on two parameters, the crosslinker cleavage rate (kL2invitro) and the time to reverse degelation (tRGinvitro), that are readily measured in vitro. We have further developed a painless, noninvasive method for following the in vivo degradation of microsphere hydrogel depots involving ultrasound imaging.



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*Source: 9483127-2019-02-10.xml*