Kelly M. Schultz’s research while affiliated with Lehigh University and other places

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Publications (8)


Characterizing rheological properties and microstructure of thioester networks during degradation
  • Article

October 2023

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22 Reads

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2 Citations

Soft Matter

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Benjamin James Carberry

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Kelly M Schultz

Covalent adaptable networks are designed for applications including cell and drug delivery and tissue regeneration. These applications require network degradation at physiological conditions and on a physiological timescale with microstructures...



Figure 1: Oscillatory frequency sweeps measure the viscoelastic character of (a) PEG-BCA hydrogels and (b) PEG-CBCA hydrogels formulated at a range of polymeric concentrations. The storage moduli (G') and loss moduli (G'') corresponding to a single-mode Maxwell model are shown in solid and dashed lines, respectively. Data points in the shaded region were dominated by inertial torque of the instrument. 33 Therefore, only data points to the left of the shaded region are considered in the analysis of the data. (c) The frequency sweep data from (a) and (b) all collapsed on a single curve when scaling the data by the Deborah number (on the x-axis) and the plateau modulus (on the y-axis). (d) The relaxation time for each hydrogel formulation was compared when calculating it either as the inverse of the crossover frequency (ωCO) or as η0/G∞, according to a single-mode Maxwell model. In some cases, the data points fell on top of each other and are therefore not visible on the plot.
Figure 2: (a) A representative shear rate sweep (here, for a 1.75 wt% PEG-CBCA hydrogel) shows that the rheological properties of the hydrogels depended on the applied shear rate. In region 1, the hydrogels exhibited Newtonian behavior. In region 2, shear thickening behavior was observed until in region 3, a flow instability occurred. Eventually, in region 4, samples were expelled out from underneath the geometry. (b) To visualize the gel during measurements, a parallel plate geometry was used with a raised bottom plate. In regions 1 and 2, the hydrogel was uniformly loaded. Edge fracture was apparent in region 3 and was followed by material expulsion. For the configuration shown here, expulsion occurred at the flow instability, though for measurements directly on the Peltier plate, material expulsion was delayed until region 4, as labeled in part a.
Figure 3: Shear rate sweeps for (a) PEG-BCA and (b) PEG-CBCA hydrogels characterized shear thickening behavior in the experimentally accessible regime. Following the last data point that is shown for each curve, a flow instability occurred. The shear rates corresponding to (c) the onset of shear thickening and (d) the shear rate at the onset of the flow instability are shown as a function of the total polymer concentration.
Figure 4: (a) Shear rate sweep data for PEG-BCA and PEG-CBCA hydrogels normalized by the Weissenberg number (x-axis) and the zero-shear viscosity (y-axis). To more easily visualize the data, error bars are omitted. (b) Degree of shear thickening (ηp/η0) for both hydrogel formulations. (c) Weissenberg number at the onset of shear thickening for both hydrogel formulations. (d) Weissenberg number at the onset of the flow instability for both hydrogel formulations.
Figure 6: (a) A load cell, positioned behind a syringe plunger on a syringe pump, was used to quantify the injection force. The injection force is shown as a function of (b) concentration, (c) plateau modulus, and (d) zero-shear viscosity. In (c) and (d), the force for an empty syringe (1.4 ± 0.1 N) was subtracted from the absolute force required for injection, shown in (b).

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Shear Thickening Behavior in Injectable Tetra-PEG Hydrogels Cross-Linked via Dynamic Thia-Michael Addition Bonds
  • Preprint
  • File available

August 2023

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65 Reads

Injectable poly(ethylene glycol, PEG)-based hydrogels were reversibly crosslinked through thia-conjugate addition bonds and demonstrated to shear thicken at low shear rates. Crosslinking bond exchange kinetics and dilute polymer concentrations were leveraged to tune hydrogel plateau moduli (from 60 - 650 Pa) and relaxation times (2 - 8 seconds). Under continuous flow shear rheometry, these properties affected the onset of shear thickening and the degree of shear thickening achieved before a flow instability occurred. The changes in viscosity were reversible whether the shear rate increased or decreased, suggesting that chain stretching drives this behavior. Given the relevance of dynamic PEG hydrogels under shear to biomedical applications, their injectability was investigated, and injection forces were found to increase with higher polymer concentrations and slower bond exchange kinetics. Altogether, these results characterize the nonlinear rheology of dilute, dynamic covalent tetra-PEG hydrogels and offer insight to the mechanism driving their shear thickening behavior.

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Figure 3: Shear rate sweeps for a) PEG-BCA and b) PEG-CBCA hydrogels characterized shear thickening behavior in the experimentally accessible regime. Following the last data point that is shown for each curve, a flow instability occurred. The shear rates corresponding to c) the onset of shear thickening and d) the shear rate at the onset of the flow instability are shown as a function of the total polymer concentration.
Figure 4: a) Shear rate sweep data for PEG-BCA and PEG-CBCA hydrogels normalized by the Weissenberg number (x-axis) and the zero-shear viscosity (y-axis). To more easily visualize the data, error bars are omitted. b) Degree of shear thickening (ηp/ η0) for both hydrogel formulations. c) Weissenberg number at the onset of shear thickening for both hydrogel formulations. d) Weissenberg number at the onset of the flow instability for both hydrogel formulations.
Figure 5: (a) A load cell, positioned behind a syringe plunger on a syringe pump, was used to quantify the injection force. The injection force is shown as a function of (b) concentration, (c) plateau modulus, and (d) zero-shear viscosity.
Scheme 1: Crosslinking between conjugate acceptor-functionalized 4-arm PEG and thiol-functionalized 4-arm PEG resulted in hydrogel formation. The bond exchange kinetics of the crosslinking reaction were tuned through a molecular substitution to the para position on the aromatic group. A nitrile-substituted conjugate acceptor (PEG-CBCA) resulted in accelerated bond exchange kinetics compared to an unsubstituted conjugate acceptor (PEG-BCA).
Shear Thickening Behavior in Injectable Tetra-PEG Hydrogels Cross-Linked via Dynamic Thia-Michael Addition Bonds

April 2023

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111 Reads

Injectable poly(ethylene glycol)-based hydrogels were reversibly crosslinked through thia-conjugate addition bonds and demonstrated to shear thicken at low shear rates. In this system, crosslinking bond exchange kinetics and polymer concentration were leveraged to tune hydrogel plateau moduli (about 60 - 650 Pa) and relaxation times (2 - 8 seconds). These properties affected the shear thickening behavior of the hydrogels, including the onset of shear thickening (at a Weissenberg number of 0.2) and the degree of shear thickening (up to 4.5 fold) that was achieved before a flow instability occurred. Despite the shear thickening behavior of the hydrogels at low shear rates, the hydrogels were injectable, with injection forces that increased with a higher polymer concentration and slower bond exchange kinetics. Altogether, these results demonstrate shear thickening in reversibly crosslinked, injectable tetra-PEG hydrogels and show design parameters by which the shear thickening behavior and injection force can be tuned.


Human mesenchymal stem cell-engineered length scale dependent rheology of the pericellular region measured with bi-disperse multiple particle tracking microrheology

December 2020

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10 Reads

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11 Citations

Acta Biomaterialia

Biological materials have length scale dependent structure enabling complex cell-material interactions and driving cellular processes. Synthetic biomaterials are designed to mimic aspects of these biological materials for applications including enhancing cell delivery during wound healing. To mimic native microenvironments, we must understand how cells manipulate their surroundings over several length scales. Our work characterizes length scale dependent rheology in a well-established 3D cell culture platform for human mesenchymal stem cells (hMSCs). hMSCs re-engineer their microenvironment through matrix metalloproteinase (MMP) secretions and cytoskeletal tension. Remodeling occurs across length scales: MMPs degrade cross-links on nanometer scales resulting in micrometer-sized paths that hMSCs migrate through, eventually resulting in bulk scaffold degradation. We use multiple particle tracking microrheology (MPT) and bi-disperse MPT to characterize hMSC-mediated length scale dependent pericellular remodeling. MPT measures particle Brownian motion to calculate rheological properties. We use MPT to measure larger length scales with 4.5 µm particles. Bi-disperse MPT simultaneously measures two different length scales (0.5 and 2.0 µm). We measure that hMSCs preferentially remodel larger length scales measured as a higher mobility of larger particles. We inhibit cytoskeletal tension by inhibiting myosin-II and no longer measure this difference in particle mobility. This indicates that cytoskeletal tension is the source of cell-mediated length scale dependent rheological changes. Particle mobility correlates with cell speed across length scales, relating material rheology to cell behavior. These results quantify length scale dependent pericellular remodeling and provide insight into how these microenvironments can be designed into materials to direct cell behavior.


Microrheological characterization of covalent adaptable hydrogel degradation in response to temporal pH changes that mimic the gastrointestinal tract

June 2020

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23 Reads

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6 Citations

Soft Matter

Covalent adaptable hydrogels (CAHs) reversibly adapt their structure in response to external stimuli, emerging as a new platform for biological applications. Due to the unique and complex nature of these materials, a characterization technique is needed to measure the rheology of these CAHs in biological processes. μ²rheology, microrheology in a microfluidic device, is a technique that can fully characterize real-time CAH degradation in a changing environment, such as the pH environment of the GI tract. This characterization will enable design and tailoring of these materials for controlled and targeted oral drug delivery. Using μ²rheology, we can exchange the fluid environment without sample loss and measure the change in CAH rheological properties. We show degradation kinetics and material property evolution are independent of degradation history. However, the initial cross-link density at each pH exchange can be decreased by degradation history which decreases the time for the CAH to degrade to the gel-sol transition. These results indicate that CAH degradation can be tuned by changing the initial material properties by varying polymer concentration and ratio of functional groups. We also show that μ²rheology will enable the design of new dynamic materials for targeted drug delivery by enabling these materials to be characterized and tailored in vitro.


Multiple particle tracking microrheological characterization: Fundamentals, emerging techniques and applications

May 2020

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64 Reads

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51 Citations

Multiple particle tracking microrheology (MPT) is a passive microrheological technique that measures the Brownian motion of probe particles embedded in a sample to characterize material rheological properties. MPT is a powerful tool that quantifies material rheology in the low moduli range while requiring only small sample volumes and relatively simple data acquisition using video microscopy. MPT quantitatively characterizes spatiotemporal rheological properties and is particularly well suited for the investigation of evolving materials with complex microenvironments. MPT has expanded the study of a variety of materials including biofilms, colloidal gels, hydrogels, stimuli-responsive materials, and cell-laden biomaterials. The aim of this Tutorial is to summarize the fundamentals, illustrate the versatility, and highlight recent advances in MPT. In each application, we will highlight how MPT is uniquely positioned to gather rheological properties, which would be difficult, if not impossible, to attain with other rheological characterization techniques and highlight how MPT can be used to supplement other measurement techniques. This Tutorial should provide researchers with the fundamental basis and skills needed to use MPT and develop new MPT techniques to characterize materials for their unique applications.


Microrheological characterization of covalent adapt- able hydrogels for applications in oral delivery

July 2019

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28 Reads

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14 Citations

Soft Matter

The feasibility of a covalent adaptable hydrogel (CAH) as an oral delivery platform is explored using μ²rheology, microrheology in a microfluidic device. CAH degradation is initiated by physiologically relevant pHs, including incubation at a single pH and consecutively at different pHs. At a single pH, we determine CAH degradation can be tuned by changing the pH, which can be exploited for controlled release. We calculate the critical relaxation exponent, which defines the gel-sol transition and is independent of the degradation pH. We mimic the changing pH environment through part of the gastrointestinal tract (pH 4.3 to 7.4 or pH 7.4 to 4.3) in our microfluidic device. We determine that dynamic material property evolution is consistent with degradation at a single pH. However, the time scale of degradation is reduced by the history of degradation. These investigations inform the design of this material as a new vehicle for targeted delivery.

Citations (5)


... At lower shear stresses, shear thickening is observed indicating that the rate of bond formation is slower than the chain relaxation time, however, at higher shear stresses, the solution exhibits shear thinning property. Similar behaviors have been observed by other injectable hydrogels [43]. Furthermore, we tested the injectability of peroneal and sciatic decell + delipid uncrosslinked and 1 mM genipincrosslinked hydrogels using 25-G needles, the most widely used needle for cell delivery [9,10,44]. ...

Reference:

Decellularized porcine peripheral nerve based injectable hydrogels as a Schwann cell carrier for injured spinal cord regeneration
Shear Thickening Behavior in Injectable Tetra-PEG Hydrogels Cross-Linked via Dynamic Thia-Michael Addition Bonds
  • Citing Article
  • September 2023

Macromolecules

... Most hydrogels are crosslinked by peptides that are cleaved by soluble proteases that induce bulk hydrogel degradation. [6][7][8] The mechanical properties of hydrogels are important for cell behavior 9 and these properties are dependent on the extent of crosslinking between polymer chains. 6,10 While synthetic matrices are often treated as relatively inert scaffolds that can be modified with specific ligands or properties, the extent to which the encapsulated cells degrade the hydrogel network will alter the local network structure. ...

Human mesenchymal stem cell-engineered length scale dependent rheology of the pericellular region measured with bi-disperse multiple particle tracking microrheology
  • Citing Article
  • December 2020

Acta Biomaterialia

... A sequence of different pH conditions based on the expected pH and duration in the GI tract was developed. 116 The device was used to measure gel properties and kinetic transitions through repeated gelation and degradation cycles induced by pH changes. 117 Particle tracking methods have also been integrated with microfluidics to study cell properties. ...

Microrheological characterization of covalent adaptable hydrogel degradation in response to temporal pH changes that mimic the gastrointestinal tract
  • Citing Article
  • June 2020

Soft Matter

... The MSD power law exponent, α, is a derivative quantitative parameter based on the EAMSD. It describes the diffusive mode of tracked particles and is calculated as the logarithmic gradient of the MSD-curve 27 : ...

Multiple particle tracking microrheological characterization: Fundamentals, emerging techniques and applications
  • Citing Article
  • May 2020

... The effect of pH on covalently adaptable hydrogels was studied, which have a wide variety of applications including cell culturing, tissue regeneration, and drug delivery due to their ability to change properties with external stimuli. 115 The microfluidic device was also used to probe the change in structure as a function of time after a change in pH, similar to what would occur in the gastrointestinal (GI) tract. A sequence of different pH conditions based on the expected pH and duration in the GI tract was developed. ...

Microrheological characterization of covalent adapt- able hydrogels for applications in oral delivery
  • Citing Article
  • July 2019

Soft Matter