Kristen L. Mills

Tunable elastomeric nanochannels for nanofluidic manipulation

Fluidic transport through nanochannels offers new opportunities to probe fundamental nanoscale transport phenomena and to develop tools for manipulating DNA, proteins, small molecules and nanoparticles. The small size of nanofabricated devices and the accompanying increase in the effect of surface forces, however, pose challenges in designing and fabricating flexible nanofluidic systems that can dynamically adjust their transport characteristics according to the handling needs of various molecules and nanoparticles. Here, we describe the use of nanoscale fracturing of oxidized poly(dimethylsiloxane) to conveniently fabricate nanofluidic systems with arrays of nanochannels that can actively manipulate nanofluidic transport through dynamic modulation of the channel cross-section. We present the design parameters for engineering material properties and channel geometry to achieve reversible nanochannel deformation using remarkably small forces. We demonstrate the versatility of the elastomeric nanochannels through tuneable sieving and trapping of nanoparticles, dynamic manipulation of the conformation of single DNA molecules and in situ photofabrication of movable polymeric nanostructures.

The mechanical properties of a surface-modified layer on polydimethylsiloxane

Surface-modification of the elastomer poly(dimethylsiloxane) by exposure to oxygen plasma for four minutes creates a thin, stiff film. In this study, the thickness and mechanical properties of this surface-modified layer were determined. Using the phase image capabilities of a tapping-mode atomic-force microscope, the surface-modified region was distinguished from the bulk PDMS; specifically, it suggested a graded surface layer to a depth of about 200 nm. Load-displacement data for elastic indentation using a compliant AFM cantilever was analyzed as a plate bending on an elastic foundation to determine the elastic modulus of the surface (37 MPa). An applied uniaxial strain generated a series of parallel nano-cracks with spacing on the order of a few microns. Numerical analyses of this cracking phenomenon showed that the depth of these cracks was in the range of 300-600 nm and that the surface layer was extremely brittle, with its toughness in the range of 0.1-0.3 J/m(2).

Instantaneous fabrication of arrays of normally closed, adjustable, and reversible nanochannels by tunnel cracking

A direct fabrication method capable of producing fully-reversible, tunable nanochannel arrays, without the use of a molding step, is described. It is based on tunnel cracking of a readily-prepared brittle layer constrained between elastomeric substrates. The resulting nanochannels have adjustable cross-sections that can be reversibly opened, closed, widened and narrowed merely by applying and removing tensile strains to the substrate. This permits reversible trapping and release of nanoparticles, and easy priming or unclogging of the nanochannels for user-friendly and robust operations. The ease of fabrication and operation required to open and close the nanochannels is superior to previous approaches.

In silico estimates of the free energy rates in growing tumor spheroids

The physics of solid tumor growth can be considered at three distinct size scales: the tumor scale, the cell-extracellular matrix (ECM) scale and the sub-cellular scale. In this paper we consider the tumor scale in the interest of eventually developing a system-level understanding of the progression of cancer. At this scale, cell populations and chemical species are best treated as concentration fields that vary with time and space. The cells have chemo-mechanical interactions with each other and with the ECM, consume glucose and oxygen that are transported through the tumor, and create chemical by-products. We present a continuum mathematical model for the biochemical dynamics and mechanics that govern tumor growth. The biochemical dynamics and mechanics also engender free energy changes that serve as universal measures for comparison of these processes. Within our mathematical framework we therefore consider the free energy inequality, which arises from the first and second laws of thermodynamics. With the model we compute preliminary estimates of the free energy rates of a growing tumor in its pre-vascular stage by using currently available data from single cells and multicellular tumor spheroids.

Properties of the surface-modified layer of plasma-oxidized poly(dimethylsiloxane)

Exposure of poly(dimethylsiloxane) (PDMS) to oxygen plasma creates a thin, stiff surface-modified layer that reaches a submicron depth. Due to a significant modulus mismatch between the stiff surface-modified layer and the compliant bulk PDMS the surface-modified layer forms intricate patterns of surface buckles when under compressive stress and nano-cracks when under tensile stress. It is desirable to be able to design patterns of nano-cracks, or at least to have an understanding of them. Among the properties necessary to do this are the thickness and elastic modulus of the surface-modified layer. Due to the very small length scale of the surface-modified layer, it is a significant challenge to measure these properties. In this proceedings paper, a two-step method is described for determining the thickness and elastic modulus of the surface-modified layer using the atomic force microscope (AFM). First, nanoindentation is performed from which the bending stiffness of the surface-modified layer is calculated. Second, the surface-modified layer thickness is determined by using phase imaging on the cross-section of oxidized PDMS to map the region of the relatively stiffer surface-modified layer.

Elastic Free Energy Drives the Shape of Prevascular Solid Tumors

It is well established that the mechanical environment influences cell functions in health and disease. Here, we address how the mechanical environment influences tumor growth, in particular, the shape of solid tumors. In an in vitro tumor model, which isolates mechanical interactions between cancer tumor cells and a hydrogel, we find that tumors grow as ellipsoids, resembling the same, oft-reported observation of in vivo tumors. Specifically, an oblate ellipsoidal tumor shape robustly occurs when the tumors grow in hydrogels that are stiffer than the tumors, but when they grow in more compliant hydrogels they remain closer to spherical in shape. Using large scale, nonlinear elasticity computations we show that the oblate ellipsoidal shape minimizes the elastic free energy of the tumor-hydrogel system. Having eliminated a number of other candidate explanations, we hypothesize that minimization of the elastic free energy is the reason for predominance of the experimentally observed ellipsoidal shape. This result may hold significance for explaining the shape progression of early solid tumors in vivo and is an important step in understanding the processes underlying solid tumor growth.

Experimental characterization of tumor spheroids for studies of the energetics of tumor growth

Abstract Tumor growth, starting from the earliest, prevascularized state, involves complex biological, chemical, and mechanical processes that either consume or create free energy. We compute estimates of the free energy changes – a universal measure for comparison of these processes – based on experimental characterization of the relevant bio-chemo-mechanical processes for tumor growth. A well-defined, consistent experimental framework has been developed using one cancer cell line and a hydrogel-embedded tumor spheroid model. This framework may be used to systematically investigate the effects of the bio-chemo-mechanical environment on tumor growth.

Multiphysics Modeling of Reactions, Mass Transport and Mechanics of Tumor Growth

The biochemical dynamics involved in tumor growth can be broadly classified into three distinct spatial scales: the tumor scale, the cell-ECM interactions and the sub-cellular processes. This work presents the tumor scale investigations, which are expected to eventually lead to a system-level understanding of the progression of cancer. Many of the macroscopic phenomena of physiological relevance, such as tumor size and shape, formation of necrotic core and vascularization, proliferation and metastasis of cell populations, external mechanical interactions, etc., can be treated within a continuum framework by modeling the evolution of various species involved by transport equations coupled with mechanics. This framework is an extension of earlier work (Garikipati et al. in J. Mech. Phys. Solids 52:1595–1625, 2004; Narayanan et al. in Biomech. Model. Mechanobiol. 8:167–181, 2009, J. Phys. Condens. Matter. 22:194122, 2010) based on the continuum theory of mixtures for modeling biological growth. Specifically, the focus is on demonstrating the effectiveness of mechano-transport coupling in simulating tumor growth dynamics and explaining some in vitro observations like mechanics-induced ellipsoidal tumor shapes. Additionally, this work also seeks to demonstrate the effectiveness of tools like adaptive mesh refinement and automatic differentiation in handling highly nonlinear, coupled multiphysics systems.

Large-scale patterning of single cells and cell clusters in hydrogels

Biophysical properties of the extracellular matrix (ECM) are known to play a significant role in cell behavior. To gain a better understanding of the effects of the biophysical microenvironment on cell behavior, the practical challenge is longitudinally monitoring behavioral variations within a population to make statistically powerful assessments. Population-level measurements mask heterogeneity in cell responses, and large-scale individual cell measurements are often performed in a one-time, snapshot manner after removing cells from their matrix. Here we present an easy and low-cost method for large-scale, longitudinal studies of heterogeneous cell behavior in 3D hydrogel matrices. Using a platform we term “the drop-patterning chip”, thousands of cells were simultaneously transferred from microwell arrays and fully embedded, only using the force of gravity, in precise patterns in 3D collagen I or Matrigel. This method allows for throughputs approaching 2D patterning methods that lack phenotypic information on cell-matrix interactions, and does not rely on special equipment and cell treatments that may result in a proximal stiff surface. With a large and yet well-organized group of cells captured in 3D matrices, we demonstrated the capability of locating selected individual cells and monitoring cell division, migration, and proliferation for multiple days.

Toward Morphologically Relevant Extracellular Matrix in Vitro Models: 3D Fiber Reinforced Hydrogels

The extracellular matrix (ECM) is known to play an important role in the health of cells and tissues. Not only are chemical signals transmitted via bonds and tightly controlled diffusion, but the structure of the ECM also provides important physical signaling for the cells attached to it. The structure is composed of a mesh of fibrous proteins, such as collagen, embedded in a hydrated gel matrix of glycosaminoglycans. To study cell behavior with respect to the combined morphology and mechanics of such matrices is not currently possible with the types of 3D cell culture matrices available. Most of the cell culture matrices are single-phase bio- or polymeric hydrogels. Therefore, here we developed a continuous hybrid manufacturing process to make fiber-reinforced composite hydrogels. A far field electrospinning process was used to deposit the fibrous component with the aid of guiding electrodes; and a gravity-assisted, droplet-based system controlled the rate of addition of the cell-laden hydrogel component. The addition of the fibrous component slightly increased the elastic modulus of the pure hydrogel. The cells that were embedded into the fiber-reinforced hydrogels were viable for 8 days. The cells were randomly placed in the matrix such that some had no contact to the fibers and others were initially in proximity to fibers. The cells with no contact to fibers grew into spheroidal clusters within the hydrogel, and those in proximity to the fibers spread out and grew along the fibers showing that the fiber-reinforced hydrogels are able to control cell behavior with morphological cues.