0
Research Papers

# A Nonintrusive Method of Measuring the Local Mechanical Properties of Soft Hydrogels Using Magnetic Microneedles

[+] Author and Article Information

Department of Mechanical and Aerospace Engineering, Rutgers,  The State University of New Jersey, 98 Brett Road, Piscataway, NJ 08854chippada@eden.rutgers.edu

Bernard Yurke

Department of Material Science and Engineering, and Department of Electrical and Computer Engineering, Boise State University, 1910 University Drive, Boise, ID 83725bernardyurke@boisestate.edu

Penelope C. Georges

Department of Biomedical Engineering, Rutgers,  The State University of New Jersey, 599 Taylor Road, Piscataway, NJ 08854pgeorges@rci.rutgers.edu

Noshir A. Langrana1

Department of Biomedical Engineering, and Department of Mechanical and Aerospace Engineering, Rutgers,  The State University of New Jersey, 599 Taylor Road, Piscataway, NJ 08854langrana@rutgers.edu

1

Corresponding author.

J Biomech Eng 131(2), 021014 (Dec 18, 2008) (12 pages) doi:10.1115/1.3005166 History: Received October 08, 2007; Revised July 21, 2008; Published December 18, 2008

## Abstract

Soft hydrogels serving as substrates for cell attachment are used to culture many types of cells. The mechanical properties of these gels influence cell morphology, growth, and differentiation. For studies of cell growth on inhomogeneous gels, techniques by which the mechanical properties of the substrate can be measured within the proximity of a given cell are of interest. We describe an apparatus that allows the determination of local gel elasticity by measuring the response of embedded micron-sized magnetic needles to applied magnetic fields. This microscope-based four-magnet apparatus can apply both force and torque on the microneedles. The force and the torque are manipulated by changing the values of the magnetic field at the four poles of the magnet using a feedback circuit driven by LABVIEW . Using Hall probes, we have mapped out the magnetic field and field gradients produced by each pole when all the other poles are held at zero magnetic field. We have verified that superposition of these field maps allows one to obtain field maps for the case when the poles are held at arbitrary field values. This allows one to apply known fields and field gradients to a given microneedle. An imaging system is employed to measure the displacement and rotation of the needles. Polyacrylamide hydrogels of known elasticity were used to determine the relationship between the field gradient at the location of the needles and the force acting on the needles. This relationship allows the force on the microneedle to be determined from a known field gradient. This together with a measurement of the displacement of the needle in a given gel allows one to determine the stiffness $(F∕δ)$ of the gel and the elastic modulus, provided Poison’s ratio is known. Using this method, the stiffness and the modulus of elasticity of type-I collagen gels were found to be $2.64±0.05nN∕μm$ and $284.6±5.9Pa$, respectively. This apparatus is presently being employed to track the mechanical stiffness of the DNA-cross-linked hydrogels, developed by our group, whose mechanical properties can be varied on demand by adding or removing cross-linker strands. Thus a system that can be utilized to track the local properties of soft media as a function of time with minimum mechanical disturbance in the presence of cells is presented.

<>

## Figures

Figure 1

The four-magnet setup mounted on the microscope. The space between the poles is 10×10mm2 in which hydrogel containing wells are placed and viewed using the microscope

Figure 2

SEM image of the microneedles manufactured at NJNC dispersed in water. Each needle is 10×1×1μm3.

Figure 3

Flowchart of the feedback control system. Hall sensor provides a measurement of the field in Gauss, which is compared with the required value. The LABVIEW software computes the PID feedback to adjust the field at the tip of the pole.

Figure 4

(a) Force field generation with four-magnet setup. Pole 3 is set at larger magnetic flux density and needles will displace toward it as indicated by the arrow. (b) Magnetic field map of the space between the four poles for the case when a field gradient is generated. The magnitude of arrows are the normalized values with respect to the maximum value and represent the magnetic flux density at the location, while the direction of the arrows represent the actual direction of the flux density at the corresponding location. The length of the arrows decreases from the stronger pole toward the weaker pole.

Figure 5

(a) Constant torsional field generation with the four-magnet setup. The needles rotate as indicated by the arrow. (b) Magnetic field map for the case when a nearly uniform magnetic field is generated. The arrows represent the magnitude and the direction of the magnetic flux density and are equal in length. Needles placed in this field at an angle to the field experience torque acting on them based on their orientation with respect to the field. A larger angle with the horizontal yields a larger torque.

Figure 6

Relationship between the magnetic field and the displacement of the needles is linear. This leads to the conclusion that the force is directly proportional to the magnetic field acting on the needles. Thus needles behave as permanent magnets.

Figure 7

Graph showing field gradient versus needle displacement for gels of differing stiffness. The slope of each line is an indirect measure of the stiffness of the gels. 5% gels have the highest stiffness.

Figure 8

Finite element analysis using ANSYS . Gel is modeled using a cylinder of radius 50μm and height 100μm. The 10×1×1μm3 needle is glued using contact elements.

Figure 9

Results of the 3%, 4% and 5% polyacrylamide gels. The values for the 4% and 5% are normalized with respect to the values of the 3% gel.

Figure 10

Relation between the stiffness and Young’s Modulus of using the 3%, 4%, and 5% polyacrylamide gels. This linear curve allows us to approximately obtain the modulus of elasticity of hydrogels by knowing the stiffness of the gels.

Figure 11

Biocompatibility study showing the growth of neurons and astrocytes on hydrogels with nickel needles embedded in them

Figure 12

Phase image of the cells in conjunction with the needles

## Discussions

Some tools below are only available to our subscribers or users with an online account.

### Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related Proceedings Articles
Related eBook Content
Topic Collections