Real-Time Determination of Cardiac Spheroid Internal Pressures Using Photoelastic Polydimethylsiloxane Microspheres

We describe a method whereby soft, hollow photoelastic microspheres made of polydimethylsiloxane (PDMS) serving as cellular scaffolds are imaged using a polarized light microscope.  This microscope can allow quantification of the internal pressures within such spheres through measurement of birefringence differences between the cell layer and the inner pressure-indicating PDMS sphere.  We present literature showing that under polarized light, these pressure-indicating spheres will respond to forces 3 orders of magnitude smaller than those typically produced by smooth muscle cell contraction, which will allow for fine determination of the pressures within a contracting spheroid.  Additionally, temporal resolutions of approximately 1 second are achievable from the microscope system, which will allow for real-time assessment.

Section 1. Description of the Proposed Core

A. Physico-Chemical Properties

Requirement 1: Inertness
The spheres must be an inert, sterile, and gas-permeable material.  Plastic should be autoclavable.

We propose a hollow core made of PDMS and coated with fibronectin to allow for good cell adhesion.  PDMS is an inert silicone-based elastomer that has high permeability to various solvents and gases, and has found use in a variety of lubricants, sealants, and medical products (Jiang et al. 2012).  Additionally, PDMS is autoclavable (Skaalure et al. 2008), allowing it to meet the first requirement for the pressure-sensing core.

Requirement 2: Compressibility
The spheres should be capable of approximately 50% compression.

The compressibility of solid PDMS varies with viscosity and pressure as follows (Polymer Data Handbook, 1999).  Volume reductions of over 30% are achievable at viscosities from 0.65-12,500 cs and at pressures of 30,000 kgf/cm2, which translate to 2.94 MPa.  At higher pressures the amount of volume reduction decreases.   We show in Section 2 that internal pressures produced by contracting cells fall within a range of 90-300 kPa, which is not enough to compress PDMS to a volume reduction of 30%.  Thus for substantial compressibility we must make the core hollow.

B. Diameter Range of Spheres

Requirement 3: Diameter
The spheres must have a diameter within the range of 100-200 μm.

The size of the spheres can be varied from ~10 to 200 μm by either altering the flow rates in the microfluidics setup described by Jiang et al. (2012) or by using microchannels of different diameters.

C. Rationale for Cell Growth Amenability

Requirement 4: Cell Growth
The surface of the spheres must enable the growth of cells over its entire surface area.

Fibronectin is an extracellular matrix glycoprotein that serves as a general cell adhesion molecule.  Its presence on the surface of the PDMS sphere will facilitate the adhesion of cells, which is necessary for good growth and measurement of contractile forces.

Section 2. Description of the Pressure Sensing Method

Requirement 5: Pressure
When the tissue has been grown, the spheroid must be able to sense and report the pressure exerted by the spheroid in a way that can be calibrated in mm Hg.

Our method description begins first with a determination of the typical forces a spheroid will encounter when coated with contractile cells.  We then show that these forces can be visualized using a photoelastic method, and present a solution that will allow determination of the pressure exerted by the spheroid.

Typical Contractile Forces within Spheroids

A research paper by Cyr et al. (2012) describe a device developed to measure the contractile force of tissue rings comprised of smooth muscle cells in response to chemical stimuli.  As the tissue ring was made to contract, it caused the deflection of microscopic posts.  The amount these tiny posts were deflected was used to calculate the contractile force.  An average contractile force of 32.00 +/- 5.71 μN was observed for rat aortic smooth muscle cell rings induced with potassium + physiological saline solution, and 10.28 +/- 5.72 μN for the same cellular rings induced with the physiological saline solution alone.

Pressure measurements from the literature were also supplied in this article; cells of blood vessels were stated to contract with pressures between 9-30 μN/cm2 and human airway smooth muscle cells were stated to contract with a pressure of 29.4 μN/cm2.  Thus we have a pressure range of 9-30 μN/cm2 which translates to 90-300 kPa, or 675-2250 mm Hg.

Since the diameter of the pressure-indicating spheres will be between 100-200 μm, their surface area will be between 31,415-125,663 μm2.  Typical forces that the pressure-indicating spheres should indicate would thus need to be as low as 2.83 nN and as high as 3.77 nN.

Photoelastic Method of Measuring Cellular Forces

In the method by Curtis et al. (2007), cells were grown on a photoelastic substratum of polydimethylsiloxane (PDMS) coated with a fibronectin monolayer.  Changes in the force applied by the cells led to changes in the birefringence of the PDMS, which can be measured and recorded by a computer-controlled polarizing microscope (PolScope).  This microscope translated birefringence measurements into force measurements and was sensitive down to forces of 1 pN/m2, an order of magnitude greater resolution than what the pressure-indicating spheres will typically encounter.  Additionally, this method has a ~1 second temporal resolution which will allow the force changes characteristic of contracting cells to be resolved.

A problem with this method was that the cytoskeleton and other components of a cell would interfere with the birefringence measured from areas beneath a cell, where a pressure-indicating sphere would reside.  The authors of Curtis et al. (2007) suggest this interference would tend to cause smaller values of measured forces.

Compensating for Cellular Birefringence

Another article featuring the PolScope described the dynamically changing nature of cellular birefringence due to a cell’s cytoskeletal activity (Katoh et al. 1999). These changes would appear to prevent any attempt to subtract out the birefringence of a cell from the birefringence of a pressure-indicating sphere that was underneath.  Thankfully this is not the case; we present what we believe to be a novel solution to this problem.

The PolScope can display images and video of live cells at an incredibly fine resolution.  We propose that a cardiac spheroid be imaged so that it fills the screen, and that its entire periphery is brought into focus.  As viewed from the PolScope, the periphery will be composed of a single layer of cells with no pressure-indicating sphere underneath.  Thus 100% of the visible birefringence will be due to cellular components.  This birefringence should then be subtracted from that being measured at the very center of the spheroid to obtain the birefringence of the pressure-indicating sphere.  This can be done with measurements made during subsequent video analysis, or perhaps even in real time given sufficiently capable object recognition software that could recognize the periphery and center of a cell and perform the necessary birefringence subtraction.  Note that the software provided for the PolScope is open-source and extendable.1

Section 3. Suppliers of the Proposed Sphere

Requirement 6: Production Cost
The solution should be widely available or amenable to large-scale production at a low cost per sphere/core.

PDMS microspheres are currently not widely available, but they can be manufactured to high specifications and in useful quanitities using a microfluidics technique licensed by the University of Maryland.  More information is available at the following link:

The following companies specialize in tailor-made, monodisperse microspheres, and should be able to manufacture the proposed sphere at a competitive cost using the above technique.  As an alternative, they may also use the more traditional emulsion processing method for manufacturing hollow PDMS microspheres (Ji and Lee, 2011), which lends itself to the production of bulk quantities of the material but with less control over size compared with the microfluidics method.



Section 4. Assay Development

We would be interested in providing support for the development of the initial assay.    In this supportive role, we offer our availability to answer any questions concerning the content of this proposal to ensure the Seeker’s development of the desired assay.  In addition, we have a software developer who has worked with open-source image processing libraries that would enable the real-time birefringence subtraction described above.

Section 5.  References

Curtis et al.  2007.  Measuring Cell Forces by a Photoelastic Method.  Biophys J.  92(6): 2255-2261.  Available at

Cyr et al.  2012.  Design of a Tissue Ring Contractile Force Measurement Device.  Worcester Polytechnic Institute.  Available at

Fassina et al.  2014.  Modulation of the Cardiomyocyte Contraction inside a Hydrostatic Pressure Bioreactor: In Vitro Verification of the Frank-Starling Law.  BioMed Research International, Article ID 542105.  Available at

Ji, S. And Lee, I.  2011.  Recent progress on the Preparation Processes of Hollow Polymer Nano and Microspheres.  Current Trends in Polymer Science 15: 63-75.  Available at

Jiang et al.  2012.  Microfluidic synthesis of monodisperse PDMS microbeads as discrete oxygen sensors.  Soft Matter, 8, 923.  Available at

Katoh et al.  1999.  Birefringence Imaging Directly Reveals Architectural Dynamics of Filamentous Actin in Living Growth Cones.  Mol Biol Cell. 10(1): 197-210.  Available at

Polymer Data Handbook.  1999.  Oxford University Press.  Available at

Skaalure et al.  2008.  Characterization of Sterilization Techniques on a Microfluidic Oxygen Delivery Device.  Journal of Undergraduate Research 2, 1.  Available at

Web Sources

1.   GitHub, LC-PolScope repository.

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