In biology, organization at multiple scales potentiates biological function. Current advances in staining and imaging of biological tissues provide a wealth of data, but there are few metrics to quantitatively describe these findings. In particular there is a need for a metric that would characterize the correlation and consistency of orientation of different biological constructs within a tissue. We aimed to create such a metric and to demonstrate its use with images of cardiac tissues. The co-orientational order parameter (COOP) was based on the mathematical framework of a classical parameter, the orientational order parameter (OOP). Theorems were proven to illustrate the properties and boundaries of the COOP, which was then applied to both synthetic and experimental data. We showed the COOP to be useful for quantifying the correlation of orientation of constructs such as actin filaments and sarcomeric Z-lines. As expected, cardiac tissues showed perfect correlation between actin filaments and Z-lines. We also demonstrated the use of COOP to quantify the consistency of construct orientation within cells of the same shape. The COOP provides a quantitative tool to characterize tissues beyond co-localization or single construct orientation distribution. In the future, this new parameter could be used to represent the quantitative changes during maturation of cardiac tissue, pathological malformation, and other processes.

The heart is a complex organ whose structure and function are intricately linked at multiple length scales. Although several advancements have been achieved in the field of cardiac tissue engineering, current in vitro cardiac tissues do not fully replicate the structure or function necessary for effective cardiac therapy and cardiotoxicity studies. This is partially due to a deficiency in current understandings of cardiac tissue organization's potential downstream effects, such as changes in gene expression levels. We developed a novel (to our knowledge) in vitro tool that can be used to decouple and quantify the contribution of organization and associated downstream effects to tissue function. To do so, cardiac tissue monolayers were designed into a parquet pattern to be organized anisotropically on a local scale, within a parquet tile, and with any desired organization on a global scale. We hypothesized that if the downstream effects were muted, the relationship between developed force and tissue organization could be modeled as a sum of force vectors. With the in vitro experimental platforms of parquet tissues and heart-on-a-chip devices, we were able to prove this hypothesis for both systolic and diastolic stresses. Thus, insight was gained into the relationship between the generated stress and global myofibril organization. Furthermore, it was demonstrated that the developed quantitative tool could be used to estimate the changes in stress production due to downstream effects decoupled from tissue architecture. This has the potential to elucidate properties coupled to tissue architecture, which change force production and pumping function in the diseased heart or stem cell-derived tissues.

In a properly contracting cardiac muscle, many different subcellular structures are organized into an intricate architecture. While it has been observed that this organization is altered in pathological conditions, the relationship between length-scales and architecture has not been properly explored. In this work, we utilize a variety of architecture metrics to quantify organization and consistency of single structures over multiple scales, from subcellular to tissue scale as well as correlation of organization of multiple structures. Specifically, as the best way to characterize cardiac tissues, we chose the orientational and co-orientational order parameters (COOPs). Similarly, neonatal rat ventricular myocytes were selected for their consistent architectural behavior. The engineered cells and tissues were stained for four architectural structures: actin, tubulin, sarcomeric z-lines, and nuclei. We applied the orientational metrics to cardiac cells of various shapes, isotropic cardiac tissues, and anisotropic globally aligned tissues. With these novel tools, we discovered: (1) the relationship between cellular shape and consistency of self-assembly; (2) the length-scales at which unguided tissues self-organize; and (3) the correlation or lack thereof between organization of actin fibrils, sarcomeric z-lines, tubulin fibrils, and nuclei. All of these together elucidate some of the current mysteries in the relationship between force production and architecture, while raising more questions about the effect of guidance cues on self-assembly function. These types of metrics are the future of quantitative tissue engineering in cardiovascular biomechanics.