Cinemechanometry (CMM): A Method to Determine the Forces that Drive Morphogenetic Movements from Time-Lapse Images P. GRAHAM CRANSTON, 1 JIM H. VELDHUIS, 1 SRIRAM NARASIMHAN, 1 and G. WAYNE BRODLAND 1,2 1 Department of Civil and Environmental Engineering, University of Waterloo, Waterloo, ON N2L 3G1, Canada; and 2 Department of Biology, University of Waterloo, Waterloo, ON N2L 3G1, Canada (Received 20 December 2009; accepted 3 March 2010; published online 8 July 2010) Associate Editor Michael S. Detamore oversaw the review of this article. Abstract—Although cell-level mechanical forces are crucial to tissue self-organization in contexts ranging from embryo development to cancer metastases to regenerative engineer- ing, the absence of methods to map them over time has been a major obstacle to new understanding. Here, we present a technique for constructing detailed, dynamic maps of the forces driving morphogenetic events from time-lapse images. Forces in the cell are considered to be separable into unknown active driving forces and known passive forces, where actomyosin systems and microtubules contribute primarily to the first group and intermediate filaments and cytoplasm to the latter. A finite-element procedure is used to estimate the field of forces that must be applied to the passive components to produce their observed incremental deforma- tions. This field is assumed to be generated by active forces resolved along user-defined line segments whose location, often along cell edges, is informed by the underlying biology. The magnitudes and signs of these forces are determined by a mathematical inverse method. The efficacy of the approach is demonstrated using noisy synthetic data from a cross section of a generic invagination and from a planar aggregate that involves two cell types, edge forces that vary with time and a neighbor change. Keywords—Cinemechanometry (CMM), Video force micros- copy, Cell mechanics, Morphogenetic movements, Driving forces, Tissue mechanics, Computational modeling, Finite elements, Inverse methods. INTRODUCTION Although the crucial role that mechanical forces play in embryo development, angiogenesis, cancer metastasis, engineered tissue constructs, and other important biological contexts is well known, measur- ing these forces has proved extremely challenging. These forces can arise from cytoskeletal components, the cell membrane and cell–cell adhesion systems (Fig. 1a). The magnitudes of the forces that these components generate cannot be inferred from ultra- structure alone since they are modulated by gene expression and biochemical factors. 24 Recent studies show that the forces in individual cells can change with time 26 and can vary significantly from one edge to another within a single cell. 31 To adequately describe the mechanics of such systems requires a detailed, dynamic, sub-cellular force map. Measurement of forces in cells is difficult because cells are typically 5–20 lm in size and the forces present are of the range 50–900 pN. 1 Atomic force microscopy can reveal the forces acting along the surface of single cells and it can provide information about the mechanics of cell–cell interactions, 22,30 but it is not suitable for mapping dynamic forces over large areas or for measuring internal forces such as the tensions that act along cell–cell interfaces in epithelia, a primary force in the cell-level self-organization of tis- sues. 2,23 Laser microsurgery 8,19,25 is a powerful method for identifying the forces along cell edges but the observed recoils are significantly affected by far-field stresses and the method is inherently destructive. The molecular pathways that construct structural protein systems and regulate the forces they produce can now be manipulated a variety of ways. 37 These techniques can reveal how specific proteins regulate construction and operation of various force-generating structures, but they cannot reveal the magnitudes of the forces produced. Computational modeling, an important complement to these experimental methods, allows hypotheses about the forces that drive specific mor- phogenetic movements to be tested. In silico experi- ments carried out using suitable models can reveal much about the mechanics of cells and tissues. 7,9 A primary drawback to modeling, however, is that the Address correspondence to G. Wayne Brodland, Department of Civil and Environmental Engineering, University of Waterloo, Waterloo, ON N2L 3G1, Canada. Electronic mail: brodland@ uwaterloo.ca Annals of Biomedical Engineering, Vol. 38, No. 9, September 2010 (Ó 2010) pp. 2937–2947 DOI: 10.1007/s10439-010-9998-1 0090-6964/10/0900-2937/0 Ó 2010 Biomedical Engineering Society 2937