Our research deals with the mechanics of growth, remodeling, and morphogenesis during development and functional adaptation. We focus primarily on the following problems:
2. Artery growth and remodeling
4. Unified theory for morphogenesis
The heart is the first functioning organ in the embryo. In human embryos, the heart begins to beat about three weeks post-conception. During development, the heart undergoes a remarkable transformation from a single muscle-wrapped tube without valves into a complex four-chambered pump, while simultaneously providing continuous circulatory support to the rapidly growing embryo. Since form and function are intimately interrelated, these changes must be carefully coordinated.
Our current work in heart development deals primarily with the formation of the early heart tube and the subsequent process of cardiac looping, as the initially straight heart tube bends and twists into a curved tube that normally is directed toward the right side of the embryo. Looping is a crucial process during heart development. Looping abnormalities cause many of the cardiac malformations that occur in as many as 1% of liveborn and 10% of stillborn human births. Moreover, such defects may result in numerous spontaneous abortions during the first trimester. Rapid progress is being made in defining the genetic perturbations behind abnormal looping, but the biophysical mechanisms of gene action remain poorly understood. To fully understand the origins of congenital heart disease, it is important to determine the biomechanical factors that drive and regulate looping.
To study this problem, we use a combination of experimental and theoretical techniques. Because development of the chick heart parallels that of the human heart, our experimental model is the chick embryo. (Contractions begin at about 30 hr of incubation in the chick.) Our theoretical models are based on computational solutions of the equations of continuum mechanics, modified to include morphogenetic effects of tissue growth and contraction. Using this strategy, we recently have identified forces that cause cardiac bending and torsion during looping, findings that had eluded researchers for more than 80 years.
Figure 1: Illustrative examples from our work on heart development. (A) Actin cytoskeleton of stage 12 chick heart (two days of development). Note the circumferentially aligned fibers on the inner curvature compared to the randomly aligned fibers of the outer curvature. (B-B'') First phase of looping; the initially straight heart tube (B) heart bends and twists into a c-shaped tube (B'). Our finite element model yields similar changes in morphology (B''). (C-C'') Development of heart with primitive left atrium removed; heart loops abnormally to the left (C,C'). The same model as in (B'', but with left atrium removed, yields a strikingly similar result (C'').
It long has been acknowledged that arteries adapt to changes in loading conditions. For example, in response to acute changes in blood flow rate, many arteries actively contract or dilate to maintain a constant fluid shear stress on the endothelium. Due to a chronic increase in systemic blood pressure, arteries thicken and their residual stress patterns change, presumably to restore wall stresses to their homeostatic values.
Long-term changes in arterial structure are achieved via two main processes: smooth muscle growth and collagen remodeling. To study these processes, we have developed a thick-walled computational model for an artery that is composed of a mixture of smooth muscle cells, elastin, and collagen. The analysis of the model includes smooth muscle growth and contraction, collagen remodeling, and residual stress. We have used experimental data to minimize the number of free parameters and to independently test model predictions. In general, the results given by the model agree well with measured variations in geometry, pressure-radius relations, and residual stress (opening angles) under normal and perturbed loading conditions.
Figure 2: Illustrative results from our work on artery growth and remodeling. (A) Model-predicted opening angles along the length of the aorta are compared to experimental data of Liu and Fung (1988). (B) Model-predicted opening angle following an acute pressure jump is compared to experimental data of Fung and Liu (1989). (C) Circumferential stress distribution in pressurized curved tube model for the aortic arch (half symmetry). (D) Model-predicted opening angles and stress distributions of aortic arch following radial cuts at the inner and outer curvatures.
Like the heart, the brain begins life as a single tube. Early in development, local expansions arise at the cranial end of the neural tube to create the primitive forebrain, midbrain, and hindbrain. In many large mammals, the growing brain later begins to fold. The human cerebral cortex undergoes substantial folding from the fifth fetal month and continuing into the first post-natal year. This folding allows the surface area of the cortex to grow several times larger than if convolutions were absent. Major folding defects are usually associated with severe neurological dysfunction. More subtle abnormalities in folding are apparently linked to schizophrenia and epilepsy.
Despite many speculative papers on the mechanisms of brain morphogenesis, particularly cortical folding, the biomechanical factors responsible for normal and abnormal brain development are largely unknown. Extending ideas from our work on heart development, we recently have begun a study of the mechanics of brain development during the early phase of brain expansion and the later phase of brain folding.
Unified Theory for Morphogenesis
In the field of physics, an ongoing search is underway for a unified "theory of everything." Obviously, living systems must obey the same physical laws as nonliving systems, laws that can be expressed mathematically. But most investigators consider it unlikely that universal quantitative biophysical laws exist. One reason for this pessimism is that living systems have a mind of their own and strive for advantages under the laws of natural selection. A metal bar, for example, does not need to worry about surviving to have kids. Hence, the theory of evolution is formulated qualitatively. Moreover, different tissues serve different functions and likely are optimized to carry out these functions.
Despite these arguments, we believe that it is not beyond the realm of possibility that some developmental processes may indeed be governed by biophysical laws. In this regard, we note that the fundamental morphogenetic processes (e.g., convergent-extension and bending of epithelia) and the cellular mechanisms that drive these processes (e.g., cytoskeletal contraction and microtubule polymerization) are relatively small in number and appear to be similar across species.
One of our long-range goals, therefore, is to determine the fundamental biomechanical laws of morphogenesis. As in our other projects, this requires integrating mathematical models and experiments. Initially, we are exploring the Hyper-restoration Theory for morphogenesis, as described by Beloussov in his book The Dynamic Architecture of a Developing Organism: An Interdisciplinary Approach to the Development of Organisms. Preliminary results from this study are encouraging, but much remains to be done.
