Mathematical model of mechanical behavior of micro/nanofibrous materials designed for extracellular matrix substitutes

Electrospun micro/nanofibrous biomaterials are widely used as extracellular matrix substitutes in tissue engineering applications because of their structural and mechanical properties. To explore the influence of microstructure on the mechanical behavior of fibrous material, a mathematical model of the fiber system was developed. The model describes the microstructural properties of a fibrous matrix using a probability density function, and enables study of their mechanical properties. The results from the mathematical model were validated by qualitative comparison with the experimental results of mechanical testing of polystyrene electrospun nanofibrous materials. The analyses show a trend of three-phase load–displacement behavior. Initially, as an increasing number of fibers are recruited for load bearing, the load–displacement curve has a ‘J’-shaped toe region, which is followed by a nearly linear load–displacement curve, in which the number of load-bearing fibers remains nearly steady. Finally, there is a phase when the load–displacement curve descends, indicating failure of the material. The increase in flexibility of the fibrous material makes it stronger, but the randomness of fiber orientation makes the fibrous structure more flexible at the cost of lower strength. The measured mechanical properties of a fibrous matrix were also observed to be dependent on sample size. Therefore, the analyses establish a clear link between the structure and strength of fibrous materials for optimized design and fabrication of fibrous biomaterials with targeted use in tissue engineering, regenerative medicine and drug delivery. The model also establishes a need for standardization of experimental protocols for mechanical characterization of fibrous materials for consistency.