Lubkin S R, Wan X
Biomathematics Program, Department of Mathematics, North Carolina State University, Raleigh, North Carolina 27695-8205, USA.
Bull Math Biol. 2006 Nov;68(8):1873-91. doi: 10.1007/s11538-006-9074-z. Epub 2006 Jul 20.
Fluorescence recovery after photobleaching (FRAP) has been widely used to measure fluid flow and diffusion in gels and tissues. It has not been widely used in detection of tissue anisotropy. This may be due to a lack of applicable theory, or due to inherent limitations of the method. We discuss theoretical aspects of the relationship between anisotropy of tissue structure and anisotropy of diffusion coefficients, with special regard to the size of the tracer molecule used. We derive a semi-mechanistic formula relating the fiber volume fraction and ratio of fiber and tracer molecule diameters to the expected anisotropy of the diffusion coefficients. This formula and others are tested on simulated random walks through random simulated and natural media. We determine bounds on the applicability of FRAP for detection of tissue anisotropy, and suggest minimum tracer sizes for detection of anisotropy in tissues of different composition (fiber volume fraction and fiber diameter). We find that it will be easier to detect anisotropy in monodisperse materials than in polydisperse materials. To detect mild anisotropy in a tissue, such as cartilage, which has a low fiber fraction would require a tracer molecule so large that it would be difficult to deliver to the tissue. We conclude that FRAP can be used to detect tissue anisotropy when the tracer molecule is sufficiently large relative to the fiber diameter, volume fraction, and degree of polydispersivity, and when the anisotropy is sufficiently pronounced.
光漂白后荧光恢复（FRAP）已被广泛用于测量凝胶和组织中的流体流动及扩散。它尚未广泛应用于组织各向异性的检测。这可能是由于缺乏适用的理论，或者是该方法存在固有限制。我们讨论组织结构各向异性与扩散系数各向异性之间关系的理论方面，特别关注所使用示踪分子的大小。我们推导了一个半机械公式，将纤维体积分数以及纤维与示踪分子直径之比与扩散系数的预期各向异性联系起来。这个公式及其他公式在通过随机模拟和天然介质的模拟随机游走中进行了测试。我们确定了FRAP用于检测组织各向异性的适用范围，并针对不同组成（纤维体积分数和纤维直径）的组织检测各向异性提出了最小示踪剂尺寸。我们发现，检测单分散材料中的各向异性比检测多分散材料更容易。要检测纤维分数低的组织（如软骨）中的轻度各向异性，需要示踪分子大到难以递送至该组织。我们得出结论，当示踪分子相对于纤维直径、体积分数和多分散程度足够大，且各向异性足够明显时，FRAP可用于检测组织各向异性。
