Probing Cell Sizes Using Short Diffusion Times

将开发一种新的磁共振成像（MRI）技术，该技术具有推断具有复杂几何形状的样品中水扩散的微米级限制的能力。******在接下来的五年里，该方法将被开发用于活体对象，并扩展到使用更精确的白质几何模型，其中包括方向分散、隔室之间的交换和脑脊液。简而言之，目前的方法使用了简化的样本几何模型；在我们的案例中，我们将纤维中的轴突建模为不同直径的平行不透水圆柱体的分布。找到了垂直于圆柱体的水的扩散作为频率函数的解析表达式。将实验数据或蒙特卡罗模拟数据拟合到该分析模型中，得到不同直径轴突的比例。******我们将改进模型，包括可渗透膜，以获得更准确的白质结果。有了可渗透膜，水分子可以扩散到比轴突直径还长的距离。目前的模型没有考虑到这一点，可能会扭曲结果，使轴突看起来比实际要大。******我们也会用髓磷脂双层包裹轴突。髓磷脂脂双分子层会增加更多的扩散屏障，其作用尚未得到充分的研究。此外，与中枢神经系统其他部分的水相比，髓磷脂脂质双层内的水具有非常短的松弛时间。虽然髓磷脂会对信号造成更多的限制，但髓磷脂双层内的水的磁化会更快地放松，可能达到水对信号没有贡献的程度。我们将找到模型的解析公式，并通过蒙特卡罗模拟和胼胝体和脊髓样本测试几何形状和假设。******我们还将优化新方法，因此它将成为解决磁共振束状图中接吻或交叉纤维问题的关键。磁共振束状图使用复杂的方法收集图像，使用许多梯度方向来确定几何纤维是否在连接处接吻或交叉。如果两根纤维含有不同直径的轴突，那么测量两根纤维的轴突直径分布就可以简单地确定两根纤维是亲和还是交叉。这对神经科学来说是极其重要的，因为神经束造影被用来了解大脑的哪些区域是相互连接的。新方法将在选择梯度频率、振幅和方向方面进行优化，以便在结处工作，目的是使结处的牵引成像方法更加准确和快速。******该方法将使用白质、蔬菜和其他微米尺度的多孔样品（如水泥和肺空气）进行验证。

A new magnetic resonance imaging (MRI) technique will be developed with the capability to infer micron-scale restrictions to water diffusion in samples with complicated geometries.******Over the next five years the method will be developed to work on live subjects and extended to use more accurate geometric models of white matter which include orientation dispersion, exchange between compartments and cerebrospinal fluid. In short, the current method uses a simplified model of the geometry of the sample; in our case we model axons in fibres as a distribution of parallel impermeable cylinders of varying diameters. An analytical expression is found for the diffusion of water measured perpendicular to the cylinders as a function of frequency. Data from experiments or Monte Carlo simulations are fitted to this analytical model to obtain the fraction of axons with different diameters.******We will improve the model to include permeable membranes for more accurate results in white matter. With permeable membranes, water molecules can diffuse distances longer than an axon diameter. The failure of the current model to take this into account could skew the results making axons seem larger than they actually are.******We will also surround the axons with myelin bilayers. Myelin lipid bilayers will add more diffusion barriers, the effect of which has not been fully studied. In addition, water within the myelin lipid bilayers has a very short relaxation time compared to water in other parts of the central nervous system. While the myelin will cause more restriction to the signal, the magnetization of the water within the myelin bilayers will relax much quicker possibly to the point that that water does not contribute to the signal. We will find analytical formulae for the model and test the geometries and assumptions with Monte Carlo simulations and corpus callosum and spinal cord samples.******We will also optimize the new method so it will be a key in solving the problem with kissing or crossing fibres in MR tractography. MR tractography uses sophisticated methods collecting images using many gradient directions to determine geometrically whether fibres kiss or cross at junctions. Measuring the axon diameter distributions of fibres on either side of the junction will allow a simple determination of whether the fibres kiss or cross if the two fibres contain axons of different diameters. This is of extreme importance to neuroscience because tractography is being used to understand which regions of the brain are connected to each other. The new method will be optimized in terms of the selection of gradient frequencies, amplitudes, and directions to work at junctions with the goal of making a more accurate and faster method for tractography at junctions.******The method will be verified using white matter, vegetables, and other micron-scale porous samples such as cement and lung airspaces.