AI 中文总结
研究表面弛豫率对轴突内扩散分数和髓磷脂水分数的影响，推导有髓圆柱体表面速率封闭形式并验证，量化偏差，发现生理白质中表面弛豫率使轴突内信号加权过高，还揭示了相关物理原理及不同偏差特点。
AI 中文摘要
表面弛豫率和随时间变化的扩散是同一壁碰撞在一个底物上的两种读出方式：微观结构成像拟合的横向速率为体速率加上表面速率$\rho\,(S/V)$，轴突内和轴突外的水具有不同的$S/V$，因此它们的$T_2$不同，任何通过TE加权的$b = 0$进行归一化的隔室估计都会产生偏差。我们推导了有髓圆柱体内部（Brownstein-Tarr）和外部（Novikov-Burcaw）表面速率的封闭形式，通过壁计数蒙特卡罗方法进行验证，并量化了对轴突内扩散信号分数$f_{\mathrm{intra}}$和髓磷脂水分数（MWF）产生的偏差。内部/外部$S/V$比为$(1 - \mathrm{VF})/(g\,\mathrm{VF})$，与管径分布无关，并在纤维体积分数$\mathrm{VF}^{\ast}=1/(1 + g)$时超过1。生理白质位于这个交叉点之上，因此表面弛豫率使轴突内信号加权过高，在临床PGSE（$\mathrm{TE}=80\,\mathrm{ms}$）时使$f_{\mathrm{intra}}$偏差约12%。已知分数与TE有关；这里新的是表面弛豫率和堆积归因、封闭形式的符号定律以及可测试的依赖于堆积的TE漂移。相同的物理原理通过弛豫测量表现为较小的MWF偏差：最细轴突的水在髓磷脂窗口以下穿过并被计为髓磷脂，因此精细白质显示出更富含髓磷脂（$\sim 0.33\,\mathrm{pp}$，低于单像素噪声但在不确定的$\rho$中呈超线性），而在原发性管腔保留性脱髓鞘中，这种偏差几乎恒定并在纵向变化中抵消。因此，一种$S/V$物理原理会使扩散和弛豫测量微观结构估计都产生偏差，$f_{\mathrm{intra}}$偏差是一阶的且依赖于堆积，MWF偏差较小且与结构有关。
英文摘要
Surface relaxivity and time-dependent diffusion are two readouts of the same wall collisions on one substrate: the transverse rate that microstructure imaging fits is a bulk rate plus a surface rate $ρ\,(S/V)$, and intra- and extra-axonal water carry different $S/V$, so their $T_2$ differ and any compartment estimate that normalises by a TE-weighted $b=0$ is biased. We derive closed forms for the interior (Brownstein-Tarr) and exterior (Novikov-Burcaw) surface rates over myelinated cylinders, validate them with wall-counting Monte Carlo, and quantify the resulting bias on the diffusion intra-axonal signal fraction $f_{\mathrm{intra}}$ and on the myelin water fraction (MWF). The interior/exterior $S/V$ ratio is $(1-\mathrm{VF})/(g\,\mathrm{VF})$, independent of the calibre distribution and crossing unity at fibre volume fraction $\mathrm{VF}^{\ast}=1/(1+g)$. Physiological white matter sits above this crossover, so surface relaxivity over-weights the intra-axonal signal, biasing $f_{\mathrm{intra}}$ by $\approx 12\%$ at clinical PGSE ($\mathrm{TE}=80\,\mathrm{ms}$). That fractions are TE-dependent is known; new here are the surface-relaxivity and packing attribution, a closed-form sign law, and a testable packing-dependent TE drift. The same physics reads through relaxometry as a smaller MWF bias: the thinnest axons' water crosses below the myelin window and is counted as myelin, so fine white matter reads myelin-richer ($\sim 0.33\,\mathrm{pp}$, beneath single-voxel noise but super-linear in the uncertain $ρ$), while in primary lumen-preserving demyelination this bias is nearly constant and cancels in the longitudinal change. One $S/V$ physics thus biases both diffusion and relaxometry microstructure estimates, the $f_{\mathrm{intra}}$ bias being first-order and packing-dependent, the MWF bias small and structural.
