下面我们将为大家提供四期连载内容，本文为第四期。本次介绍2016年关于膝关节骨性关节炎预测的最新综述，继续研究模型建立方法，并探讨如何将模型应用于风险预测。
接下来，我们建立了软骨细胞nt，蛋白聚糖at和胶原蛋白ct的损伤和修复方程。软骨细胞通过增殖可以在一定程度上进行修复；尽管健康组织中软骨细胞的周转率较低，这在患有骨性关节炎的情况下仍较明显，目的可能是为了对降解的软骨细胞进行补充同时增加细胞外基质的修复能力。反之，软骨细胞也会发生细胞凋亡，重复高载荷或单一极端高载荷（创伤性），两者均会导致每日活动水平At增高。为了模拟这两种竞争过程，我们建立如下的公式：
公式中ρ(n)表示每日最大增殖率，最大值为健康状态下的密度值n(0)，D(n)(At)表示软骨细胞损伤函数，以0-1之间的数代表每日活动At造成的损伤程度，软骨细胞每日潜在的最高清除量为λ(n)。损伤函数是一个变化的S形函数
其中S形函数的斜率为μ(n)，阈值点为A(0)。后者代表了活动水平影响组织的发病阈值，作为一个通用阈值，它在其他成分的函数中也会出现；前者描述了损伤发生的突然性，数值具有软骨细胞特异性。
某些活动状态下蛋白聚糖可由软骨细胞合成。然而，蛋白聚糖也会通过组织表面的退化和压力诱导移流而损耗。损失率随着胶蛋白含量的减少而增加，因为胶原蛋白具有保持蛋白聚糖的作用。我们列出公式
其中R(a)(At)是每个细胞的活动依赖型合成率，当ct = c(0)时，蛋白聚糖的基线损失率为λ(a,0)，c(0)是健康胶原蛋白的含量基线，λ(a,1)是因胶原蛋白损耗造成的蛋白聚糖最大损失率。活动依赖型合成率公式为
其中ρ(a,0)和ρ(a,1)分别表示每个软骨细胞的最小和最大合成率，软骨细胞A(0)值与之前一样。
胶原蛋白也由软骨细胞合成。另一方面，胶原网络因蛋白水解存在自然损失率，也会因力学载荷或过度摩擦和磨损而直接受损。这些过程可以表示为
公式中λ(c,0)为基线损失率，λ(c,1)为每日最大损失率。合成率的公式与蛋白聚糖相同
赋予胶原蛋白新的速率系数值。损伤函数的形式与软骨细胞的损伤函数相同，为
同样，赋予μ(c)新的系数值。
模型应用于风险预测
一种统计方法是使部分或全部输入值（和/或模型参数）随机变化，同时经过反复模拟运行，模型输出值以组织健康轨迹随时间变化的概率分布情况呈现。这为骨性关节炎长期预测提供了一个更现实和个性化的方法，这种方法可以很容易地整合参数估计的不确定性和不同患者生活方式的差异性。通过这种方法，特定患者一旦应用此模型，就可评估发病预测，同样重要的是，此方法可通过改变参数探讨缓解策略。
此案例中应用的参数见表2。尽管我们至少了解其中一些参数，如细胞和胶原蛋白密度，其他参数仍缺乏可靠的定量数据，如因活动造成的损失率。我们选择易发病患者中能给出合理结果的变量来构建模型，同时认识到将来对模型进行这种验证和校准是必要的。人群不确定性研究对应于每次模拟运行时这些参数的改变。在此案例中我们保持这些参数不变，而是随机改变每日活动来研究个体不确定性。对于活动变量σt和ft的分布情况，两变量对应的均值和，方差和均选择正态分布。为和 选择不同的数值，进而模拟低强度、适度和高强度的活动方式。
TABLE 2. Parameter values in OA model. See Ref. 39 for component densities.
表2.骨性关节炎模型的参数值。成分密度请见参考文献39。
我们使用该模型模拟活动的突然变化。在这种情况下，通过调整分布参数，数值，表征个体生活方式从“正常影响力”的每日载荷变为“高影响力”或“低影响力”的载荷分布。正常影响力载荷是在一个能维持组织内平衡健康的水平，而其他潜在有害因素为高影响力为代表的超负荷损伤（例如，肥胖或异常活动）和低影响力为代表的合成下降（例如，长期久坐的生活方式）。
为了表征软骨在每个时间点的整体健康状态，我们定义健康组织为400 kPa测试载荷，实质应变35%，其中35%为经典的组织可耐受最大应变。测试载荷前提下应变大于35%，即转变为不健康，因此提示关节炎发病的潜在可能。凭借再生能力人们还可以构建一个健康替代品，以提高骨性关节炎发病风险的长期预防。
图6显示了从适度活动状态变为高强度活动或低强度活动状态的影响，呈现了活动分布由
FIGURE 6. Cartilage health (as defined in the text) during an abrupt shift from medium to high activity (left) or from medium to low activity (right). Grey lines are individual activity realizations; solid black lines are the means over all realizations, with 95% confidence intervals in dashed black lines. Red dash-dotted line indicates the zero health OA danger threshold.
图6.从适度突然转变到高强度活动（左）或从适度突然转变到低强度活动（右）的软骨健康状况（如文本定义的）。灰色线表示个体活动情况，黑色实线表示所有活动值的平均值，95%置信区间以黑色虚线表示。红色虚线表示最低健康状况下的骨性关节炎危险阈值。
高强度活动的转变表现出一系列不同的潜在骨性关节炎发病阈值，这取决于每日活动分布的特定实现情况。这种信息可通过骨性关节炎各时间点发病的统计学分布情况最好地呈现给患者，也就是说，骨性关节炎首次发病时间即为特定曲线轨迹与组织健康零点轴线的交叉点。对于文中所示数据，图7给出了分布情况，并预测骨性关节炎发病时间为第345±47周。
FIGURE 7. Distribution of OA danger threshold hitting times in the high activity example of Fig.6.
图7.以图6显示的高强度活动为例，各时间点骨性关节炎风险阈值的分布。
结论
我们认为，在结构可靠性分析的前提下将力学数学模型与统计方法结合有着广阔的应用前景。现阶段预防骨性关节炎发作和为保守治疗中病情发展给出个体特异性建议仍有许多困难，通过上述方法可以克服这些挑战。尽管多角度个体特异性模型需要涵盖骨性关节炎患者可能表现的更多显著特点，但是文中列举的模型已呈现出了组织变化，能够很好地展现骨性关节炎的软骨降解过程。我们相信如果为组织力学环境压力（如实变和液体渗透）确立直接的参数，而不采用体重指数和体力活动这种间接参数，应用这种模型可以发现更强的骨性关节炎患者个性化风险因素。
然而，可靠的患者个性化预测还未成真，这种方法什么时候能出现主要取决于人们可以支付建立高质量的患者个性化数据的时间。目前，获取足量和可输入到力学模型的信息是一项挑战。不过，技术在迅速发展，随着高通量基因组和蛋白质组学技术和成像技术（包括步态计算机视觉）的持续发展，以及从步态实验室和手机活动监控中获得的肌肉骨骼数据，以这些数据建立患者个性化的模型可能比你想象得要更快实现。事实上，高质量的完整基因组测序现在只需不到一千美元即可实现，蛋白质组学分析正迅速发展，为了更好地了解由炎症引起的骨性关节炎，目前已可以通过血液和关节液进行分析。此外，核磁共振成像可以量化因关节创伤引起的胶原网络损伤，长年跟踪胶原网络康复情况。
模型开发和验证可能具有迭代性和机会性。这是贝叶斯方法意义下的迭代：新的数据集首次用于验证时，这些数据通过更新模型参数对模型进行校准，所以模型随着每个数据周期一直在更新。另一方面，模型开发具有机会性，条件是当一项新技术产生（如电话应用，可以真实地记录人们的活动水平），并推动该邻域的模型得到改善，从而优先于其他模型。新数据始终来自于人群研究、实验室基础研究以及社区研究项目如膝关节骨性关节炎倡议。我们可以想象有一天相比这些相对不协调的数据采集，骨性关节炎社区调研可以收集数据并用来构建模型。这最早出现于其他疾病的研究中。
最后，需要着重记住的是人们选择患者个性化模型或风险预测，并不希望了解个人的所有信息。在采集哪些数据，花费多少成本和造成患者不便之间始终要做出妥协。那么，问题就应该是：什么数据能给出骨性关节炎风险最多的信息，并可被合理测量？这种方法中，需假定所有其他的未知变量为群体平均值，或从一个假设的群体分布中随机抽样得到的更优值。自然，这种方法的临床实用性取决于采集的数据与已有的整体人群风险评估的数据相比，是否能更准确地进行风险评估。这仍有待观察。然而，其实用性超出了直接临床应用。与桥梁设计师一样，将风险评估简便地通过这种满足结构可靠性分析的力学统计学方式有助于明确问题，使我们确立新颖有效的策略以尽可能减小失败风险。
Next, we formulate the damage and repair equations for the chondrocytes nt, aggrecan at and collagen ct. Chondrocytes can repair, to some extent, by proliferation; this is noticeable in osteoarthritic conditions, perhaps to replenish chondrocyte loss and increase the ECM repair capacity, though in healthy tissue chondrocyte turnover is low. Conversely, chondrocytes can be driven to apoptosis either by repetition of high load events or by one single extremely high load (traumatic) event, both of which result in a high level of the activity At. To model these two competing processes, we write
Where ρ(n) is a maximal proliferation rate per day up to a healthy number density n(0), and D(n)(At) is the chondrocyte damage function rating how deleterious the day’s activity At was on a scale from 0 to 1, with λ(n) the maximum fraction of chondrocytes potentially removed per day. The damage function is taken to be a shifted sigmoid function
with sigmoid gradient μ(n) and threshold position A(0). The latter encodes the onset threshold of tissue-affecting activity levels, and will also appear in other components as a universal threshold; the former encodes the suddenness of damage onset, whose value is chondrocyte-specific.
Aggrecan is synthesized by each chondrocyte at some activity-dependent rate. However, it is also lost through the tissue surface by degradation and pressure-driven advection. This loss rate will increase as the collagen content decreases, because collagen acts to retain aggrecan. We write
where R(a)(At) is the activity-dependent synthesis rate per cell, λ(a,0) is the baseline aggrecan loss rate when ct = c(0), with c(0) the baseline healthy collagen content, and λ(a,1) is the maximal additional aggrecan loss rate as collagen depletes. The activity-dependent synthesis rate is given by
Where ρ(a,0) and ρ(a,1) are the minimal and maximal synthesis rates per chondrocyte, respectively, and A(0) is as for the chondrocytes.
Collagen is also synthesized by each chondrocyte. On the other hand, the collagen network has a natural rate of loss by proteolytic degradation, and can also be directly damaged through mechanical loading or excessive friction and wear. These processes are encoded as
Where λ(c,0) is the baseline loss rate and λ(c,1) is the maximal daily damage rate. The synthesis rate, identical in form to the aggrecan, is
with new rate coefficients for collagen. The damage function is identical in form to the damage for the chondrocytes, reading
again with a new coefficient μ(c).
MODEL APPLICATION TO RISK PREDICTION
A statistical approach is to view some, or all, of the inputs (and/or model parameters) as randomly varying, and the model outputs, on repeated simulation runs, as realizations of an underlying probability distribution for the trajectory of the tissue health over time. This provides a more realistic and more person-alizable approach to OA prediction on longer time scales, as both uncertainty in parameter estimation and variability in different patients’ lifestyles can be incorporated readily. From this approach, onset predictions can be estimated once the model is tuned to a particular patient, and, importantly, mitigation strategies can be explored by altering these parameters.
The parameters we will use for this example are given in Table 2. While some variables are at least approximately known, such as cell and collagen densities, others, such as loss rates in response to activity, lack solid quantitative data. We have chosen variables that give plausible results for susceptible patients in order to illustrate the model, on the understanding that future work is necessary to verify and calibrate models like this. Exploring population uncertainty would then correspond to varying these parameters for each simulation run. In this instance, we will hold these parameters constant and instead explore individual uncertainty through randomly varying daily activity. For the distributions of the activity variables σt and ft, we choose normal distributions of respective means ，and respective variances ，. Choosing different values of and then allows us to simulate low-, medium- and high-activity lifestyles.
We use the model to simulate an abrupt change in activity. In this scenario, a person switches lifestyle from ‘normal impact’ daily loading to either ‘high impact’ or ‘low impact’ loading distributions, characterized by adjusting the distribution parameters
To characterize the overall health of the cartilage at every point in time, we define the tissue health as the difference of consolidated strain from 35% under a 400 kPa test load, with 35% chosen as a typical tolerable maximal tissue strain. A strain greater than 35% under the test load then translates into a negative health metric and therefore indicates potential OA onset. One could also construct a health surrogate based on regenerative capacity, say, to highlight longer-term regimes of OA danger.
Figure 6 shows the effects of switching from medium activity to high activity or low activity. After a stable period at = 350 kPa and = 0.1 Hz, the activity distribution is abruptly switched to either = 450 kPa and = 0.12 Hz (high activity) or = 200 kPa and = 0.02 Hz (low activity). In high activity case, an initial rise in tissue health from increased activity-driven synthesis is soon outweighed by the long-term effects of damage leading to a slow but persistent decline in tissue health. In the low activity case, the decrease in activity-driven synthesis is sufficient to quickly drop the tissue below the indicated danger threshold; though it does not keep decreasing like in the high activity case, the tissue is now more susceptible to sudden impact loading and may be at increased risk of age-related OA. These two circumstances correspond to respectively shifting either the load or resistance curves in Fig. 5, as discussed earlier.
The high activity switch exhibits a range of different potential OA onset thresholds depending on the particular realizations of the daily activity distribution. This information can be best presented to a patient through statistics of the distribution of OA onset hitting times; that is, the first time at which a particular trajectory crosses the zero health axis. For our example data, this distribution is given in Fig. 7, which predicts an OA onset time of 345 ± 47 weeks.
CONCLUSIONS
We have argued that combining mechanistic computational models with statistical approaches under the umbrella of structural reliability analysis provides a promising framework for overcoming the current challenges in providing subject specific recommendations for avoiding OA onset and conservatively managing OA progression. Although multiscale subject-specific models are likely needed to encompass more of the salient characteristics that OA patients may present with, the example model presented here does develop tissue changes that may well represent the OA cartilage degradation process. We believe that by using such models, stronger OA patient-specific risks will be found if direct metrics for the tissue mechanical environmental stressors, such as consolidation and fluid exudation, rather than indirect measures like BMI and physical activity, are used.
While reliable patient-specific predictions are not yet possible, how quickly they will emerge depends mainly on the speed with which high quality patient-specific data becomes available at an affordable price. At present, getting sufficient information to feed into a mechanistic model is a challenge. However, technology is evolving rapidly. With the ongoing developments in high-throughput genomic and proteomic technologies and imaging technologies (including computer vision of gait), alongside musculoskeletal data obtained from gait laboratories and activity monitors in mobile phones, data to drive patient-specific models may become available sooner than one may think. Indeed, high quality complete genome sequencing can now be accomplished for less than one thousand dollars, proteomic analysis is developing rapidly, and it is now possible to analyze the blood and synovial fluid to better understand inflammatory drivers of OA. Furthermore, MRI imaging can now quantitate damage to the collagen network following joint trauma and track collagen network recovery over a number of years.
Model development and validation will likely be both iterative and opportunistic. It will be iterative in the sense of a Bayesian approach: a new data set is first used for validation, then folded into the model calibration by updating model parameters, so the model is always improving with each data cycle. On the other hand, development will be opportunistic in the sense that when a new technology arises, such as phone applications that faithfully record a person’s activity levels, then improvements in this aspect of the model may be driven ahead of others. New data is arriving all the time from population and lab based studies, as well as community wide projects such as the Knee Osteoarthritis Initiative. We can dream of a time when, in contrast to these relatively uncoordinated data collections, the OA community starts collecting data specifically to inform a model. This is beginning to occur in the study of other diseases.
Finally, it is important to remember that when people refer to patient-specific models or risk predictions, it is not expected that everything is known about the individual. A compromise must always be made as to what data can be obtained, and at what financial cost and patient inconvenience. The question should then be: what data is most informative about the risk of OA amongst that which can be reasonably measured? In such an approach all other unknown variables would be assumed to be either at the population average, or better sampled randomly from an assumed population distribution. Naturally, the clinical utility of this approach rests on whether or not the obtainable data yields a risk assessment more accurate than that already known for population risk as a whole. This is yet to be seen. However, there is utility beyond immediate clinical application. As with bridge designers, simply putting the risk assessment into this mechanistic-statistical frame-work of structural reliability analysis helps to define the problem, allowing us to identify new and efficient strategies to minimize the risk of failure.
由MediCool医库软件 王露黔 编译
原文来自：Predicting Knee Osteoarthritis
Ann Biomed Eng. 2016 Jan;44(1):222-33.
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