Delft University of Technology, Department of Biotechnology, Environmental Biotechnology Group, The Netherlands.
J Theor Biol. 2012 Sep 21;309:159-75. doi: 10.1016/j.jtbi.2012.05.024. Epub 2012 Jun 8.
A mathematical model of dental plaque has been developed in order to investigate the processes leading to dental caries. The one-dimensional time-dependent model integrates existing knowledge on biofilm processes (mass transfer, microbial composition, microbial conversions and substrate availability) with tooth demineralisation kinetics. This work is based on the pioneering studies of Dibdin who, nearly two decades ago, build a mathematical model roughly describing the metabolic processes taking place in dental plaque. We extended Dibdin's model with: multiple microbial species (aciduric and non-aciduric Streptococci, Actinomyces and Veillonella), more metabolic processes (i.e., aerobic and anaerobic glucose conversion, low and high glucose uptake affinity pathways, formation and consumption of storage compounds), ion transport by Nernst-Planck equations, and we coupled the obtained pH and chemical component gradients inside the plaque with tooth demineralisation. The new model implementation was complemented with faster and more rigorous numerical methods for the model solution. Model results confirm the protective effect of Veillonella due to lactate consumption. Interestingly, on short term, the storage compounds may not necessarily have a negative effect on demineralisation. Individual feeding patterns can also be easily studied with this model. For example, slow ("social") consumption of sugar-containing drinks proves to be more harmful than drinking the same amount over a short period of time.
为了研究导致龋齿的过程，已经开发出一种牙菌斑的数学模型。这个一维时变模型将现有的生物膜过程（质量传递、微生物组成、微生物转化和基质可用性）与牙齿脱矿动力学知识结合起来。这项工作基于 Dibdin 的开创性研究，将近二十年前，Dibdin 构建了一个大致描述牙菌斑中发生的代谢过程的数学模型。我们用以下内容扩展了 Dibdin 的模型：多种微生物物种（耐酸和非耐酸链球菌、放线菌和韦荣球菌）、更多的代谢过程（即有氧和无氧葡萄糖转化、低和高葡萄糖摄取亲和力途径、储存化合物的形成和消耗）、用 Nernst-Planck 方程进行离子运输，以及将获得的 pH 值和斑块内的化学组分梯度与牙齿脱矿联系起来。新模型的实现还辅以更快、更严格的模型求解数值方法。模型结果证实了韦荣球菌由于消耗乳酸而具有保护作用。有趣的是，在短期内，储存化合物不一定对脱矿有负面影响。个体喂养模式也可以很容易地用这个模型来研究。例如，缓慢（“社交”）消耗含糖饮料比短时间内喝相同量的饮料更有害。
