Calculating the Growth of Vascular Cambium in Woody Plants as the Cylindrical Surface

The expansion of the vascular cambium cylinder in the stem of woody plants has been modeled many times, using different approaches and focusing on contributions of different cell events (cell divisions, intrusive cell growth and symplastic cell growth). Although there are many case studies in the literature, a universal model is still lacking. Therefore, the aim of this study is to estimate the quantitative changes in the contribution of symplastic growth of a single cambial cell (a sector of the cambial circumference) to the expansion of the vascular cambium cylinder, as the stem increases in girth. The proposed calculations, using the number π, and considering the actual dimensions of cambial cells, show (a) that the average symplastic increase per one initial cell in the circumferential direction decreases exponentially with the enlargement of cambial circumference, and (b) that the significant difference in the magnitude of symplastic increment of a single initial in the radial and circumferential directions increases proportionally to the increase in the circumference of the cambial cylinder. The proposed mathematical formula helps to understand the general rules that govern the gradual increase of the vascular cambium cylinder during wood production and would further facilitate the description/modeling of stem growth and formation of wood structural patterns.