摘要 A logarithmic spiral is a self-similar spiral curve, which often appears in nature, e.g., mollusk shells. In the normal tissues of the human body, the cochlea is also an approximate logarithmic spiral. However, approximate logarithmic spirals are rarely, if ever, reported in tumors. Recently, we treated a 26-year-old woman with a one-year history of headache. Preoperative magnetic resonance imaging showed a possible brain tumor with radiological characteristics similar to a typical logarithmic spiral, which has seldom been observed before. Because of the obvious clinical symptoms and discomfort, as well as the possible presence of an intracranial tumor, we performed a craniotomy and tumor resection. Perioperatively, we found an intact tumor capsule, with contents that appeared like egg-drop soup mixed with hairs. A post-operative pathological diagnosis of a dermoid cyst was made. However, more interestingly, the logarithmic spiral could be described mathematically with a high goodness of fit. In this paper, we present this case with various clinical images.
Abstract: A logarithmic spiral is a self-similar spiral curve, which often appears in nature, e.g., mollusk shells. In the normal tissues of the human body, the cochlea is also an approximate logarithmic spiral. However, approximate logarithmic spirals are rarely, if ever, reported in tumors. Recently, we treated a 26-year-old woman with a one-year history of headache. Preoperative magnetic resonance imaging showed a possible brain tumor with radiological characteristics similar to a typical logarithmic spiral, which has seldom been observed before. Because of the obvious clinical symptoms and discomfort, as well as the possible presence of an intracranial tumor, we performed a craniotomy and tumor resection. Perioperatively, we found an intact tumor capsule, with contents that appeared like egg-drop soup mixed with hairs. A post-operative pathological diagnosis of a dermoid cyst was made. However, more interestingly, the logarithmic spiral could be described mathematically with a high goodness of fit. In this paper, we present this case with various clinical images.
Meiqing Lou, Yaodong Zhao. A "logarithmic spiral" in the brain: Images of an intracranial dermoid cyst[J]. 临床转化神经科学, 2016, 2(4): 241-243.
Meiqing Lou, Yaodong Zhao. A "logarithmic spiral" in the brain: Images of an intracranial dermoid cyst. Translational Neuroscience and Clinics, 2016, 2(4): 241-243.
20170308102244 Figure 1 a. Image of the intracranial dermoid cyst. Magnetic resonance imaging revealed a 4-cm lesion with isointense or hypointense mixed signals on T1-weighted images and scanty enhancement after gadolinium injection. b. Tumor contents with an appearance like egg-drop soup. c. Graphical representation of the equation describing the spiral pattern in the cyst. d. Merged image of the calculated spiral curve and spiral seen in the tumor demonstrating a good fit.
[1]
Douady S, Couder Y. Phyllotaxis as a physical self-organized growth process. Phys Rev Lett 1992, 68(13): 2098-2101.
[2]
Marinkovi S, Stankovi P, Štrbac M, Tomi I, Eetkovi M. Cochlea and other spiral forms in nature and art. Am J Otolaryngol 2012, 33(1): 80-87.
[3]
Oldershaw RL. Self-similar cosmological model: Introduction and empirical tests. Int J Theor Phys 1989, 28(6): 669-694.
2016, Vol. 2 
