The meningioma surface factor: a novel approach to quantify shape irregularity on preoperative imaging and its correlation with WHO grade

OBJECTIVE Atypical and anaplastic meningiomas account for 20% of all meningiomas. An irregular tumor shape on preoperative MRI has been associated with WHO grade II–III histology. However, this subjective allocation does not allow quantification or comparison. An objective parameter of irregularity could substantially influence resection strategy toward a more aggressive approach. Therefore, the aim of this study was to objectively quantify the level of irregularity on preoperative MRI and predict histology based on WHO grade using this novel approach. METHODS A retrospective study on meningiomas resected between January 2010 and December 2018 was conducted at two neurosurgical centers. This novel approach relies on the theory that a regularly shaped tumor has a smaller surface area than an irregularly shaped tumor with the same volume. A factor was generated using the surface area of a corresponding sphere as a reference, because for a given volume a sphere represents the shape with the smallest surface area possible. Consequently, the surface factor (SF) was calculated by dividing the surface area of a sphere with the same volume as the tumor with the surface area of the tumor. The resulting value of the SF ranges from > 0 to 1. Finally, the SF of each meningioma was then correlated with the corresponding histopathological grading. RESULTS A total of 126 patients were included in this study; 60.3% had a WHO grade I, 34.9% a WHO grade II, and 4.8% a WHO grade III meningioma. Calculation of the SF demonstrated a significant difference in SFs between WHO grade I (SF 0.851) and WHO grade II–III meningiomas (SF 0.788) (p < 0.001). Multivariate analysis identified SF as an independent prognostic factor for WHO grade (OR 0.000009, 95% CI 0.000–0.159; p = 0.020). CONCLUSIONS The SF is a proposed mathematical model for a quantitative and objective measurement of meningioma shape, instead of the present subjective assessment. This study revealed significant differences between the SFs of WHO grade I and WHO grade II–III meningiomas and demonstrated that SF is an independent prognostic factor for WHO grade.

Explaining the emergence of complex networks through log-normal fitness in a Euclidean node similarity space

Networks of disparate phenomena—be it the global ecology, human social institutions, within the human brain, or in micro-scale protein interactions—exhibit broadly consistent architectural features. To explain this, we propose a new theory where link probability is modelled by a log-normal node fitness (surface) factor and a latent Euclidean space-embedded node similarity (depth) factor. Building on recurring trends in the literature, the theory asserts that links arise due to individualistic as well as dyadic information and that important dyadic information making up the so-called depth factor is obscured by this essentially non-dyadic information making up the surface factor. Modelling based on this theory considerably outperforms popular power-law fitness and hyperbolic geometry explanations across 110 networks. Importantly, the degree distributions of the model resemble power-laws at small densities and log-normal distributions at larger densities, posing a reconciliatory solution to the long-standing debate on the nature and existence of scale-free networks. Validating this theory, a surface factor inversion approach on an economic world city network and an fMRI connectome results in considerably more geometrically aligned nearest neighbour networks, as is hypothesised to be the case for the depth factor. This establishes new foundations from which to understand, analyse, deconstruct and interpret network phenomena.

Impact of Insulation Type and Thickness on the Dynamic Thermal Characteristics of an External Wall Structure

The dynamic thermal characteristics of external wall structures are directly related to indoor thermal comfort and energy savings in buildings; they are also complicated and worth investigating. Thermal insulation in external wall structures has become a popular topic of investigation in the domain of building energy efficiency. This study aims to find the impact of insulation type and thickness on the dynamic thermal characteristics of external wall structures using a homogeneous multi-layer building external wall structure and three types of insulation materials that are widely used in Japan. The impact of insulation type and thickness on seven thermal characteristics of external walls, including thermal transmittance, decrement factor or amplitude attenuation, time lag, thermal admittance, time lead for thermal admittance, surface factor, and thermal capacity, was evaluated by numerical methods in this study. It was shown that insulation type and thickness would have a significant effect on thermal transmittance, decrement factor and time lag, but yield no significant change in thermal admittance, time lead for thermal admittance, surface factor, and the thermal capacity of external wall structures.