Variation Rate of Multivariate Cumulative Function and Its Applications

2021 ◽  
Vol 11 (11) ◽  
pp. 1871-1878
Author(s):  
天勇 韩
Keyword(s):  
Cumulative Function ◽  
Variation Rate

Abstract 562: Human Carotid Atherosclerosis Plaque Progression and Vessel Material Stiffness at Follow Up Had Positive Correlation: An in vivo Vessel Stiffness MRI Follow Up Study

2017 ◽  
Vol 37 (suppl_1) ◽  
Author(s):  
Qingyu Wang ◽  
Dalin Tang ◽  
Gador Canton ◽  
Jian Guo ◽  
Xiaoya Guo ◽  
...  
Keyword(s):  
Negative Correlation ◽  
Material Properties ◽  
Stretch Ratio ◽  
Patient Specific ◽  
Plaque Progression ◽  
Material Stiffness ◽  
Variation Rate ◽  
Vessel Material

It is hypothesized that artery stiffness may be associated with plaque progression. However, in vivo vessel material stiffness follow-up data is lacking in the literature. In vivo 3D multi-contrast and Cine magnetic resonance imaging (MRI) carotid plaque data were acquired from 8 patients with follow-up (18 months) with written informed consent obtained. Cine MRI and 3D thin-layer models were used to determine parameter values of the Mooney-Rivlin models for the 81slices from 16 plaques (2 scans/patient) using our established iterative procedures. Effective Young’s Modulus (YM) values for stretch ratio [1.0,1.3] were calculated for each slice for analysis. Stress-stretch ratio curves from Mooney-Rivlin models for the 16 plaques and 81 slices are given in Fig. 1. Average YM value of the 81 slices was 411kPa. Slice YM values varied from 70 kPa (softest) to 1284 kPa (stiffest), a 1734% difference. Average slice YM values by vessel varied from 109 kPa (softest) to 922 kPa (stiffest), a 746% difference. Location-wise, the maximum slice YM variation rate within a vessel was 306% (139 kPa vs. 564 kPa). Average slice YM variation rate within a vessel for the 16 vessels was 134%. Average variation of YM values from baseline (T1) to follow up (T2) for all patients was 61.0%. The range of the variation of YM values was [-28.4%, 215%]. For progression study, YM increase (YMI=YM T2 -TM T1 ) showed negative correlation with plaque progression measured by wall thickness increase (WTI), (r= -0.6802, p=0.0634). YM T2 showed strong negative correlation with WTI (r= -0.7764, p=0.0235). Correlation between YM T1 and WTI was not significant (r= -0.4353, p= 0.2811). Conclusion In vivo carotid vessel material properties have large variations from patient to patient, along the vessel segment within a patient, and from baseline to follow up. Use of patient-specific, location specific and time-specific material properties could potentially improve the accuracy of model stress/strain calculations.

The curve of knowledge transfer: a theoretical model

2019 ◽  
Vol 25 (1) ◽  
pp. 10-26 ◽  
Author(s):  
Pasquale De Luca ◽  
Mirian Cano Rubio
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Theoretical Model ◽  
Knowledge Transfer ◽  
Transfer Process ◽  
Content Type ◽  
Positive Effects ◽  
Variation Rate ◽  
Effectiveness And Efficiency ◽  
Amount Of Knowledge

Purpose The knowledge transfer plays a key role in the firm’s capability to develop and to maintain a strategic competitive advantage over time. The capability of the firm to develop an efficient and effective process of knowledge transfer increases the internal skills and then the capability to compete in the business with positive effects on the performance. In order to maximize the effectiveness and efficiency of the knowledge transfer process it must be consider two main variables: the amount of knowledge to be transferred and the speed of the process. In this contest, the purpose of this paper is to developed a theoretical model, defined the knowledge transfer curve, able to evaluate the knowledge transfer process on the basis of its speed. Design/methodology/approach The curve of the knowledge transfer is based on the methodology of the learning curve. The curve of the knowledge transfer process can be evaluated on the basis of two main variables: the first is the content of knowledge to be transferred. It refers to the quality and quantity of the information to be transferred within the firm; and the second is the speed of the knowledge transfer process. It refers to the time in which the knowledge transfer can be realized. The function of the knowledge transfer is defined using ordinary differential equation. Findings There is an inverse relationship between time t and the variation rate r. The higher the variable r, the faster the knowledge transfer toward the level K. Therefore, the variable r measures the efficiency and effectiveness of the knowledge transfer process. On the basis of these considerations, manager must evaluate their policies about the knowledge transfer on the basis of their effects on the variable r: only the policy that increases its value can be considered effective for the knowledge transfer process. Originality/value The originality resides in the development of a theoretical model that is able to capture and measure the effectiveness and efficiency of the knowledge transfer. It is possible to define a curve of knowledge transfer on the basis of these two variables: content of the knowledge to be transferred and the time of the transfer process, by using an ordinary differential equation.

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