Runge-Kutta scheme is one of the versatile numerical tools for the simulation of engineering systems. Despite its wide and acceptable engineering use, there is dearth of relevant literature bordering on visual impress...Runge-Kutta scheme is one of the versatile numerical tools for the simulation of engineering systems. Despite its wide and acceptable engineering use, there is dearth of relevant literature bordering on visual impression possibility among different schemes coefficients which is the strong motivation for the present investigation of the third and fourth order schemes. The present study capitalise on results of tedious computation involving Taylor series expansion equivalent supplemented with Butcher assumptions and constraint equations of well-known works which captures the essential relationship between the coefficients. The simulation proceeds from random but valid specification of two out of the total coefficients possible per scheme. However the remaining coefficients are evaluated with application of appropriate function relationship. Eight and thirteen unknown coefficients were simulated respectively for third and fourth schemes over a total of five thousand cases each for relevant distribution statistics and scatter plots analysis for the purpose of scheme comparison and visual import. The respective three and four coefficients of the slope estimate for the third and fourth schemes have mix sign for large number of simulated cases. However, none of the two schemes have above three of these coefficients lesser than zero. The percentages of simulation results with two coefficients lesser than zero dominate and are respectively 56.88 and 77.10 for third and fourth schemes. It was observed that both popular third and fourth schemes belong to none of the coefficients being zero classification with respective percentage of 0.72 and 3.28 intotal simulated cases. The comparisons of corresponding scatter plots are visually exciting. The overall difference between corresponding scatter plots and distribution results can be used to justify the accuracy of fourth scheme over its counterpart third scheme.展开更多
目的:探究双眼外直肌倾斜后徙术(Slanted lateral rectus recession,S-LR)矫治集合不足型间歇性外斜视(Convergence insufficiency type of IXT,CI-IXT)的美学效果及对视觉功能的影响。方法:回顾性分析2021年8月-2023年8月笔者医院收治...目的:探究双眼外直肌倾斜后徙术(Slanted lateral rectus recession,S-LR)矫治集合不足型间歇性外斜视(Convergence insufficiency type of IXT,CI-IXT)的美学效果及对视觉功能的影响。方法:回顾性分析2021年8月-2023年8月笔者医院收治的80例CI-IXT患儿的临床资料,按手术治疗方式的不同分成双眼外直肌后徙术组(LR组,42例)和S-LR组(38例)。随访3个月比较两组疗效、视斜视度[视远/近斜视度、远/近斜视度差(Near-distant disparity,NDD)]、视觉功能(立体视、融合视、同时视功能)、间歇性外斜视生活质量量表(The Chinese version of intermittent exotropia questionnaires,CIXTQ)评分、复发率和美学效果的差异。结果:术后3个月,S-LR组手术矫正的优良率高于LR组,复发率低于LR组(P<0.05);两组视近斜视度、远斜视度、NDD均低于同组术前,且S-LR组低于LR组(P<0.05);两组立体视、融合视、同时视功能恢复占比均高于同组术前(P<0.05),而S-LR组与LR组间视功能恢复情况无明显差异(P>0.05);两组CIXTQ量表中儿童/家长代理量表、家长量表评分均高于同组术前,且S-LR组高于LR组(P<0.05);S-LR组斜视角度、眼球位置、眼球对称、眼部外观、面部整体外观等美学效果评分均高于LR组(P<0.05)。结论:应用S-LR治疗CI-IXT能有效提高手术矫正优良率,改善患儿的斜视度,促进视觉功能恢复,提高生活质量和美学效果,减少病情复发。展开更多
文摘Runge-Kutta scheme is one of the versatile numerical tools for the simulation of engineering systems. Despite its wide and acceptable engineering use, there is dearth of relevant literature bordering on visual impression possibility among different schemes coefficients which is the strong motivation for the present investigation of the third and fourth order schemes. The present study capitalise on results of tedious computation involving Taylor series expansion equivalent supplemented with Butcher assumptions and constraint equations of well-known works which captures the essential relationship between the coefficients. The simulation proceeds from random but valid specification of two out of the total coefficients possible per scheme. However the remaining coefficients are evaluated with application of appropriate function relationship. Eight and thirteen unknown coefficients were simulated respectively for third and fourth schemes over a total of five thousand cases each for relevant distribution statistics and scatter plots analysis for the purpose of scheme comparison and visual import. The respective three and four coefficients of the slope estimate for the third and fourth schemes have mix sign for large number of simulated cases. However, none of the two schemes have above three of these coefficients lesser than zero. The percentages of simulation results with two coefficients lesser than zero dominate and are respectively 56.88 and 77.10 for third and fourth schemes. It was observed that both popular third and fourth schemes belong to none of the coefficients being zero classification with respective percentage of 0.72 and 3.28 intotal simulated cases. The comparisons of corresponding scatter plots are visually exciting. The overall difference between corresponding scatter plots and distribution results can be used to justify the accuracy of fourth scheme over its counterpart third scheme.
文摘目的:探究双眼外直肌倾斜后徙术(Slanted lateral rectus recession,S-LR)矫治集合不足型间歇性外斜视(Convergence insufficiency type of IXT,CI-IXT)的美学效果及对视觉功能的影响。方法:回顾性分析2021年8月-2023年8月笔者医院收治的80例CI-IXT患儿的临床资料,按手术治疗方式的不同分成双眼外直肌后徙术组(LR组,42例)和S-LR组(38例)。随访3个月比较两组疗效、视斜视度[视远/近斜视度、远/近斜视度差(Near-distant disparity,NDD)]、视觉功能(立体视、融合视、同时视功能)、间歇性外斜视生活质量量表(The Chinese version of intermittent exotropia questionnaires,CIXTQ)评分、复发率和美学效果的差异。结果:术后3个月,S-LR组手术矫正的优良率高于LR组,复发率低于LR组(P<0.05);两组视近斜视度、远斜视度、NDD均低于同组术前,且S-LR组低于LR组(P<0.05);两组立体视、融合视、同时视功能恢复占比均高于同组术前(P<0.05),而S-LR组与LR组间视功能恢复情况无明显差异(P>0.05);两组CIXTQ量表中儿童/家长代理量表、家长量表评分均高于同组术前,且S-LR组高于LR组(P<0.05);S-LR组斜视角度、眼球位置、眼球对称、眼部外观、面部整体外观等美学效果评分均高于LR组(P<0.05)。结论:应用S-LR治疗CI-IXT能有效提高手术矫正优良率,改善患儿的斜视度,促进视觉功能恢复,提高生活质量和美学效果,减少病情复发。
