CN101947145B - 计算复曲面植入体的必需屈光力的方法 - Google Patents
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Abstract
本发明涉及一种使用测出的术前角膜/眼散光和预测的外科诱发散光来计算复曲面植入体的必需柱面屈光力的方法。使用外科医生采用的外科技术的屈光力向量分析来预测术后角膜/眼散光。这样的方法提供了计算植入体的必需球柱面屈光力的更准确方法。该方法可以手动实现,但是优选地通过适当的软件在计算机上实现来自动化。
Description
本申请是申请日为2005年3月23日、申请号为200580010245.1、发明名称为“计算复曲面植入体的必需屈光力的方法”的发明专利申请的分案申请。
技术领域
本发明总体涉及眼科晶体(lens)的领域,更具体地涉及复曲面人工晶体(toric intraocular lenses)(例如,人工晶状体IOL、AC有晶体眼IOL(AC phakic IOL)、PC有晶体眼IOL、虹膜固定式IOL等)。
背景技术
最简单地说,人类的眼睛通过使光透射穿过被称为角膜的透明外部,并利用晶状体将图像聚焦到视网膜上而产生视觉。聚焦图像的质量取决于很多因素,包括眼睛的大小和形状、以及角膜和晶体的透明度。
眼睛的屈光力(optical power)是由角膜和晶状体的屈光力决定的。在正常的、健康的眼睛中,在视网膜上形成清晰的图像(正常眼)。在很多眼睛中,因为眼睛不正常地长(轴向近视)而在视网膜前面形成图像,或者因为眼睛不正常地短(轴向远视)而在视网膜的后面形成图像。角膜和晶状体也可能不是球面的、规则的,而是不对称的或者复曲面的,导致未补偿的柱面屈光误差(refractive error),这被称为角膜散光和眼球散光,它们合在一起形成了眼散光。最后,如果对眼睛进行外科治疗,该治疗过程本身可能诱发角膜散光。
这些屈光误差都可以矫正,当保留自然晶体时,利用屈光植入体来矫正,或者通过用于取代自然晶体的人工晶体(IOL)来矫正。关 于复曲面植入体,为了矫正角膜/眼睛的规则散光,植入体的柱面屈光力的大小以及植入体与自然发生或者诱发的角膜/眼睛的不对称之间的精确对准是必需的。植入体的轴与角膜/眼睛的轴对准是非常重要的,因为即使柱面的大小匹配,只要轴未对准,就会导致在球面和柱面两种情况下出现不希望的残余屈光误差。因此,植入体的柱面的轴与角膜/眼睛的轴之间的不对准将对最佳视网膜成像的最终目标造成损害。所需对准的临界程度取决于角膜/眼柱面的大小,特别是对于较大的角膜/眼柱面来说。
在美国专利No.5,709,218(Holladay等人)中公开了一种现有技术的方法,该方法基于外科技术来预测必需的球面IOL屈光力。但是,该方法不使用屈光力向量分析来确定复曲面植入体的矫正能力或者取向。存在多种数学模型可用于估计外科诱发的散光。关于使用屈光力向量分析来估计由Lasik外科技术导致的屈光误差,Thibos、Holladay、Horner、Cravy和Koch等作者已出版了很多论文。以上方法为矫正效果提供了评估手段。但是,它们没有在如何正确地做外科手术以实现最佳屈光结果方面为外科医生提供直接的指导。此外,这些模型没有考虑晶体在眼睛内的位置。
因此,一直需要一种考虑到自然发生的和外科诱发的散光误差两方面,计算所预测的术后眼内屈光误差的方法。
发明内容
本发明对现有技术的改进在于提供了一种使用测出的术前角膜/眼散光和预测的外科诱发散光来计算复曲面植入体的必需屈光力的方法。使用对外科医生所采用的外科技术的屈光力向量分析来预测外科诱发的散光。这样的方法提供了计算植入体的必需术后屈光力的更准确的方法。该方法可以手动实施,但是优选地通过适当的软件在计算机上实现来自动化。
由此,本发明的一个目的是提供一种使用测出的术前角膜/眼散光和预测的外科诱发散光来计算复曲面植入体的必需屈光力的方法。
本发明的另一个目的是提供一种使用外科医生所采用的外科技术的屈光力向量分析来计算复曲面植入体的必需屈光力的方法。
本发明还有一个目的是提供一种计算植入体的必需术后屈光力的更准确的方法。
从以下具体实施方式部分和权利要求书中将会清楚本发明的这些及其他优点和目的。
附图说明
图1是指示本发明的方法的步骤的流程图。
图2是具有物理放置在植入体平面以及虚拟放置在角膜平面的人工晶体的眼睛的示意图。
图3和图4是因失误引入的,与本发明不相关。
具体实施方式
本发明的方法10一般包括基于患者因素和外科医生因素来确定患者的散光误差的大小。患者因素(12)包括:(i)植入体的平均球体等效值(MSE),(ii)最陡子午线(K1)和轴(A1)的K读数以及最平子午线(K2)和轴(A2)的K读数,(iii)前室深度(ACD)或者有效晶体位置(ELP)和(iv)整只眼睛的屈光度验光结果(manifest refraction)(在计算眼散光的情况下)。外科医生因素(14)包括每个外科医生特有的切口尺寸和位置(incision)以及外科诱发屈光变化(SIRC)。在步骤16使用屈光力向量分析法来分析患者因素12和外科医生因素14。步骤16可以使用本领域公知的多项数学等式中的任何一项,这里将讨论一个适合的等式。可以如下用M、J0和J45来描述验光常规(-cyl格式)或者眼科常规(+cyl格式)的球柱面处方(S、C和α):
其中B被称为模糊强度。它是在最低混淆的平面上的等效屈光散焦。
屈光力向量格式的屈光误差可以被转换回球柱面格式。由于验光(-cyl格式)和眼科(+cyl格式)常规很容易互换,所以在等式(2)中给出了从M、J0和J45到验光(-cyl格式)常规的转换:
临床处方中的柱轴通常落在0°和180°之间。为了使轴在合理的范围内,可能遇到四种不同的条件,如等式(2)中所示。
当前的白内障外科手术的角膜切割过程会引起与切割位置相关联的子午线处的角膜平面的平坦化和陡峭化。这在术后屈光度(refraction)中产生了可测的柱面屈光力改变和柱轴偏移。在预测术后散光时应当考虑外科诱发的散光变化,这样才有可能使用复曲面植入体来中和整只眼睛的散光。使用等式(1),角膜屈光误差SCornea、CCornea和αCornea以及外科诱发屈光变化(SIRC)SSIRC’、CSIRC’和αSIRC’可以被转换为屈光力向量。为了简化,角膜屈光误差的屈光力向量被表示为(M,J0,J45),SIRC的屈光力向量被表示为(M’,J0’,J45’)。用于预测的术后角膜屈光误差的屈光力向量是角膜和SIRC屈光力向量的和。
RxCornea=(M,J0,J45);RxSIRC′=(M′,J0′,J45′)
RxXcyl=RxCornea+RxSIRC ′=(M+M′,J0+J0′,J45+J45′) (3)
在整只眼睛的情况下,整只眼睛的屈光误差是SEye、SEye和αEye, 因此以上等式可以被改写为:
RxEye=(M,J0,J45);RxSIRC′=(M′,J0′,J45′)
RxXcyl=RxEye+RxSIRC′=(M+M′,J0+J0′,J45+J45′)
预测的术后角膜/眼向量可以使用等式(2)被转换为常规的球柱面格式。转换结果被标注为SXcyl、CXcyl和αXcyl,因为它们是横截柱面计算的结果。
为了复曲面植入体的选择,关注点将是柱面分量CXcyl和αXcyl。在角膜平面,需要利用CXcyl和αXcyl来进行复曲面矫正。然而,由于从角膜平面到植入体平面的屈光力转移特性,因此植入体平面上所需的复曲面矫正与角膜平面的不同。复曲面植入体具有如等式(4)所描述的柱面屈光力和柱轴。
CImplant=CF*CXcyl
αImplant=αXcyl (4)
其中,CF是角膜平面和植入体平面之间的转换因子。由计算出的CImplant和αImplant值,可以选择适当的复曲面植入体模型,并且选定的植入体将被放在αImplant所指示的子午线处。在步骤16中构想的向量分析导致计算出的术后角膜/眼散光18,它考虑了患者因素12和外科医生因素14两方面。如果植入体是人工晶体(IOL),则在步骤18处计算出的在角膜平面上的预测柱面误差在步骤20处被转换为在植入体平面上的必需柱面误差。
在以下讨论中,总的原则是光学元件的屈光力用“P”表示,聚散度(vergence)用“L”表示。我们将Pcornea定义为在某个子午线处的角膜屈光力,将PImplant定义为植入体的屈光力,将PImplant’定义为植入体在角膜平面上的等效屈光力,将Lcornea定义为紧临在角膜平面后的聚散度,将LImplant定义为在植入体的第一主平面上的聚散度,将LImplant’定义为在植入体的第二主平面上的聚散度,将n定义为水状体的折射率,将d定义为在角膜和植入体的第一主平面之间的距离。
通常,Lcornea等于在角膜平面上的眼镜矫正的聚散度和角膜的屈光力之和。
Lcornea=LRx+Pcornea (5)
其中,LRx是在角膜平面上的眼镜校正的聚散度。对于白内障外科手术后的正视眼,LRx等于0。在以下讨论中,如果没有特别指出,我们认为Lcornea与Pcornea相同
如图2所示,在上部的图示中,植入体被物理放置在植入体平面上。在下部的图示中,植入体被虚拟放置在角膜平面上。在植入体平面上的植入体的第一主平面被表示为FP,在植入体平面上的植入体的第二主平面被表示为SP。在两种情景中,聚散度在玻璃室前(即,在SP平面)应当相同。通过使在两种不同情景下计算出的聚散度相同,可以发现关系来决定在植入体平面上的所需植入体屈光力。更具体地说,在植入体平面上的所需植入体屈光力将是紧临在角膜后的聚散度(LCornea)、在角膜平面的所需植入体屈光力(PImplant’)、角膜的第二主平面(靠近前角膜平面)和植入体的第一主平面之间的距离(d)以及水状体的折射率(n)的函数。在有关复曲面值计算的讨论中,d和n可以被固定为常数。
PIOL=f(Lcornea,PImplant′,d,n)=fd,n(Lcornea,PImplant′) (6)
根据第一光学系统,在SP平面的聚散度是:
根据第二虚拟光学设置,考虑植入体的位置偏移,在SP平面的聚散度是:
通过使等式(7)和(8)的右侧相等,
获得下式:
等式(10)针对在植入体平面上的给定植入体,计算在角膜平面上的等效植入体。等式(11)根据在角膜平面上的必需屈光力来计算在植入体平面上的所需植入体屈光力。采用最大和最小屈光力之差可以获得所需的复曲面值。
假定光轴长度是ALO,则在角膜平面上的必需植入体屈光力可以被计算为:
例如,患者的k读数K1=42.75D×120°,K2=44.75D×30°。假定没有外科医生导致的散光,则正视眼具有轴长23.65mm,d=5.20mm,n=1.336。在角膜平面上的必需植入体屈光力是13.74D×120°和11.74D×30°。将这些值放入等式(11)中,在植入体平面上的植入体屈光力是21.13D×120°和18.22D×30°。比较角膜的复曲面值2.00D,植入体应当具有-2.91 D的复曲面值,转换因子为1.46。
等式(11)包括Lcornea和PImeplant’,因此,通过对等式(11)求微分,必须确定哪个变量对球面屈光力和柱面屈光力的计算影响最大,确定这两个因素对复曲面值的影响是不变的。
其中,dPImplant可以被认为是球面屈光力因选择不同的子午线而产生的变化,因此可以被视为植入体的柱面屈光力,类似地,dPImplant’可以被视为植入体在角膜平面上的柱面屈光力,dLcornea可以被视为角膜的柱面屈光力。直观上,等式(14)意味着植入体的柱面屈光力是它在角膜平面上的屈光力和角膜的柱面屈光力的函数,如等式(15)所示。如果dPImplant’(CylImplant’)和dLcornea(Cylcornea)之前的系数
和
是常数,那么等式(14)将是线性等式。然而,这两个系数通常不是常数,而是PImplant’和Lcornea的函数。
利用进一步的计算,可以确定
在等式(25)中,在角膜平面的所需IOL柱面值(CylIOL’)等于CXcyl,角膜柱面(Cylcornea,包括外科诱发的散光)等于所要矫正的屈光误差-CXcyl。因此,等式(15)可以被改写为:
CylImplant=(C1-C2)*CXcyl=CF*CXcyl (20)
CF=C1-C2高度依赖于d和角膜K值。对于35D-55D的正常范围内的角膜屈光力,通过将d固定为感兴趣的每个区域的平均值,利用等式(18)和(19)来计算转换因子(CF)。
对于0mm≤d<0.25mm,CF=1.00;
对于0.25mm≤d<0.75mm,CF=1.02-1.04;
对于0.75mm≤d<1.25mm,CF=1.05-1.09;
对于1.25mm≤d<1.75mm,CF=1.08-1.14;
对于1.75mm≤d<2.25mm,CF=1.11-1.19;
对于2.25mm≤d<2.75mm,CF=1.15-1.24;
对于2.75mm≤d<3.25mm,CF=1.18-1.30;
对于3.25mm≤d<3.75mm,CF=1.21-1.37;
对于3.75mm≤d<4.25mm,CF=1.25-1.43;
对于4.25mm≤d<4.75mm,CF=1.29-1.51;
对于4.75mm≤d≤5.25mm,CF=1.32-1.59;
对于5.25mm<d≤5.75mm,CF=1.37-1.67;
对于5.75mm<d≤6.25mm,CF=1.41-1.76;
对于6.25mm<d≤6.75mm,CF=1.45-1.86;
对于6.75mm<d≤7.25mm,CF=1.50-1.97。
对于将被放在角膜附近或者角膜中的植入体,例如屈光植入体,屈光力转移步骤20不是必要的。一旦在步骤18和/或步骤20确定了植入体的必需屈光力,则该计算出的屈光力可以被用来选择适当的晶体模型,并且分别在步骤22和24中向手术者报告晶体模型。也可以分别在步骤26和28中向手术者报告晶体屈光力计算结果和轴向放置。本发明因而提供了一种使用测出的术前角膜/眼散光和预测的外科诱发散光来计算复曲面植入体的必需屈光力的准确方法。
本说明书只是为了说明和解释的目的。本领域的技术人员将会清楚可以对上述发明作出改变和修改,而不会偏离其精神和范围。
Claims (1)
1.一种计算眼科植入体在角膜平面上以及在植入体平面上的必需复曲面屈光力的方法,包括以下步骤:
a)使用聚散度等式来描述人眼的光学系统;
b)使所述植入体位于角膜平面上时以及位于植入体平面上时的两个等效光学系统相同;
c)用以下等式来计算所述植入体的屈光力PImplant以及所述植入体在角膜平面上的等效屈光力PImplant′:
其中,d=在角膜和植入体的主平面之间的距离,n=水状体的折射率,Lcornea为紧临在角膜平面后的聚散度;以及
d)使用在陡子午线和平坦子午线之间的球面屈光力的屈光差来计算植入体在角膜平面上以及在植入体平面上的复曲面值。
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