IOL formula & Personalization in IOL master 2009.6.4 IOL formula & Personalization in IOL master 변용수 / Prof. 김만수

정확한 IOL power calculation이 더욱 중요해진 이유? Small, sutureless incision 등 수술기법 향상  난시에 의한 안경착용 감소  Sph. Ref. 이 술후 안경착용 여부에 결정적인 요소가 됨. Premium IOL (Toric IOL, multifocal IOL) 발달  Spectacle free가 백내장 수술의 목표가 되는 시대 도래

정확한 IOL power calculation이 더욱 중요해진 이유? 측정 기기의 발달  axial length, corneal power 등 측정값의 Precision, reproducibility, observer-independency의 향상

정확한 IOL power calculation의 요건 1. 정확한 measurements (ex. IOL master) - 적은 오차범위, 높은 재현성 (inter-observer & intra-observer) 2. 정확한 IOL formula (ex. Holladay 2, Haigis) - 높은 예측도, wide range AL에 적용, personalization용이 3. Personalization - Entire clinical environment에 의한 오차 보정 (측정장비, IOL shape, 수술법, 수술자, 인종 등)

IOL formula

Theoretical formula <Basics> 1. 곡면을 경계로 상이한 매질의 Refractive index F=(RI2-RI1)/r Cornea - aqueous - Lens - vitreous – vitreoretinal interface

Theoretical formula 2. Vergence plane Vergence power=RI / d Effective lens position Vergence plane Vergence plane change  Refractive change

Theoretical formula Thin lens formula - cornea, lens를 curvature line으로 단순화 Thick lens formula - cornea, lens thickness, ant. & post. curvature 고려 Exact ray tracing - higher order of aberrations 까지 고려 문제점) - 수많은 가정(assumptions) - 복잡한 다항식에 대입되는 수많은 변수(variables)의 측정 한계

Statistical Regression formula (Empirical) 실측 data set으로부터 도출 수많은 가정(assumptions)이 필요없다. Sum to zero - 도출된 data set내에서 예측치 error의 평균은 ‘0’ ex) 0.00 ± 0.60, 0.00 ± 0.25, 0.00 ± 0.05

Statistical Regression formula (Empirical) Data set 내에서만 유효하다 다른 data set (측정기기, 술자, 수술기법, IOL종류, 인종) 에 대한 상수 보정이 필요 ex) +0.5 ± 0.25  0.0 ± 0.25 SRK2/T – ‘A-constant ’(IOL constant) Holladay 1 – ‘Surgeon Factor’ Hoffer Q – ‘Anterior Chamber Depth’ Holladay 2 – ‘Anterior Chamber Depth’ IOL-constant로부터 구함

SRK (Sanders-Retzlaff-Kraff) SRK I : P = A - 0.9 K - 2.5 L SRK Ⅱ : P = A’ - 0.9 K - 2.5 L A’ = A + 3 (L < 20) A’ = A + 2 (20 ≤ L < 21) A’ = A + 1 (21 ≤ L < 22) A’ = A (22 ≤ L < 24.5) A’ = A - 0.5 (24.5 ≤ L) Desired postop refraction R P’ = Pemme - cr R cr : empirical constant defined as cr = 1 (P ≤ 14) cr = 1.25 (P > 14)

SRK1/2 formula는 AL와 K값만으로 empirical approach In different eyes with the same AL & K  계산된 IOL 동일  but 실제로는 다른 결과 Why? post-op. IOL position = Effective lens position = ACD

(SRK/T, Hoffer Q, Holladay 1) : simple linear regress formula 3rd generation formula (SRK/T, Hoffer Q, Holladay 1) : ACD-constant (술 후 IOL의 위치에 대한 고려)

Hoffer Q P = f (AL, K, Rx, pACD) A : axial length K : average corneal refractive power (K-reading) Rx : refraction pACD : personalized ACD (ACD-constant) K = 337.5/corneal radius pACD = ACD-const = 0.58357 * A-const - 63.896

HAIGIS DL = n/(L-d) - n/(n/z-d) (1) with z = DC + ref/1-ref dBC and DC = (nC-1)/RC DL : refractive power of IOL DC : refractive corneal power RC : corneal radius nC : (fictitious) refractive index of cornea ref : desired refraction dBC : vertex distance between cornea and glasses d : optical ACD L : axial length n : refractive index of aequeous and vitreous (1.336) nC = 1.3315, dBC = 12 mm L : axial length as measured by ultrasound

HAIGIS d = a0 + a1 ACDpr + a2 ALpr (2) with a0 = ACD-Const - a1 MW(ACDpr) - a2 MW(ALpr) (3) ACDpr : preop. anterior chamber depth measured ultrasonically ALpr : preop. axial length from ultrasound MW(..) : means of ACDpr(=3.37) mm and ALpr(=23.39) mm ACD-Const : ACD constant of manufacturer A-Const = (ACD-Const + 68.747) / 0.62467 constant a0 is directly related to the lens makers' ACD-constant. The default values are used for a1 and a2: (a1=0.4, a2=0.1)

Measurements needed for power formulas Axial Length K's ACD WTW Holladay 1 Hoffer Q SRK/T Haigis Holladay 2* *Holladay 2 formula is only available on Holladay IOL Consultant

Holladay 2 Easy to optimize Wide range of axial length It requires input of 7 variables (AL, K, lens thickness, horizontal WTW, ACD, pre-refraction, age ) IOLMaster does not include Holladay 2 formula (IOLMaster cannot measure the lens thickness)

IOL Master data set에 대한 Personalization

Ultrasound vs. Optical biometry averaging across foveal cup reflection at Bruch's membrane

Visual axis RPE가 end-point No indentation Quickly 높은 재현성 높은 정확성 매질에 의한 영향을 덜 받는다

why personalize lens constants? accuracy vs. precision Ultrasound Good accuracy (clustered around center) Low precision (large spread) Unpersonalized IOLMaster higher precision (tight cluster) lower accuracy (clustered away from center) Personalized IOLMaster high precision high accuracy 22

Can I use the IOL manufacturers‘ IOL constants? NO! IOL constants from IOL Manufacturers are typically based on applanation or contact ultrasound.

IOL constants are DIFFERENT on the IOLMaster ! IOLMaster상에 표시되는 axial length는 true optic path length가 아니다. IOLMaster optic path length와 immersion ultrasound로 측정한 axial length를 비교하여 만든 변환 공식을 사용하여 기기내에서 calibration되어 있다. 이유?) 기존에 사용되어 온 A-constant (IOL constant) based formula를 활용해야 하기 때문에 IOL constants are DIFFERENT on the IOLMaster !

Parallel path method for lens constant personalization For first 20-30 patients: Measure with IOLMaster Measure with current methods (ultrasound/ manual k) Calculate IOL power using current methods (ultrasound/ manual k) Perform Surgery Measure post-op refraction Axial Length Keratometry ACD, WTW Collect 20-30 successful, uneventful outcomes IOLMaster Optimization Feature Enter post-op refraction and lens power used for these 20-30 outcomes System calculates new IOLMaster-specific personalized lens constant You may now use IOLMaster measurements and IOL power calculations based on this new personalized lens constant!