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A brief history of IOL Formula & the
importance of A constant optimization
Subhabrata Bhattacharya
A Brief history of IOL Formula & the importance of Aconstant
optimization
Subhabrata Bhattacharya
Biometry is the art of applying mathematics to
biology
BRIEF HISTORY OF BIOMETRY
The first IOL was implanted by Sir
Harold Ridley on November 29, 1949.
The second implantation by Ridley
was performed at Moorfield’s Hospital
the following year.
Over the next couple of years Ridley
had implanted over a thousand lenses
So how were the power (diopter) of the IOL determined prior to A scan machines ?
1. IOL power was calculated on the basis of clinical history – pre operative
refractive error prior to cataract development in eye.
2. Empirical Method – Adherents to the empirical method would implant a 19.0
diopter lens thinking that this would behave like the natural lens
3. The Basic Refractive Error method – One would add or substact 1.25 diopter to
every pre operative refractive error in the eye on a 18.0 diopter lens
The first Biometry A scan machines were introduced in 1970s
Hence IOL implantation predates Biometry and A scan machines
Introduction of A scan machines brought in a host of first generation
theoretical formulae for the calculation of IOL power
1. Binkhorst (1972)
2. Colenbander ( 1973)
3. Fyododrov ( early 70s)
4. Thijssen (1975)
These were all theoretical formulae or two – lens formulae based on
theoretical calculation of IOL power based on the Cornea and the
Lens.
The concept of the A constant was not there
All lenses were assumed to have a pre determined fixed position in the
eye
This was the age of Anterior Chamber Lenses
The assumption of a fixed position of the lens was not incorrect given
the fact that it was an age of ICCE or Intra Capsular Cataract Surgery
The mid 1980s saw the introduction and acceptance of Phacoemulsification.
By then the issues faced with AC IOLs ware widely felt.
The concept of IOL implantation in the bag started getting widely recognized.
The stage was set for the second generation IOL calculation formulae and the concept of
A constant
The difficulty of predicting the IOL in the capsular bag due to capsular
contraction, vaulting characteristic, etc, set the stage for a host of pioneering work
involving constants.
Second Generation formulae –
Holladay, Prager Chandler et al (1988)
Colliac (1990)
Olsen ( 1987)
Sanders, Retzlaff, and Kraff (1988)
The SRK Formulae
P= A-2.5L-.9K
The original SRK formulae through introduced the concept of A constant,
was still a theoretical formulae and the A constant was directly derived from
the manufacturer’s lens box
Second Generation SRK II Formulae
The second generation theoretical formulae were distinct from first
generation formulae in the sense that the value for the position of the IOL
was not fixed but varies as a function of at most two variables – axial
length and corneal curvature.
Though the word ELP or Effective Lens Position is
comparatively a new term, the concept was
recognized now in the form of ACD.
Later the ACD was replaced by ELP as a term
which suitably describes the lens position in the eye
after cataract surgery.
ELP – Distance from corneal vertex to principal
plane of thin IOL
Same as ACD, but avoids confusion with anatomy
SRK II formulae
Notable among the second generation formulae was the
development of the original SRK formulae into SRK II
formulae .
The SRK II was a regression formulae which attempted to fit a
function to the distribution of Axial Length and IOL power
through a polynomial regression analysis.
This regression analysis was linear for average axial length eyes
, it exhibited non linearity in non average eyes
Adjustments to the Axial Length through A constants by SRK II
formulae.
The below table shows the relationship between A constant of SRK and
the adjustments done in SRK II
However though the SRK II formulae was a vast improvement and predicted fairly
accurately the IOL position in the bag for average eyes, yet there were unexpected error in
longer and shorter eyes.
The reason was that until 1996 it was assumed that a longer eye would
have a longer ACD , and a shorter eye would have proportionately
shorter ACD.
The works of Holladay (1996) showed this was often not to be.
Hence a formulae like SRK II that predicts the ELP or the IOL
position in the eye as a linear function of axial length only, does not do
justice in non average eyes.
The SRK T formulae was a further improvement and combined the linear regression method
with the theoretical eye model to predict the IOL position correctly even in non average eyes.
It is a non linear theoretical optical formula empirically optimized to predict the ELP.
It combines the advantages of theoretical and regression formulas
The SRK T now took into account the corneal curvature in addition to Axial Length to predict IOL
position in non average eyes through alteration of A constant over the SRK II
Fourth Generation Formulae like Holladay II takes into account several
variables to predict the IOL position ( ELP ) in the eye.
 Axial Length
 K readings
 White to White
 ACD
 Manifest Refraction
 Lens Thickness
 Age
Fourth generation Olsen formulae – the concept of C
constant.
A key feature of the Olsen formulae is the C constant which
can be regarded as a ratio by which the capsular bag will
encapsulate the IOL in the bag.
The Olsen formulae takes the c constant as a function of Lens
Thickness and ACD.
Brief history biometry iol calculation formula & a constant optimization
There are largely three IOL constants in use :
The SRK T as indicated earlier uses A const
The Holladay I formula uses Surgeon Factor or SF
The Holladay II and the Hoffer Q formula uses ACD
The Haigis uses three constants – A0, A1, A2
d ( ELP ) = a0 + (a1*ACD)+(a2*AL)
HAIGIS
The a0 constant behaves like the other constants in SRKT,
Holladay I, Holladay II, etc.
The a1 constant is tied to the measured anterior chamber depth
The a2 constant is tied to the measured axial length
The Importance of Constant optimization !
A CONSTANT & OPTIMIZATION
At a glance
In an average IOL patient, there would be no difference if you use the IOL
Master or Lenstar or an immersion ultrasound device, as long as you use the
proper constants – Dr. Haigis
CALCULATING IOL POWER ??
Best biometry
Best keratometry
Best formulae
Right A constant
Keratometric Index
White to White
Preoperative Refraction
EVEN DOING THINGS RIGHT MAY
STILL NOT BE ENOUGH
HENCE CONSTANT OPTIMIZATION IS
IMPORTANT
WHY OPTIMIZE ??
If you have your a constant optimized then the number of patients falling
within .5D of target refraction increases four fold.
WHY OPTIMIZE ??
WHY OPTIMIZE ?
 No two surgeons’s have the same technique.
 Rhexis ??
Surgeons NEED to UPDATE biometers;
Lens Constant Database !
UPDATE Lens Constant Database !
AcrySof® IQ Toric
‘A-Constant’
See USER MANUAL for instruction !
IOL DATA OPTIMIZATION
• It is strongly recommended to customize and personalize A-constant,
ACD, and Surgeon Factor based on their individual biometry
techniques.
• Data obtained from at least 30 patients should be used.
• To successfully customize, refractive surprises should be consistently
hyperopic or myopic when compared with predicted values before
adjustments are made.
Thank you !!

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Brief history biometry iol calculation formula & a constant optimization

  • 1. A brief history of IOL Formula & the importance of A constant optimization Subhabrata Bhattacharya
  • 2. A Brief history of IOL Formula & the importance of Aconstant optimization Subhabrata Bhattacharya
  • 3. Biometry is the art of applying mathematics to biology
  • 4. BRIEF HISTORY OF BIOMETRY The first IOL was implanted by Sir Harold Ridley on November 29, 1949. The second implantation by Ridley was performed at Moorfield’s Hospital the following year. Over the next couple of years Ridley had implanted over a thousand lenses
  • 5. So how were the power (diopter) of the IOL determined prior to A scan machines ? 1. IOL power was calculated on the basis of clinical history – pre operative refractive error prior to cataract development in eye. 2. Empirical Method – Adherents to the empirical method would implant a 19.0 diopter lens thinking that this would behave like the natural lens 3. The Basic Refractive Error method – One would add or substact 1.25 diopter to every pre operative refractive error in the eye on a 18.0 diopter lens
  • 6. The first Biometry A scan machines were introduced in 1970s Hence IOL implantation predates Biometry and A scan machines
  • 7. Introduction of A scan machines brought in a host of first generation theoretical formulae for the calculation of IOL power 1. Binkhorst (1972) 2. Colenbander ( 1973) 3. Fyododrov ( early 70s) 4. Thijssen (1975)
  • 8. These were all theoretical formulae or two – lens formulae based on theoretical calculation of IOL power based on the Cornea and the Lens. The concept of the A constant was not there All lenses were assumed to have a pre determined fixed position in the eye This was the age of Anterior Chamber Lenses
  • 9. The assumption of a fixed position of the lens was not incorrect given the fact that it was an age of ICCE or Intra Capsular Cataract Surgery
  • 10. The mid 1980s saw the introduction and acceptance of Phacoemulsification. By then the issues faced with AC IOLs ware widely felt. The concept of IOL implantation in the bag started getting widely recognized. The stage was set for the second generation IOL calculation formulae and the concept of A constant
  • 11. The difficulty of predicting the IOL in the capsular bag due to capsular contraction, vaulting characteristic, etc, set the stage for a host of pioneering work involving constants.
  • 12. Second Generation formulae – Holladay, Prager Chandler et al (1988) Colliac (1990) Olsen ( 1987) Sanders, Retzlaff, and Kraff (1988)
  • 13. The SRK Formulae P= A-2.5L-.9K The original SRK formulae through introduced the concept of A constant, was still a theoretical formulae and the A constant was directly derived from the manufacturer’s lens box
  • 14. Second Generation SRK II Formulae
  • 15. The second generation theoretical formulae were distinct from first generation formulae in the sense that the value for the position of the IOL was not fixed but varies as a function of at most two variables – axial length and corneal curvature.
  • 16. Though the word ELP or Effective Lens Position is comparatively a new term, the concept was recognized now in the form of ACD. Later the ACD was replaced by ELP as a term which suitably describes the lens position in the eye after cataract surgery. ELP – Distance from corneal vertex to principal plane of thin IOL Same as ACD, but avoids confusion with anatomy
  • 17. SRK II formulae Notable among the second generation formulae was the development of the original SRK formulae into SRK II formulae . The SRK II was a regression formulae which attempted to fit a function to the distribution of Axial Length and IOL power through a polynomial regression analysis. This regression analysis was linear for average axial length eyes , it exhibited non linearity in non average eyes
  • 18. Adjustments to the Axial Length through A constants by SRK II formulae. The below table shows the relationship between A constant of SRK and the adjustments done in SRK II
  • 19. However though the SRK II formulae was a vast improvement and predicted fairly accurately the IOL position in the bag for average eyes, yet there were unexpected error in longer and shorter eyes.
  • 20. The reason was that until 1996 it was assumed that a longer eye would have a longer ACD , and a shorter eye would have proportionately shorter ACD. The works of Holladay (1996) showed this was often not to be.
  • 21. Hence a formulae like SRK II that predicts the ELP or the IOL position in the eye as a linear function of axial length only, does not do justice in non average eyes.
  • 22. The SRK T formulae was a further improvement and combined the linear regression method with the theoretical eye model to predict the IOL position correctly even in non average eyes. It is a non linear theoretical optical formula empirically optimized to predict the ELP. It combines the advantages of theoretical and regression formulas The SRK T now took into account the corneal curvature in addition to Axial Length to predict IOL position in non average eyes through alteration of A constant over the SRK II
  • 23. Fourth Generation Formulae like Holladay II takes into account several variables to predict the IOL position ( ELP ) in the eye.  Axial Length  K readings  White to White  ACD  Manifest Refraction  Lens Thickness  Age
  • 24. Fourth generation Olsen formulae – the concept of C constant. A key feature of the Olsen formulae is the C constant which can be regarded as a ratio by which the capsular bag will encapsulate the IOL in the bag. The Olsen formulae takes the c constant as a function of Lens Thickness and ACD.
  • 26. There are largely three IOL constants in use : The SRK T as indicated earlier uses A const The Holladay I formula uses Surgeon Factor or SF The Holladay II and the Hoffer Q formula uses ACD The Haigis uses three constants – A0, A1, A2 d ( ELP ) = a0 + (a1*ACD)+(a2*AL)
  • 27. HAIGIS The a0 constant behaves like the other constants in SRKT, Holladay I, Holladay II, etc. The a1 constant is tied to the measured anterior chamber depth The a2 constant is tied to the measured axial length
  • 28. The Importance of Constant optimization !
  • 29. A CONSTANT & OPTIMIZATION At a glance In an average IOL patient, there would be no difference if you use the IOL Master or Lenstar or an immersion ultrasound device, as long as you use the proper constants – Dr. Haigis
  • 30. CALCULATING IOL POWER ?? Best biometry Best keratometry Best formulae Right A constant Keratometric Index White to White Preoperative Refraction
  • 31. EVEN DOING THINGS RIGHT MAY STILL NOT BE ENOUGH HENCE CONSTANT OPTIMIZATION IS IMPORTANT
  • 32. WHY OPTIMIZE ?? If you have your a constant optimized then the number of patients falling within .5D of target refraction increases four fold.
  • 34. WHY OPTIMIZE ?  No two surgeons’s have the same technique.  Rhexis ??
  • 35. Surgeons NEED to UPDATE biometers; Lens Constant Database !
  • 36. UPDATE Lens Constant Database ! AcrySof® IQ Toric ‘A-Constant’ See USER MANUAL for instruction !
  • 37. IOL DATA OPTIMIZATION • It is strongly recommended to customize and personalize A-constant, ACD, and Surgeon Factor based on their individual biometry techniques. • Data obtained from at least 30 patients should be used. • To successfully customize, refractive surprises should be consistently hyperopic or myopic when compared with predicted values before adjustments are made.