Haigis Constants Optimization

Description

Returns the optimized Haigis constants a0, a1 and a2 for a particular lens model from a series of treatment data (limited to 1500 cases).

Iterativ calculation of the lens constants require much processing power. In fact, for each case more than 42'000 constant configurations get tested. The configuration showing the best outcome is finally provided. The calculation time is approx. 4s for 100 cases.

Background
In comparison to SRK/T, and to improve accuracy for a broader range of eye conditions, the Haigis formula requires anterior chamber depth (ACD) measurement to predict the lens power. The formula uses 3 lens constants (a0, a1 and a2). The a0 constant moves the power prediction curve up, or down (similar to the SRK/T A-constant). The a1 constant is linked to the ACD and the a2 constant to the axial length (AL). Both the a1 and the a2 constants are used to vary the shape of the power prediction curve. All of this gives the Haigis Formula a new level of mathematical flexibility allowing optimisation for a wide range of ALs and ACDs. However, because of 3 independent lens constants the optimization process (regression analysis) is much more complex.

URL

POST https://www.zubisoft.com/api/hconstants_opti

Permission

Standard authentication with public key, hashed private key and user key is required.

Parameters

Requests must contain an array with objects with the following parameters. You can submit keratometrie values in diopter or radius format (only choose one of them).

Name Format Example Comment
axial_length Float 23.82 The optical axial length in mm
k_flat_pre Float 42.08 The flatter meridian (lower K-value) in D
r1 Float 8.02 The flatter meridian (higher R1 value) in mm
k_steep_pre Float 45.25 The steeper meridian (higher K-value) in D
r2 Float 7.46 The steeper meridian (lower R2 value) in mm
iol_se_power Float 20.5 The SE power of the IOL in D
anterior_chamber_depth Float 3.525 The measured depth of the anterior chamber in mm
manifest_sphere_post Float 0.75 The postoperative manifest sphere in D
manifest_cylinder_post Float -0.75 The postoperative manifest cylinder in D. Can be in plus or minus format (diopters)
gate Float 0.5 Optional. Default is 0.5D. The gate desfines the range of refractive error, the difference between predicted SE and postoperative SE. 

"data": [
        {
            "axial_length": 23.88,
            "k_flat_pre": 42.08,
            "k_steep_pre": 45.25,
            "anterior_chamber_depth": 3.12,
            "iol_se_power": 19.5,
            "manifest_sphere_post": -0.25,
            "manifest_cylinder_post": 0.75
        },
        {
            "axial_length": 24.55,
            "r1": 8.02,
            "r2": 7.46,
            "anterior_chamber_depth": 2.99,
            "iol_se_power": 23,
            "manifest_sphere_post": 0.5,
            "manifest_cylinder_post": -1.25
        }
    ],
    "gate": 0.5
}




curl --location --request POST 'https://www.zubisoft.com/api/hconstants_opti' \
--header 'Content-Type: application/json' \
--header 'X-Public-Key: yourPublicKey' \
--header 'X-User-Key: yourUserKey' \
--header 'X-Private-Key: hashOfYourPrivateKey' \
--data-raw '{ "data":
    [
	{
		"axial_length": 25.09,
		"k_flat_pre": 42.45,
		"k_steep_pre": 43.89,
		"anterior_chamber_depth": 3.35,
		"iol_se_power": 17,
		"manifest_sphere_post": -0.75,
		"manifest_cylinder_post": 0.75
	},
	{
		"axial_length": 24.55,
		"k_flat_pre": 42.56,
		"k_steep_pre": 43.27,
		"anterior_chamber_depth": 3.26,
		"iol_se_power": 19.5,
		"manifest_sphere_post": -1,
		"manifest_cylinder_post": 0.25
	},
	{
		"axial_length": 24.43,
		"k_flat_pre": 46.54,
		"k_steep_pre": 46.85,
		"anterior_chamber_depth": 3.18,
		"iol_se_power": 15,
		"manifest_sphere_post": -0.75,
		"manifest_cylinder_post": 0.25
	},
	{
		"axial_length": 22.85,
		"k_flat_pre": 43.49,
		"k_steep_pre": 44.5,
		"anterior_chamber_depth": 2.9,
		"iol_se_power": 24,
		"manifest_sphere_post": -0.75,
		"manifest_cylinder_post": 1
	},
	{
		"axial_length": 24.17,
		"k_flat_pre": 44.74,
		"k_steep_pre": 45.15,
		"anterior_chamber_depth": 3.13,
		"iol_se_power": 17.5,
		"manifest_sphere_post": -0.75,
		"manifest_cylinder_post": 0
	},
	{
		"axial_length": 23.77,
		"k_flat_pre": 43.76,
		"k_steep_pre": 45.09,
		"anterior_chamber_depth": 3.22,
		"iol_se_power": 20.5,
		"manifest_sphere_post": 0,
		"manifest_cylinder_post": 0
	},
	{
		"axial_length": 24.81,
		"k_flat_pre": 41.89,
		"k_steep_pre": 42.02,
		"anterior_chamber_depth": 3.27,
		"iol_se_power": 19.5,
		"manifest_sphere_post": 0,
		"manifest_cylinder_post": 0
	}
],
    "gate": 0.5
}'

Response

The response includes the following values

Name Format Example Comment
a0 Float -1.7 This is the optimized a0 constant.
a1 Float 0.066 This is the optimized a1 constant.
a2 Float 0.28 This is the optimized a2 constant.
percentageInsideGate Integer 72 This is the percentage of cases that are within a certain refractive error (gate). 

{
    "a0": -1.7,
    "a1": 0.066,
    "a2": 0.28,
    "percentageInsideGate": 72
}