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Abstract/summary:

Alpins Performing Vector Analyses,
Vector Analysis of Astigmatism - includes examples in ablative and incisional procedures
There will be a lot of interest in these presentations that you are providing, particularly with people wanting to perform their own vector analyses on their own data. Let’s discuss the analysis of different procedures using the Alpins Method.
I think it is a good idea for people to take it up themselves because it gives them a deeper understanding of it. So to give you an overview of it, you need to calculate three principle vectors, the SIA, TIA and the Difference Vector. So looking at the TIA first. That is actually the treatment – Target induced astigmatism vector. The astigmatic treatment is either what numbers you put into the laser, the numbers you put into your nomogram for incisional surgery or the astigmatic power of a Toric implant at the corneal plane. That gives you a magnitude and an orientation which is your TIA. Your SIA is the astigmatic change measured by any device. It has to be the same device post-operatively versus pre-operative. So it is cornea versus cornea, it’s refractive versus refractive or it’s hybrid which is for a Toric analysis comparing postop refractive cylinder to corneal astigmatism. So that’s important to use a refractive analysis or a corneal analysis and I think it is effective to use both because the corneal analysis is based on objective values, whereas refractive analysis is more subjective.
So you will find the two analyses are parallel but a little bit different and often the answer lies somewhere in between the two.
And what does the Difference Vector tells us?
So the Difference Vector is the third one. The difference vector is what is left over in the astigmatism, what you have missed your target by. the difference vector is a very objective means of measuring how much astigmatism is left over in absolute terms. But if you want to relate it to the difficulty of the treatment then the difference vector divided by the TIA gives you a relative measure of success known as the Index of Success so that you if you have got a big astigmatic treatment versus a small treatment but the same leftover then obviously the big treatment is more accurate.
So if you have no astigmatism remaining postoperatively then the Difference Vector and the Index of Success are both zero.
When analysing hundreds or even thousands of cases how is the mean of the various parameters calculated in the Alpins Method?
So when you look at a lot of vectors you can do a mean magnitude. But if you want to bring the axis into the equation you want to do a summated vector mean. Also, some people call this a centroid. So the summated vector mean is when you do a head to tail summation of many vectors and you take the end point of the last to the starting point of the first and you divide it by the number of components which gives you the overall effect of any number of treatments. So the summated vector mean is a very useful number when determining trends, especially when you compare it to the original mean magnitude because if the trend is random you are going to have a very small ratio. If the trend is strong you are going to have a larger number closer to one.