A novel spreadsheet method for calculating the free testosterone, free DHT, and free estradiol.

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Nelson Vergel

Founder, ExcelMale.com

Abstract​

In humans, testosterone (T), dihydrotestosterone (DHT), estradiol (E2), estrone (E1) and cortisol (C) bind to the serum proteins sex hormone-binding globulin (SHBG), albumin (Alb) and corticosteroid-binding globulin (CBG). Equilibrium dialysis is considered to be the "gold standard" for measuring the free concentrations of these steroids but is technically difficult and not widely available. Based on a mathematical model of the 5-ligand/3-protein binding equilibria, we developed a novel spreadsheet method for calculating the free and bioavailable (free+Alb-bound) concentrations of each steroid in terms of the total steroid and protein concentrations. The model uses 15 association constants K(SHBG-X), K(Alb-X), and K(CBG-X) (X=T, DHT, E2, E1 and C) that have been estimated from a systematic review of published binding studies. The computation of the free and bioavailable concentrations uses an iterative numerical method that can be readily programmed on a spreadsheet. The method is illustrated with six examples corresponding to young men (YM), old men (OM), obese men (Ob M), young women (YM), pregnant women in the 3rd trimester (Preg T3) and oophorectomized women on oral conjugated equine estrogens (CEE). The resulting free hormone concentrations for YM and YW fall within the normal references ranges obtained by equilibrium dialysis for all five hormones. The model also accounts for the competitive binding effects of high estrogen levels on the free T levels in Preg T3. This novel spreadsheet method provides a "user-friendly" approach for estimating the free concentrations of circulating sex hormones and cortisol in men and women.



Spreadsheet attached

I need help from a fellow engineer. @readalot ?
 

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  • calculation of free estradiol testosterone.xls
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Abstract​

In humans, testosterone (T), dihydrotestosterone (DHT), estradiol (E2), estrone (E1) and cortisol (C) bind to the serum proteins sex hormone-binding globulin (SHBG), albumin (Alb) and corticosteroid-binding globulin (CBG). Equilibrium dialysis is considered to be the "gold standard" for measuring the free concentrations of these steroids but is technically difficult and not widely available. Based on a mathematical model of the 5-ligand/3-protein binding equilibria, we developed a novel spreadsheet method for calculating the free and bioavailable (free+Alb-bound) concentrations of each steroid in terms of the total steroid and protein concentrations. The model uses 15 association constants K(SHBG-X), K(Alb-X), and K(CBG-X) (X=T, DHT, E2, E1 and C) that have been estimated from a systematic review of published binding studies. The computation of the free and bioavailable concentrations uses an iterative numerical method that can be readily programmed on a spreadsheet. The method is illustrated with six examples corresponding to young men (YM), old men (OM), obese men (Ob M), young women (YM), pregnant women in the 3rd trimester (Preg T3) and oophorectomized women on oral conjugated equine estrogens (CEE). The resulting free hormone concentrations for YM and YW fall within the normal references ranges obtained by equilibrium dialysis for all five hormones. The model also accounts for the competitive binding effects of high estrogen levels on the free T levels in Preg T3. This novel spreadsheet method provides a "user-friendly" approach for estimating the free concentrations of circulating sex hormones and cortisol in men and women.



Spreadsheet attached

I need help from a fellow engineer. @readalot ?
Thanks @Nelson Vergel. I remember "playing" with this spreadsheet a couple years back. Nice tool to have on your desktop.

Gets into details behind cfTV and cfTz and assumptions with binding sites, etc. As I've gone back and forth with @madman, it's unclear which model best fits the yet to be determined harmonized fT data. Reviewing the literature indicates two camps where some data agrees cfTV better and some fits cfTz

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Cataceous

Super Moderator

In this thread it was found that when using @Gman86's prodigious lab data, calculated free estradiol values agreed well with measured values when the standard estradiol test was used, but not when the sensitive test was used. The agreement almost seems too good to be true, as if the lab results were calculated by the same method.
 

Nelson Vergel

Founder, ExcelMale.com
What formula would you use with standard estradiol to calculate free estradiol ? Use albumin and SHBG as you do for free T?
 

Cataceous

Super Moderator
What formula would you use with standard estradiol to calculate free estradiol ? Use albumin and SHBG as you do for free T?
You use the same spreadsheet, entering at least testosterone, estradiol and SHBG. Presumably there's less sensitivity to the other parameters, such as DHT and cortisol, so using the default values doesn't create large errors.

Here's @Simon7's entire comparison post from that thread:
I used Gman86's values which he posted above to compare his Free E2 measurement vs. the calculated Free E2 by the spreadsheet.

For all of Gman86's tests except for the first one he provided values for both sensitive E2 and NON sensitive E2, so I calculated Free E2 twice for each of test based on the sensitive + NON sensitive E2 result.

Here are the results:

View attachment 6508


Analysis:

1. Twelve out of the thirteen results of calculated Free E2 (with the exception of the result with the 78% difference) provided close approximation of measured Free E2 for the evaluation of where the Free E2 result lies on on the normal range of [0.2.....1.5] - which is the evaluation used to decide on future treatment dosage

2. The difference between the measured and calculated Free E2 result was much smaller (average difference of only 5.8%) when the calculation was based on the NON sensitive E2 result (vs. average difference of 30.5% when based on sensitive E2 results). One possible explanation for this is that perhaps the Free E2 test used was a NON sensitive test as well. Gman86 can you provide a link to the lab Free E2 test code that you used?
 
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