Calculating your path to a better health

in the distance past I wrote about the use of a Generic Body Health index  as replacement of the Body Mass Index in its role as target variable for diet and workout. In the mean time I have been tuning and fitting this concept and have started working on an on-line calculator for helping people setting diet and workout goals. So after the last beta of my calculator I thought it time to revisit the subject in this blog post. In this post I shall try to describe how my calculator can help you to create a path to a better health for yourself by not focusing on weight loss or on getting a six-pack beach body before summer as a goal but by combining different non-intrusive measurements with your strength statistics in a way that accounts for your age and gender and aims for incremental and sustainable progress towards lowering your overall health risks.


Your health is not about your weight. Not your TOTAL body weight anyway. High muscle mass is more healthy than low muscle mass for example and your subcutaneous fat mass might not be helpful in attracting members of whatever sex(es) you are attracted to, we can’t really classify it a risk factor outside of a dating context. Well maybe there are other social risks, but the base line is that there is zero evidence for the hypothesis that subcutaneous fat mass is a serious independent medical risk factor. For you as an individual however, subcutaneous will be strongly correlated to a weight related variable that is very likely to be a risk factor: Visceral Adipose Tissue (VAT). The fat mass in between your organs. Many diets and diet and sport consultants will focus on total weight, expressed commonly bu the Body Mass Index (BMI).  ce9fx35uaamat2z

The BMI in short, is a body length adjusted measure of your TOTAL Body Mass (TBM). Total body weight that includes both the VAT risk factor “AND” the actual protective Lean Body Mass (LBM) that consists of your bones, muscles, organ meat and extracellular water mass. Basically:

  • High VAT is a potential risk factor
  • Low LBM is a potential risk factor
  • SAT in itself is neutral but correlated relatively strongly to your VAT
  • TBM is composed of VAT+SAT+LBM and as a whole quite useless as target variable.
  • BMI is a height corrected measure of TBM and thus useless as a target variable.

If you have a BMI of 40, according to the BMI definition you will be class III obese. As a statistical tool for whole populations, this might be a relatively decent assessment. You as an individual might have a BMI of 40 because you have been doing strong man training six hours a day six days per week for more than a decade with the result that you’ve become a 150 kg mountain of pure muscles who could wrestle a grizzly bear to the ground with one arm behind his back. Your body fat might be as little as 10% of your body weight, but according to the statistics you would be in with the morbidly obese. Given the low percentage of people who actually spent 36 hours a week at the gym lifting the weight equivalent of a small car when  looking at the total population, for an assessment of obesity in whole populations, BMI might indeed be somewhat useful. BMI is completely useless however as a tool in fighting individual obesity or more importantly as a tool for total health risk reduction. If you want to reduce your risks through body composition, then you need to make sure to:

  1. Reduce your VAT
  2. Increase your LBM

So what will be the net result of this for your BMI you may ask. The most direct answer to that question is: ‘it depends’. The more important answer to that question though is: ‘it doesn’t matter, not even a bit!’. Your BMI is irrelevant. it may not be irrelevant as a filter for discovering that you might have a health risk problem, but that is all that it is useful for you as an individual. If you found out your BMI is 35, don’t ignore it, use it as a reason to find out more and if needed take action. Don’t, however think that you need to FIX your BMI, you don’t and if you try to it will only get in the way of sustainability of your progress. The thing that needs fixing is your body composition.

Bio-electrical Impedance Analysis

biaIf you have been reading my blog before, you might know that I’m a real big fan of BIA scales.  Bio-electrical Impedance Analysis uses a small electrical current at different frequencies to measure the frequency-dependent impedance of different paths through your body and then uses the acquired data to estimate your body composition. There are different types of BIA scales of varying accuracy and consistency. You should not buy a consumer grade BIA scale for home usage. You will likely end up paying up to hundreds of euros for equipment with relatively inaccurate, but more importantly often inconsistent results. A better strategy is to seek out a gym that has a professional grade BIA scale, or if you are seeing a doctor or dietitian on a regular basis who has one, discuss using the one at their office with them while you are discussing your health goals. A BIA scale worth its weight will give you multiple useful numbers about your body composition. Some a bit more granular than others ans some more accurate than others.

  • Total Body Mass (TBM or weight)
  • Lean Body Mass (LBM)
  • Total Fat Mass (TFM or TAT)
  • Body Fat Percentage (BFP)
  • Visceral Fat Mass or percentage (VAT)
  • Total Protein Mass (TPM)
  • Total Water Mass
  • InterCellular Water (ICW)
  • ExtraCellular Water (ECW)

It is good to keep track of all of these and keep them neatly in a spreadsheet or journal. We shall be using TBM and BFP in our calculator while keeping an eye on VAT and TPM. VAT and TPM would actually be better measures if we were looking at it from a static risk point of view. The problem though is that due to the smaller numbers involved, the limitations in the accuracy and consistency of the measurements of these variables, these variables are difficult to use effectively in a control feedback setting needed for controlled semi-critically dampened progress. We, however do need to stay on top of these variables. protein mass going down or visceral fat mass going up more than can be accredited to measurement inaccuracy are a sign that something may be going wrong.

Alternatively: skinfold and waist circumference

If for some reason you can’t regularly make use of a BIA-scale to track your body composition, there are a few poor man alternatives to consider. The first one is the use of skinfold measurements. You can use a simple caliper to measure your skinfolds in a number of locations. I won’t go into this too deeply, but this site has a nice explanation and calculator you may use. It is important to note that while both BIA and skinfold have similar accuracy issues, the correlation between the skinfold technique measured BFP and the actual VAT is smaller than that between BIA-measured BFP and VAT. It thus becomes even more important to track something close to VAT apart from BFP. A decent way to do this without BIA is by measuring your waist circumference and your total body mass and then using them to calculate your conicity index (CI).


Consider your CI the equivalent of your protein mass and visceral fat mass measurements. If it goes up you are doing something terribly wrong. It is an important safeguard that is useful even if you are applying BIA measurements, but it is indispensable when  you are resorting to skin-fold BFP measurements.

An age and gender adjusted Body Fat Index (BFI)

What constitutes a healthy level of body fat differs depending on your age and gender.


The formula is simple. If you are a female, use zero for GENDER, if you are a male use one. Fill out your age gender and body fat percentage. The result will be a number that will go down all the way to zero if you are approaching under-fat. An obese person will probably have a BFI in the 3..5 range. Our ultimate goal would be to move the value of our BFI as close to zero as we can get it, but also considering and balancing against an other bodycompositional factor.

Lifting weights

While BFI is a good measure of individual obesity, we know low LBM also can be a possible risk factor. In order to keep this risk factor down we want to increase or at least sustain our lean body mass. While our protein mass is a good static indication of this risk factor, like VAT there are issues with accuracy, consistency and responsiveness of this variable. If we use body strength as a proxy we not only measure LBM improvement, we also get quick feedback when our diet or workout goes all wrong. If your body strength drops quickly as a result of diet that will be a real big sign that something is terribly wrong. Thus lifting weight has two goals. Measuring our body strength as indication of our LBM related health and making sure our low-LBM risk is reduced.

An age and gender adjusted Body Strength Index (BFI)

Just as with body fat, we can use body strength in an index that ideally should move to zero. Just as with the BFI, we define zero as a hard to achieve but still potentially reachable level.

We are less interested in your absolute strength than we are in your relative strength, relative to your body weight. As we care more about body composition than weight, we will see two possible paths to increasing relative strength. You can gain relative strength by getting bigger and stronger muscles and lifting bigger weights or you can gain relative strength by managing to maintain your strength and muscle mass while losing body fat. For some people, the first comes more natural and for others the second.  We define our relative strength as the sum of our three rap maximum for the big three strength exercises: deadlift, squat and bench press.


The reason that we choose three rep max rather than one rep max is that training with a three rep max is more likely to improve your lean body mass figures than a one rep max approach.

The first thing to realise is that starting at middle age, you will have to adjust your goals if you want to keep them realistically. After having looked through multiple sources, the following correction factor appears to be a decent fit for 39 to 65 year old people. :


Given that the correction factor only applies to middle aged people and younger and seniors, we define:


Or for those who prefer computer programming notation, we can write the same as:


We now define the top achievable strength for a given age and gender as:


So with this top strength metric we can finally determine our Body Strength Index (BSI)


The Body Health vector

Now about using our new BSI and BFI. Consider we put BSI on the X axis and BFI on the Y axis and define our Body health vector as a point on this graph. Ideally, BFI will be low ass will BSI but chances are one or both aren’t as low as we would like them and we need to look for a good path for our BHI vector to gradually move closer to the origin. We propose that the best and ideal route from any starting point balances the goal of reducing both components with the idea that balancing out the two risk factors is important. Realizing that many people will have to work with at most high-school level mathematics, we choose to use a circle fragment as ideal path through body health space.  There is no reason to make it any more complex than that. We want our vector to move over time from its current position to the origin, where the ideal angle for reaching the origin would be 45 degrees.  So we start by looking for a circle that fits the bill. A bit of simple geometry gives us a formula for first finding the radius of our circle:


And with this radius, we look at finding the center of our circle.


The path of 5% decrements milestones

With the center of the circle we just found ,we can look at plotting a first step to progress. A first major milestone. As progress will become harder as we come closer to the origin, we go for relative incremental milestones. A good target for such is a 5% target. Let us look at how we calculate this 5% target. It is important to realize that the center of our circle can either be in the second or the fourth quadrant depending on if BSI is bigger than BFI or if BFI is bigger than BSI.  When we look at the angle for the origin as viewed from the circle, we get:


Now for the angle of our BHI vector. Depending on the quadrant of the circle center that angle will be one of:


for fourth quadrant circle centers or


for circle centers in the second quadrant. Now with those two angles we can easily determine the angle for our next milestone:

phit That in turn gives us the milestone target for BSI and BFI



Now I hear many of you thinking, I know it’s easy high school level math, and it is not hard to understand, but it’s quite a bit of work when compared to the good old BMI formula, and you would be right. For that reason, I’ve created a simple web-based calculator for you. The web page looks a bit archaic, I know. I am not a web designer so I don’t even try. Give the calculator a spin and see for yourself what suggestions it makes using the above algorithm.

Important: I’m not a doctor and neither is my calculator!

As many of you will know or will have guessed from the above, I’ m neither a doctor not a nutritionist but my calculator above will give you very specific advice for health targets. While I feel strongly that the advice is the result of good engineering, there might be reasons why for some people the advice might go against an individual’s medical best interest. Discuss usage of this tool with your GP or dietitian, especially if you suffer from medical issues, and if using control feedback loops build using this tool yield very high or very low levels of specific foods or nutrients, discuss those with your GP or nutritionist as well. In that sense, it should not be seen any different from BMI except for the fact that this BHI approach, when practiced under professional and qualified supervision should yield better and more sustainable results than those that could potentially flow from the usage of BMI as intervention target.

Measure what goes into your cabinet/fridge/bin, deduse what goes into your mouth.

So far we only discussed our target variables and target milestones. What we did not address was our input variables such as workout timing, length, exercises, macro split, meal timing, micro nutrients, etc. While we will discuss these and I have discussed these in other posts, one thing is important to note. It is notoriously hard to keep track of your food and drink intake when you try to keep up with what goes into your mouth. A simple solution for this is to simply not do that, at least not in the early stages of your efforts. Start off by only making note of everything you buy. Keep your reseeds and keep track of spoiled items you throw away. That is, keep track of what goes into your fridge and what disappears into the bin. The difference will mostly be what went into your mouth or that of the people living with you. Surprisingly, even with a household with many family members, a fridge-bin estimate is likely to be more accurate than any attempt to keep up with what actually goes into your mouth.

The error vector and (under-)critical dampening

I’ll close this post with lifting a tip of a subject for an other day. The result of the calculator is a 5% milestone, but chances are you will miss that target. You might undershoot or overshoot your BFI target while reaching your BSI target or vice versa. What you do then is that you take the two vectors, one from your old BHI to your target BHI and one from your old BHI to the BHI you achieved, and you look at the angle between the two. This angle is your error signal, and your task in designing a personalized control feedback for your diet and workout is to find the proper variables for translating these errors into effective feedback. Don’t worry if you don’t understand this last part. You can use the target milestone even without understanding control feedback theory. The result will not quickly move towards something close to critical dampening, but that is OK for a beginning, as long as you are making progress.

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