Total Ketogenic Ratio (TKR)

The degree of ketosis produced by a particular diet has been long determined by the Ketogenic Ratio (KR), proposed by Woodyatt (1):

KR = K / AK

where, K represents the ketogenic factors and AK represents the anti-ketogenic factors. 

Experimentally determined values for each dietary component are expressed by the equation:

Where:

f = dietary fats in grams
p = dietary protein in grams
c = dietary carbohydrate in grams

Another easier way to determine the KR was proposed by Metcalf and Moriarty:

KR = f / p + c

The formula doesn't take into account the antiketogenic properties of some amino acids but gives an approximate result to the Woodyat equation. 

A paper published by I.A. Cohen (2) adressed the issue brought by these equations: they only apply to isocaloric conditions because they fail to take into account the utilization of energy stores in a hypocaloric diet, underestimating the degree of ketosis of a given diet. The Woodyatt equation then is referred as the Dietary Ketogenic Ratio (DKR), representing the effect of the dietary components on ketosis. 

The formula proposed by Cohen tries to model the impact of weight reduction dieting under ideal conditions, that is, the utilization of stored lipid without the catabolism of protein, scenario normally reached after a few days of fasting and/or low carbohydrate-high fat dieting. 

The Cohen formula is derived from the Woodyatt equation, in a series of simple, mathematical steps giving the new equation:

Where

e = total energy expenditure in calories
p = dietary protein in grams
c = dietary carbohydrate in grams

There are some limitations of this equation, as stated by the author:


1. It needs further evaluation for proving the hypothesis.
2. It describes an ideal situation in which any energy deficit is met entirely by stored lipids. 
3. Dietary energy established by bomb calorimetry may exceed from the energy obtainable by the organism consuming that diet.
4. Energy efficiencies brought about by dieting, as well as changes in the use of dietary nutrients for non-energy uses may alter the expected outcome. For instance, subjects who have not utilized particular metabolic pathways for an extended period may show changes in energy utilization over time.
5. Urinary loss of ketones is not accounted for in these formulae.
6. The nutrient mix itself, as well as the state of the organism may influence the ability to fully utilize the energy available in the consumed nutrients.
7. There is inter-individual variability for achieving the same degree of ketosis. Genetic factors and differences in intestinal flora may alter this parameter.
8. Woodyatt analysis of the ketogenic and anti-ketogenic properties of protein depends upon the proportions of specific amino acids, raising the possibility of differing properties depending upon protein sources. This may necessitate having to alter Woodyatt's constants depending upon protein mix.
9. Differences on both the absorption and utilization of fats resulting from the types of fat included in the diet might alter the response, ie. saturated vs. unsaturated, polyunsaturated vs. monounsaturated, inclusion of MCT or the presence of abnormalities in individual gall bladder functioning.
10. The antiketogenic effects of carbohydrates in food might be altered by the rapidity of their conversion to glucose, as expressed in their glycemic index. The timing of meals may alter the results, particularly if individual feedings varied greatly in their ketogenic to anti-ketogenic properties. For example, meals that contained an isolated bolus of carbohydrate might be expected to rapidly decrease ketosis, even when the total amount of carbohydrate would not be expected to do so when evaluated over a 24-h period. 
11. Ketosis is but one factor among many in weight-loss dieting. The behaviour of any particular factor, by itself, should not imply suitability nor superiority. 


Let's see some examples. 


Asume that an hypocaloric diet consisting of 100g of protein, 70g of fat and 20g of carbohydrate, for an energy expenditure of 2000kcal:


KR (Woodyatt) = 1.28
TKR (Cohen) = 2.09

The energy supplied by the diet in this example is 1110 kcal, which creates a 900kcal deficit. This additional fat increases the production of ketones, not accounted by the Woodyatt equation.

If we up the protein intake to 150g while maintaining calories, we get:

KR (Woodyatt) = 1.00

TKR (Cohen) = 1.65

So even if we consider a PSMF (Protein Sparing Modified Fast) type diet, 200g of protein with 20g of fat and 20g of carbohydrate, we get:

KR (Woodyatt) = 0.79

TKR (Cohen) = 1.37


While the Woodyatt formula might underestimate the level of ketosis, it is probable that the Cohen formula overestimates it, specially in obese and overweight subjects. 

Cohen IA (2009). A model for determining total ketogenic ratio (TKR) for evaluating the ketogenic property of a weight-reduction diet. Medical hypotheses, 73 (3), 377-81 PMID: 19410378