Does low fat diet give faster fat loss than low carb ?

A recent Poster presentation (ie not fully peer reviewed published science) posed the question

"Is a Calorie a Calorie? Metabolic Fat Balance Following Selective Isocaloric Restriction of Dietary Carbohydrate Vs. Fat in Obese Adults. - Kevin D Hall et al.

and went on to describe a clinical study where about 800 calories of either fat or carbohydrate were removed from the diet of the same group of subjects in a crossover design. So the grams of protein stayed the same, and in the low fat arm the grams of carbohydrate stayed the same with the fat remaining constant in the low carb arm.

This is quite a good design, as it saves protein changes having an effect. It does constrain the low carb arm to a relatively high carbohydrate content (30%) because the caloric reduction takes the fat in the low fat arm down to only 7% or 15 grams a day.

From the limited data in the abstract I have tried to calculate the average intakes :-

	Baseline	Low Carb	Low Fat
Calories/day (kcal)	2720	1930	1920
Carb energy %	50	30	72
Fat energy %	35	49	7
Protein energy %	15	21	21
C grams	340	145	346
F grams	106	105	15
P grams	102	101	101

During the experiment the subjects spent time in a metabolic chamber where gas analysis, temperatures and airflow measurement allows calculation of their metabolic rate and the proportion of their energy supplied by fat and carbohydrate. The authors used this data to calculate the fat loss based entirely on "fat exhaled" rather than traditional weighing and body composition analysis.

After 5 days on the baseline diet the subjects were allocated to either Low Carb or Low Fat for 6 days, then returned after two weeks to repeat the baseline diet and the opposite arm of the calorie reduction. Weight loss was greater on low carb than low fat, 1.9±0.2 vs. 1.3±0.1 kg; p=0.05. That's more than a pound greater in less than 6 days, this is often seen as the initial weight loss of water due to carbohydrate restriction and its diuretic effect.

Despite the greater weight loss on low carb, the authors report that "body fat loss was ~67% greater after 6 days of LF vs. LC (394±40 vs. 236±30 g; p=0.0003)." At 9 cals/g that equates to 591 cals/day on LF and 354 cals/day on LC. To try and understand why, and where the apparent energy imbalance occurs, we need to calculate the oxidation rates ( "burning" ) of carbs and fat. We'll do this by assuming that the food being eaten is oxidised at the same rate and that additional energy is supplied from body reserves :-

Calories expended	2720
Change in cal exp	reported	-72	-81
Extra fat burn cals		426	-53
Extra fat burn grams		47	-6
Fat Oxidation grams	106	153	100
Fat Balance in – out	0	-48	-85
Difference LC – LF		37
Total body fat loss g	reported	236	394
Per day grams	5	47	79
Extra LF vs LC			67%
Calories expended	2720	2648	2639
From fat kcal	952	1378	899
From protein kcal	408	405	403
From carbs kcal	1360	579	1382
Accounted for kcal	2720	2362	2685
Discrepancy kcal	0	286	-46
as fat grams		32
as carbs grams		71

The two diets both saw a small but similar calorie expenditure reduction from baseline of 72 and 81 calories a day. Fat oxidation increased significantly on the low carb diet giving 50% more fat burn but the extra 47 grams/day is less than the 90 grams a day taken out of the low fat diet.

Adding up the oxidised fat, protein and assuming that the carbs eaten were oxidised gives the "Accounted for kcal" row above, as the paper didn't report carbohydrate oxidation rate. There's a shortfall of 286 calories/day in the low carb case as not enough fat is being burned to provide the measured energy output. 

Without access to more data the best explanation I can offer is that the discrepancy was supplied by about 70 grams of carbohydrate oxidation from glycogen reserves - a transient resource that would not have lasted many days at this rate. Had the experiment continued for another week then glycogen would have dropped to a new equilibrium and either fat oxidation would ramp up or some other metabolic adaptation would occur (using less energy).

On the high carb diet the glycogen reserves remain topped up by carbohydrate intake and, perhaps surprisingly, the elevated carb intake and consequent insulin levels doesn't suppress fat release to the point where it can't keep up with energy demand.

The study could perhaps be improved by doing a 2 week run-in on the test diet before the 6 days under closer observation. This would make the observed days more representative of a steady state.