Calculating Dietary Fat and Carbon Differences

The output-input differences of FA and carbon from FA between milk (output) and dietary digestible intake (input) were calculated based on feed intake, milk yield, and the measured FA composition in diets and milk samples. We assumed that the total tract digestibility of dietary FA was 85% based on the data from INRA [24 ] and previous studies [13 (link), 25 ]. The FA output-input difference was calculated as follows: $$\mathrm{Dietary}\mathrm{digestible}\mathrm{FA}\mathrm{intake}(\mathrm{g}/\mathrm{d})=\mathrm{feed}\mathrm{intake}\left(\mathrm{g},/,\mathrm{d}\right)\times \frac{\mathrm{dietary}\mathrm{individual}\mathrm{FA}\mathrm{content}\left(\%\right)}{100}\times \frac{85}{100}$$ $$\mathrm{FA}\mathrm{in}\mathrm{milk}(\mathrm{g}/\mathrm{d})=\mathrm{milk}\mathrm{yield}\left(\mathrm{g},/,\mathrm{d}\right)\times \frac{\mathrm{milk}\mathrm{individual}\mathrm{FA}\mathrm{content}(\%)}{100}$$ $$\mathrm{FA}\mathrm{output}-\mathrm{input}\mathrm{difference}(\mathrm{g}/\mathrm{d})=\mathrm{FA}\mathrm{in}\mathrm{milk}(\mathrm{g}/\mathrm{d})-\mathrm{dietary}\mathrm{digestible}\mathrm{FA}\mathrm{intake}(\mathrm{g}/\mathrm{d})$$
Similar to the equations for FA difference, the output-input difference for FA-derived carbon between milk and dietary digestible intake was calculated as follows (assuming that digestibility of FA-derived carbon is 85%): $$\mathrm{Carbon}\mathrm{in}\mathrm{dietary}\mathrm{digestible}\mathrm{FA}(\mathrm{g}/\mathrm{d})=\mathrm{feed}\mathrm{intake}(\mathrm{g}/\mathrm{d})\times \frac{\mathrm{dietary}\mathrm{individual}\mathrm{FA}\mathrm{content}\left(\%\right)}{100}\times \frac{12.01(\mathrm{g}/\mathrm{mol})\times \mathrm{carbon}\mathrm{number}\mathrm{in}\mathrm{individual}\mathrm{FA}\mathrm{in}\mathrm{diet}}{\mathrm{molecular}\mathrm{weight}\mathrm{of}\mathrm{individual}\mathrm{FA}(\mathrm{g}/\mathrm{mol})}\times \frac{85}{100}$$ $$\mathrm{Carbon}\mathrm{in}\mathrm{milk}\mathrm{FA}(\mathrm{g}/\mathrm{d})=\mathrm{milk}\mathrm{yield}\left(\mathrm{g},/,\mathrm{d}\right)\times \frac{\mathrm{milk}\mathrm{individual}\mathrm{FA}\mathrm{content}(\%)}{100}\times \frac{12.01(\mathrm{g}/\mathrm{mol})\times \mathrm{carbon}\mathrm{number}\mathrm{in}\mathrm{individual}\mathrm{FA}\mathrm{in}\mathrm{milk}}{\mathrm{molecular}\mathrm{of}\mathrm{individual}\mathrm{FA}(\mathrm{g}/\mathrm{mol})}$$ $$\mathrm{FA}-\mathrm{derived}\mathrm{carbon}\mathrm{output}-\mathrm{input}\mathrm{difference}(\mathrm{g}/\mathrm{d})=\mathrm{carbon}\mathrm{in}\mathrm{milk}\mathrm{FA}(\mathrm{g}/\mathrm{d})-\mathrm{carbon}\mathrm{indietary}\mathrm{digestible}\mathrm{FA}(\mathrm{g}/\mathrm{d})$$
where the molecular weight of carbon is 12.01 g/mol. The total FA and total FA-derived carbon were the sum of individual value.