Background:For many decades, blood doping has been a hallmark for athletes that manipulate their blood to increase oxygen supply to muscles, so as to gain a competitive advantage,
particularly in endurance sports. This includes the use of homologous (HBT) and autologous blood transfusions (ABT). A robust flow cytometric test for HBT was developed and has been implemented
successfully since the 2004 Athens Olympic Games. Unlike HBT, detection of ABT has been much more challenging. Williams et al (1981) in Med Sci Sports Exerc have investigate the effect the infusion
of 920 ml equivalent of autologous blood would have upon 5-mile time and both local and cardiovascular-respiratory ratings of perceived exertion. They found the infusion of 920 ml equivalent
autologous blood increased performance capacity in an athletic event characterized by high levels of aerobic energy expenditure, but the difference with both local and cardiovascular-respiratory
ratings of perceived exertion was of no value in detecting ABT. The physiological and biochemical data was reanalyzed by introducing golden ratio in this paper.
Methods: The golden ratio, [sqrt(5) -1]/2, about 0.61803, is a natural constant of difference between two numbers. The golden logarithm (GL) was defined as the logarithm to the golden
ratio. The GL of the ratio of two numbers was used to redefined the ratio so that the absolute value of its GL is smaller than 1. For example, the GL of the ratio of red blood cell (RBC) (10(6)) and
hematocrit (Hct) (%) for the pre-saline group after running was 4.62, and 0.61803(4.7) ≈ 0.1042 so that we calculate the GL of the ratio of 0.1024 Hct and RBC.
Results: (1) The GL of the ratio of RBC and hemoglobin (Hbm) (g 100 ml-1) was a constant at about 2.36 for all the groups. (2) The GL of the ratio of 0.1024 Hct and RBC was 0.0767,
0.0948, 0.0491 and 0.153 for pre-saline, post-saline, pre-blood and post-blood after running. (3) The GL of the ratio of 3.173 2,3-diphosphoglycerate (DPG) (umol/ml whole blood) and RBC was 0.167,
0.189, 0.217 and 0.320 for pre-saline, post-saline, pre-blood and post-blood after running. (4) The GL of the ratio of Hct and 3.025Hbm was 0.02814, 0.03498, 0.02257 and 0.08555 for pre-saline,
post-saline, pre-blood and post-blood after running. (5) The GL of the ratio of 10.07 DPG and Hbm was 0.1174, 0.1280, 0.1892 and 0.2387 for pre-saline, post-saline, pre-blood and post-blood after
Conclusions: The GL of 0.1024 Hct and RBC, 3.173DPG and RBC, Hct and 3.025Hbm, 10.07 DPG and Hbm may be used to detect ABT