PAUL B. HAMILTON,1 REGINALD M. ARCHIBALD, JOHN …

1 CALCULATION OF HEMOGLOBIN FROM BLOOD SPECIFIC. GRAVITIES. BY DONALD D. VAN SLYKE,* ROBERT A. PHILLIPS,t VINCENT P. DOLE, PAUL B. hamilton , 1 reginald m . archibald , AND JOHN PLAZIN*. (From the Hospital of The Rockefeller Institute for Medical Research, New York). (Received for publication, July 18, 1949). The specific gravity of the red blood cells (normally about ) so greatly exceeds that of plasma that the difference between the gravities of whole blood and plasma can serve as a measure of the cell content of the blood. By assuming a constant hemoglobin concentration in the cells, one can estimate also the blood hemoglobin concentration from the Downloaded from by guest on February 1, 2019. gravity values. The calculation is based on two assumed constants; viz., the specific gravity of the red cells and the hemoglobin concentration of the red cells.

2 Neither of these values is in fact constant. In some abnormal types of blood cells, hemoglobin concentration may fall 20 per cent below normal, with cell specific gravity showing a parallel decrease. However, changes in cell hemoglobin concentration and cell specific gravity parallel each other in such a way that their variations almost cancel each other in their effect on the relation of blood hemoglobin concentration to the concentra- tion calculated from the gravities of whole blood and plasma. In conse- quence the error, even in grossly abnormal blood, is estimated to be only about gm. of hemoglobin per 100 ml. of blood greater than the error attributable to the limit of accuracy of the gravity method used. Ashworth and Tigertt (1) first formulated the equation for calculating blood hemoglobin concentration from the specific gravities of whole blood and plasma.

3 The present paper reports tests of the accuracy of gravity- calculated hemoglobin concentrations by comparison with hemoglobin values determined by precise gasometric methods in normal and abnormal human blood. The gravity determinations have been made by the copper sulfate method (2). A nomogram (Fig. 1) is presented for rapid calcula- tion of hemoglobin from the whole blood and plasma gravities. of Equations for Hemoglobin Calculation Let Ds, DC, and Do be the densities (D:) of whole blood, plasma, and red cells, respectively. Let G,, Gp, and Gc be the corresponding specific * Present address, Brookhaven National Laboratory, Upton, New York. t Present address, United States Naval Medical Research Unit No. 3, care of the American Embassy, Cairo, Egypt. $ Present address, Alfred I. du Pout Institute, Wilmington, Delaware.

4 349. 350 HEMOGLOBIN FBOM BLOOD SPECIFIC GRAVITIES. Line chapt forwalculating plasma proteins, hemoglobin and hematocpit from gravities of plasma and blood Hemoglobin HematocFit 34. ( ). W) ( 5. L. - - - 36. 37. 38. 39. 32 - 41. 5 15. - 42. 31 6 - 43. 20. ! 1 - 44. Downloaded from by guest on February 1, 2019. - 45. 0. \ 25 - 46. 23. L;- 62. 63. 64. - 65. - 66. - 67. 2&65 : ii 23 i - 71. 70 I 72. 73. - 74. - 75. gravities in terms of 0:. Let Vc be the volume of red cells in 1 volume of blood. Let HbB be the gm. of hemoglobin in 100 ml. of blood, and Hbc the hemoglobin in 100 ml. of red cells. The weight in gm. of 1 ml. of VAN SLYKE, PHILLIPS, DOLE, hamilton , archibald , 351. AND PLAZIN. blood, which is the density, is the weight of the plasma plus the weight of the cells in 1 ml. of blood.

5 (1) DB = DcVC+DPO - vc). Since Ge, Gc, and Gp all are the corresponding D values multiplied by the same factor ( when t = 25') the gravity (DE) values may be sub- stituted for densities 0: in all terms of Equation 1. (2) GB = GcVc + CPU - vc). whence v = GB - GP. Downloaded from by guest on February 1, 2019. (3) C- Gc - GP. Blood Hb concentration is cell volume X cell Hb concentration. GB - GP. HbB=HbcVc=HbcX - Gc - GP. Constants must be substituted for Hbc and Gc. Hbc is calculated as Hba/Vs with Hb, determined by chemical analysis and Vc by hematocrit under standard conditions. Gc is calculated by rearrangement of Equa- tion 2. GB - GP. (5) Gc = GP + _____. VC. The V, for Equation 5 is determined by hematocrit. From data given in the experimental part, Hbc for normal human blood cells is taken as gm.

6 Per 100 ml., and the corresponding Gc as We have taken these as the constants. Substituting them for Hbc and Gc in Equation 4 gives GB - GP. 03 HbI, = X _ G. P. Cause of Relative Non-Ej'ect of Cell Abnormalities on Calculation of Hemoglobin by Equation 6. As mentioned above, in blood with cells of abnormally low density deviations of Hbc from and of Gc from parallel each other in such a manner that the changes nearly cancel each other, numerator and denominator of the fraction ( (G, - GP))/( - GP) being changed in nearly the same proportion by parallel deviations of the two constants. In the hypochromic bloods of Table II, in fact, the correlation between abnormally low Gc and the error in gravity-calculated Hb, is so slight that 352 HEbfOGLOBIN FROW BLOOD SPECIFIC GRAVITIES. it is not statistically definite, although in several bloods Gc is below and Hbc below 29 gm.

7 Per 100 ml. TABLE I. Data from Twenty Normal Men Directly measured Calculated Hemat- Whole blood writ, HbO, Subject No. G:~*T&ole CP, centn- blood [b from GB and GP. plasma fuged Hp gravity gravity cf@Er BY D eviation C apacity Elquatior 1 from blood 6 HbOe - / I p. gcr Dz: D;; ml. 1. %E 100 ml. Downloaded from by guest on February 1, 2019. E 2: +o. 10. 625 262 1018 618 265 985 + 605 277 955 615 287 970 + 6 602 275 971 + 7 592 265 946 8 585 263 960 9 595 270 949 + 10 597 285 949 11 590, 265 971 12 5881 263 9501 + 13 595! 277 939' + 14 582 267 15 588 265 + 16 587 277 966 + 17 582 273 976 + 18 568 250 968 19 570 257 952 20 577 267 956 + -____- - -- _. Mean from mean Z t1 .oo 3 Maximum + devia- + tion from HbOz i Maximum minus deviation from HbOz - Estimation of Hemoglobin from Spetifi Gravity of Whole Blood Alone In blood with plasma gravities within the normal range f (Table I) one can, without much increase in error, estimate Hb, from Gs VAN SLYKE, PHILLIPS, DOLE, hamilton , archibald , 353.]

8 AND PLAZIN. TABLE II. Data from Women Rejected As Blood Donors, Apparently Healthy But with Subnormab Hemoglobin Directly measured T calculated Hemat. omit, T. I- Whole blood Subject No. bzid p%L Yiz- pecific specific ravity gravity pegOC BY DWir- g- tion blodd from 6 HbCO. -____ -~ -- ID:: 0;: ml. 0:: mm. E c: Et? 100 ml. 100 ml. Downloaded from by guest on February 1, 2019..0525 .0932 510 265 917 + 506 275 891 503 255 925 + 508 275 895 6 528 265 944 $ 7 528 275 908 8 542 290 880 9 480 260 869 + 10 504 270 838 11 500 245 940 + 12 545 270 933 + 13 522 260 869 14 520 255 944 $ 15 508 250 920 16 524 275 904 17 500 265 889 + --- -- Mean .0515 .0906 + from mean Maximum + deviation + from HbCO. Maximum minus devi- ation from HbCO. - alone, assuming that the plasma has the mean normal gravity, GP =.

9 Equation 6 then simplifies to (7) Hbr, = 480(GB - ). The maximal error in such bloods, introduced by a deviation of from the assumed Gp of , is about ~ gm. of Hb per 100 ml. of blood, or 3 per cent of normal Hbe. The data in Table IV indicate that 354 HEMOGLOBIN FROM BLOOD SPECIFIC GRAVITIES. the observed error is of this order in normal bloods, and in simple anemia, due to iron deficit or blood loss, of the type of the blood donors in Table II. When varied pathological conditions wide fluctuations in plasma protein concentration and Gp, however (last column, Table IV), greater errors can arise in Hb, estimations made from Gs alone. Each gm. per 100 ml. of plasma by which the plasma proteins deviate above or below gm. per 100 ml. causes a plus error in the same direction of about gm.

10 Per 100 ml. of blood in the hemoglobin estimated by Equation 7. The latter can be used to follow hemoglobin changes in subjects that have been found to have plasma gravities within the range to , and such use permits following Hb changes with finger blood. The extent of error that could arise, however, from undetected abnormality in plasma Downloaded from by guest on February 1, 2019. gravity is shown by a case with gm. of plasma protein per 100 ml. reported by Atchley, Bacon, Curran, and David (3), in which the Hb, calculated by Equation 7 was gm. per 100 ml. of blood too high. Forty-nine other cases reported by Atchley et al. (3) from a general medical ward showed a distribution of error (estimated as the deviation of Hbs by Equation 7 from Hbe by Equation 6) similar to that of the last column of Table IV, 94 per cent of the cases showing an error of less than gm.