Determination of Different Biological Factors on the Base of Dried Blood Spot Technology

Determination of Differen t Biologi ca l F actors on the Base of Dried Blo o d Sp ot T ec hnology V. K. Bozhenk o , A. O. Iv anov , A. S. Mishc henk o, A. A. T uz hilin, A. M. Shishkin No vem b er 22, 2 021 1 In tro duction Determination of different bio logical facto r s on the base of dr ied blo o d sp ot techn ology has a great practical importance in inv es tigation of bac k lands po p- ulations, in epidemiological studies or in sp ecial p eople contingen ts monitoring, see [1], [2 ]. This tec hnolog y presumes that blo o d sampling is p erformed by pa - tien t himself, the sample is sp otted on a dry , as a rule, p or ous sur face (filter pap er, cellulo se acetate mem brane, etc.), and the p oster ior trans p o r tation to a lab orator y , for exa mple, by p ost in a standa r d or a sp ecial env elop e. Mo dern diagnostic equipment gives an o ppo rtunity to inv estiga te many char- acteristics of dried blo o d spo t, such as metab olites (see [3], [4], [5], [6], and [7]), hormones (s e e [8], [9], [10]), g ly cated hemo globin (see [1 1]), and even some imm une system parameter s (see [12 ]). The po ssibility o f DNA and RNA in- vestigations in such samples is of gre a t impo rtance, s inc e it gives, for example, an opp ortunity for mass inv estiga tions of so cially imp ortant infections such as AIDS, hepatitis, etc. In 1992, in USA a lab ora tory standar d for dried blo o d s po t testing (DBS) was elabora ted, see [1 3]. In 2001, in Russia , Application Instruction o n Alcor Bio Ltd Reagent Kit for imm uno-enzymatic determina tio n o f thyrotropic hor mo ne in dried blo o d sp ot of newb or n was approved. Under the dried blo o d sp ot technology using, the problem of the sample sp otted v olume determination remains o ne of the main pra ctical q uestions. The existing versions of the technology may assume sp otting o f a k nown blo o d vol- ume by means of some dosing device a nd a p osterio r elution, or using of s p ecia l filtering device for the pla sma separatio n under dried spot prepara tion, see [14]. But ther e are no any universal metho d c alculating the volume of the blo o d sp ot, which do es not use a dosing dev ice. The so lutio n of this problem gives an opp ortunity to increase essentially the accurac y of the results and to s implify t he blo o d sampling pro cedure. There is a series of a rticles, where the calculations are based on the co ncent ration of s o me electr o lyte and on a cor r ection of the plasma volume by the hemato crit v alue, s ee [16 ]. In the present work we try to elab orate a universal technology for the sp otted volume calculations. 1 The solution of this pro blem is a ls o important for s uch branc he s of Medicine as Ca tastrophe Medicine a nd F orensic Lab or atory , where non-standar d situa- tions ar e typical, a nd, for exa mple, there is no opp ortunity to sample patient ’s blo o d, and so it is necessar y to use the remains of the patient’s blo od on some other o b jects, instead of the sta nda rd blo o d sample. Such a situation can app ear under inv estiga tions o f the victims to traffic acc iden ts, or other catastrophes . It is w ell-known that distinct bio logical indices (analytes) hav e distinct v ari- ability , see [15]. W e tr y to use some mathematical algo rithms to pick o ut a set of blo o d parameters which give an opp or tunit y to retrieve the initial volume of the blo o d sp otted, and use it to calculate exact conc e ntrations of analy ts int eresting to a physician. F or our analysis w e used the database of biochemical blo o d para meters obtained in Russian Scientific Center of Ro entgen-Radiology during 199 5–200 0, whic h includes more than 3000 0 of pa tients. 2 Mathematical Mo del Let us descr ibe the ma thematical mo del o f the pro blem. Let x i , 1 ≤ i ≤ m , stand for the v alue of the result of the lab or atory analys is on the i th mo lecular comp ound co nt ent. The v alue x i obtained as a r esult of the blo o d sample analysis dep ends on tw o following par ameters at least: the patient p which is selected from so me collectio n ¶ , and the volume λ of the blo o d s ample under the analys is. Thus, the v alue x i is a function of tw o par ameters: x i = x i ( p, λ ) . The problem is to find a function f ( y 1 , y 2 , . . . , y m ) whose v alue f  x 1 ( p, λ ) , x 2 ( p, λ ) , . . . , x m ( p, λ )  is close to λ from the s tatistical p oint o f vie w. Notice that due to the uniform distribution of the molecules under co ns ider- ation in the blo o d, a k -m ultiple ex tension of the volume must lead to the same increasing of all the indices x i . In other words, we hav e x i ( p, k λ ) = k x i ( p, λ ). Therefore, if f approximates the bloo d v olume, then t he follo wing relation m ust be v alid: f  x 1 ( p, k λ ) , . . . , x m ( p, k λ )  = f  k x 1 ( p, λ ) , . . . , k x m ( p, λ )  ≈ ≈ k f  x 1 ( p, λ ) , . . . , x m ( p, λ )  . This notice is a natura l mo tiv ation to lo ok for the function f in the class of po sitively homog eneous functions of degr e e 1, i.e., we a ssume that the equality f ( k y 1 , k y 2 , . . . , k y m ) = k f ( y 1 , y 2 , . . . , y m ) holds for ea ch p os itive k . Suc h functions are uniquely de fined by their v alues at the unit spher e S m − 1 defined by the equation y 2 1 + · · · + y 2 m = 1. By g we denote the res tr iction of the function f onto this unit sphere. 2 Polynomials for m the simplest but rich cla ss of functions. Let us lo ok for g among the functions which ar e the restrictions o f the po lynomials onto S m − 1 . Our statistical exp eriments show that it is enough to cons ider the p olynomia ls of degree t w o v anishing at the origin. In other words, w e put ρ = p y 2 1 + · · · + y 2 m , and lo ok for g in the fo rm X i α i y i ρ + X i ≤ j α ij y i ρ y j ρ , so the function f is supp ose d to be in the class f = X i α i y i + X i ≤ j α ij y i y j /ρ. Thu s, our problem is to find the co efficients α i and α ij such that the func- tion obtained meets our ob jectives a s well as p ossible. T o formulate the latter condition mathematically , let us wr ite down the following ob jective function. As w e ha ve alrea dy men tioned ab ov e, the a v a ila ble database gives us a t able of specific v alues x is = x i ( p s , λ s ). W e lo o k for the function f such t hat the total squared deviation fr om the v alue s λ s is as sma ll as p ossible. In o ther words, w e hav e to find the α i and α ij minimizing the o b jectiv e function h = X s  f ( x 1 s , . . . , x ms ) − λ s  2 = = X s  X i α i x is + X i ≤ j α ij x is x j s p x 2 1 s + · · · + x 2 ms − λ s  2 . Notice that h cons ide r ed as a function on α i and α ij is a non-negative quadric. In gener al p ositio n such a qua dric p os sesses a unique minimum which can be found a s a solution of linear equatio ns system, i.e., from the condition that the differential of h v anis he s . 3 Application to the sp ecific database The ab ov e a lgorithm determining the volume of a sample for calcula tion o f the individual v alues of an a r bitrary a nalyt was examined on the database of lab o- ratory indices. The b est results were obta ined, when w e reconstruct the v olume by means of the following analyts: TP , K, Na. The cor relation co efficients for the re paired a nd true v alues were 0 .9 5–0.9 7 . The algor ithm obtained gives an opp ortunity to choose distinct sets o f the indices for the volume reconstruction, that makes the a lgorithm multipurpose, i.e. it can b e used for analysis of any lab orator y blo o d indices . The metho d consider e d was a pplied to the sp ecific databas e in RSCRR. This database w as constructed from 3 5000 medical repo rts con ta ining biochem- ical measuring data . W e selected the rep orts containing the large st num be r of the bio chemical data. So, we se le cted the set of 263 7 cases with the next 17 3 bio chemical data measur ed: Chol, TBil, DBil, TP , Alb, Urea, Crea , AL T, AST, Am y , ALP , K , Ca, Na, F e, Glu, LDH. After c a lculation of the co efficients α i and α ij for the function f , we find out the following result: the num b er of patients p s which the inequality | f ( x 1 s , . . . , x ms ) − λ s | λ s > 0 , 05 holds for, do es not exce ed 5%. This estimate ag rees with the sta tis tical signifi- cance of the r esult. References [1] S. P . Parker and W. D. Cubitt, “The us e of the dried blo od sp ot sample in epidemiological studies,” J . Clin. Pathol., 52 (9), 633– 639 (19 99). [2] V. G. Pomelov a , N. S. Osin, “Outloo k of Dried Bloo d Spot T echnology Inte- gration into P o pulation Studies of Human Helth a nd En viro nment ,” V es tnik Rossiiskoi ak a demii meditsins kikh nauk, No. 1 2, 10–1 6 (200 7 ). [3] A. S. Abyholm, “Deter mination o f g lucose in dried filter pap er bloo d spots,” Scand. J. Clin. Lab. Inv es t. 4 1 (3), 269 –74 (1 981). [4] J. M. Burr in, C. P . Price, “Performance of three enzymic metho ds for filter pap er glucose determination,” Ann. Clin. Biochem., 21 (5), 411–41 6 , (1984 ). [5] D. R. Parker, A. B argiota , F. J. Cow an, R. J. Cor r all, “Susp ected hypog ly- caemia in out patient pra ctice: accur acy of dried bloo d sp ot analysis ,” Clin. Endo crinol. (Oxf.), 47 (6), 679 –683, (1997). [6] S. J. McCann, S. Gillingwater, B. G. Keevil, D. P . Co op er , M. R. Morris , “Measurement of total homo cysteine in plasma a nd bloo d sp ots using liquid chromatography-tandem mass sp ectrometr y : compariso n with the plasma Abbott IMx metho d,” Ann. Clin. B io c hem., 4 0 (2), 161–1 65 (20 0 3). [7] Anjali, F. S. Geethanjali, R. S. Kumar, M. S. Sesha dri, “Accuracy of filter pap er metho d for measuring glycated hemo globin,” J. Asso c. Physicians India, 55 , 1 15-11 9 (2007). [8] K. V. W aite, G. F. Mab erly , a nd C . J . Eastman, “Sto r age Co nditio nsand Stabilit yof Thyrotropina nd ThyroidHormones on Filter Paper ,” CLINICAL CHEMISTR Y, 33 (6), 853– 8 55 (1987 ). [9] V. G. Pomelov a , S. G. K alinenko v a, “Neo na tal screening on the c ongenital th yreoid deficie ncy a t environmen ta lly nfav o urable regio ns ,” Pro blems o f Endo crinolo g y , 46 (6), 15–19 (2002 ). [10] H. L. Levy , J . R. Simmons, R. A. MacCready , “Stability of amino acids and galactos e in the newbo rn sc reening filter paper bloo d sp ecimen,” J. Pediatr., 107 , 757 -760 (198 5). 4 [11] Anjali, F. S. Geetha njali, R. S. K umar, M. S. Seshadri, “Accuracy of Filter Paper Metho d for Me a suring Glycated Hemo g lobin,” JAPI 55 (2007) [12] H. Sha piro, F. Ma ndy , T. Rinke de Wit, P . Sandstrom, “ Dried blo o d sp ot techn ology for C D 4 + T -cell counting,” The Lancet 36 3 (9403) 164. [13] National Committee for Clinical Lab orator y Standards, N CCLS Appr ove d Standar d LA4-A2. Blo o d c ol le ction on filter p ap er for ne onatal scr e ening pr o- gr ams (Villanov a, P A:National Committee for Lab ora tory Standards 1992 ). [14] B. Evengard, E . Linder, P . Lundb ergh, “ Standardization of a filter- pa pe r techn ique for blo o d sa mpling ,” Ann. T rop. Med. Parasitol., 82 (3), 295-3 03 (1988). [15] T. I . Lukichev a, V. V. Men’shikov, L. M. P imenov a, Biolo gic al V ariation: a single ac cur ac e me asur e for lab or atorial analitics and diagnostic (Moscow, Analitik a, 20 04 [in Russian]). [16] V. K. Bo zhenko, A. D. Ber idz e , A. M. Shishk in, V. P . Guslistyi, “Use o f m ultiv ariate methods in the analysis o f la bo ratory indica to rs of bloo d”, K lin Lab Diagn., no . 10, 10– 11 (199 7). 5