Fig 1.
Two-step process of centrifugal separation of the whole blood in a tube for the preparation of platelet-rich plasma (PRP).
Fig 2.
Definition of modeled problem.
A: One-dimensional description of centrifugal sedimentation of particles in a rotating tube with a constant cross-sectional area. After spinning for a certain time duration, the concentration zones are classified as a clear liquid (α = 0), the retarded settling zone (0 < α ≤ αmax) and the packed bed (bottom layer) (α = αmax). Here, α is the volume fraction of solid phase, αmax is the maximum concentration of the solid phases (or particles) in the packed bed, L indicates height of solid-liquid mixture, D is diameter of the tube and R° is distance between the center of rotation and tube bottom. In − s and Is − d denote the position of the interfaces between supernatant/suspension and suspension/sediment, respectively. B: Two types of tube geometry considered in the present study.
Fig 3.
Temporal changes of RBC and WBC concentrations (α) in radial distribution inside the straight tube with centrifugal time (tc), predicted by one-dimensional unsteady particle sedimentation equation (Eq 9).
Considered centrifugal acceleration is ac = 1,000g, the maximum RBC concentration is αmax = 0.65, and the initial RBC concentration in the whole blood (i.e., Hematocrit) is αo = 0.4. In the graph, the solid lines denote iso-concentration lines of RBC. Also, the iso-concentration lines of WBC under the same centrifugal and initial conditions as RBC are shown together (blue dashed lines) for comparison.
Fig 4.
Comparison between the predicted and measured variations of volume of serum (VUL) with dimensionless centrifugal acceleration.
○, experimental data for the hematocrit range of 0.37–0.4 [16]. Lines (solid and dashed ones correspond to He = 0.37 and 0.4, respectively) denote the theoretical prediction based on VUL = (L − In − s)A. Centrifugation time and total blood volume are fixed at 10 minutes and 9 mL, respectively.
Fig 5.
Distribution of the ratio of platelet recovery rate (EPLT) to that of plasma (Eplas) from the experimental data available in the literature.
▼, Kahn et al. (1976) [14]; ○, Brown (1989) [38]; ◻, Araki et al. (2012) [15]; △, Perez et al. (2013) [21]; ★, Jo et al. (2013) [16]; ◊, Amable et al. (2013) [23].
Fig 6.
Variation of Π1 with Π2Π3Π4 for the available experimental data.
▲, from Perez et al. (2013) [21] (VWB = 3.5 mL tc = 10 minutes); ◻, Araki et al. (2012) [15] (VWB = 7.5 mL, tc = 10 minutes); ★, Jo et al. (2013) [16] (VWB = 9.0 mL, tc = 10 minutes); ▽, Jo et al. (2015) (VWB = 9.0 mL, tc = 5 minutes). - - -, linear regression function of Π1 = −0.0122Π2Π3Π4 + 0.5128.
Fig 7.
Comparison between the predicted and measured variations of EPLT/Eplas with dimensionless centrifugal acceleration.
—, theoretical prediction based on present model; △, experimental data from Perez et al. (2013) [21] (VWB = 3.5 mL tc = 10 minutes); ◻, Araki et al. (2012) [15] (VWB = 7.5 mL, tc = 10 minutes); ★, Jo et al. (2013) [16] (VWB = 9.0 mL, tc = 10 minutes); ▽, Jo et al. (2013) [16] (VWB = 9.0 mL, tc = 5 minutes).
Fig 8.
Variations of platelet recovery rate (EPLT) with centrifugal acceleration (ac = ω2Ro).
A: VWB = 9.0 mL (★, from Jo et al. (2013) [16]); B: 7.5 mL (◻, from Araki et al. (2012) [15]); C: 3.5 mL (△, from Perez et al. (2013) [21]). In the figure, lines denote the present theoretical predictions (- - -, He = 0.37; —, 0.52). Centrifugal time is fixed as tc = 10 minutes.
Fig 9.
Variation of white blood cell recovery rate (EWBC) with centrifugal acceleration (ac).
Centrifugal time fixed as tc = 10 minutes and VWB is 7.5 mL. Solid lines denote the boundaries of the predicted EWBC for the range of cw = 10−3–10−2, and ◻’s are from Araki et al. (2012) [15].
Fig 10.
Effects of centrifugal time (tc) on the recovery rates.
A: EPLT; B: EWBC. ▼, tc = 2 minutes; ♦, 3 minutes; ▲, 4 minutes; ■, 5 minutes; ⚫, 6 minutes; ▽, 7 minutes; ◊, 8 minutes; △, 9 minutes; ◻, 10 minutes; ○, 12 minutes; ⋆, 15 minutes. VWB is fixed as 9 mL.
Fig 11.
Variation of EPLT with Eplas for the range of ac = 100g – 1,500g at selected tc.
▽, 2 minutes; ◻, 5 minutes; ○, 10 minutes; ⋆, 15 minutes. VWB is fixed as 9 mL.
Fig 12.
Effects of whole blood volume and hematocrit.
A: VWB on EPLT; B: VWB on EWBC; C: He on EPLT; D: He on EWBC. In (A) and (B), ⋆, VWB = 9 mL; ○, 7.5 mL; △, 3.5 mL. In (C) and (D), - - -, He = 0.37; − ⋅ − ⋅ −, 0.45; ——, 0.52. Centrifugation time is fixed as tc = 10 minutes.
Fig 13.
Effects of tube bottom geometry on the recovery rates.
A: Platelet; B: WBC. ◻, flat type; ▼, conical type. Centrifugal time is fixed as tc = 10 minutes and VWB is 9 mL.
Fig 14.
Variation of ∂(EPLT/Eplas)/∂ac (solid lines) and ∂(Eplas)/∂ac (dashed lines) with ac for flat and conical bottom shapes.
Considered parameters are same as those used for the case of He = 0.52 in Fig 13A.
Fig 15.
Contours of EPLT (solid lines) and EWBC (dashed lines) with centrifugal time (tc) and acceleration (ac).
VWB is fixed as 9.0 mL.