Corrected Increment Research Articles

A comparison of the von Mises and Hencky equivalent strains for use in simple shear experiments

The von Mises equivalent strain increment is derived for the case of large strain simple shear (torsion testing). This is used, in conjunction with the von Mises yield surface, to define the von Mises equivalent stress as well as the incremental work per unit volume. Integration of the equivalent strain increment leads to the definition of the von Mises equivalent strain for torsion. The Hencky equivalent strain increment is derived from the Hencky strain defined as the logarithm of the semi major and minor axes of the strain ellipse. This is then used, via the incremental work, to derive the ‘Hencky equivalent stress’. In the Onaka approach, the numerical values of the principal strain increments were integrated without taking into account the continuous rotation of the strain ellipse. This invalid operation leads to an expression for the equivalent strain increment that cannot be applied to the large strains considered by Onaka. Using the correct increments of the Hencky strain, it is shown that the shear strain increments turn negative and consequently, the incremental work becomes negative when the shear is large.

Computing the correct Increment of Induction Pointers with application to loop unrolling

Induction pointers (IPs) are the analogue of induction variables (IVs), namely, pointers that are advanced by a fixed amount every iteration of a loop (e.g., p = p → next → next ). Although IPs have been considered in previous works, there is no algorithm to properly compute the correct amount of pointer jumping (AOPJ) by which IPs should be advanced if loop unrolling is to be applied to loops of the form while ( p ) { … p = p → next → next ; } . The main difficulty in computing the correct AOPJ of IPs is that pointers can be used to modify the data structure that is traversed by the loop (e.g., adding/removing/by-passing elements). Consequently, a simple advancement p = p → next in a loop does not necessarily mean that p is advanced by one element every iteration. This situation contrasts with the use of IVs, which cannot change the structure of arrays that are traversed by loops. Hence, if i is an IV, A [ i + 1 ] will always mean the next element of A [ ] , while if p = p → next ; is preceded by p → next = q ; it may be advanced by k > 1 elements at every iteration. The proposed method for computing the correct AOPJ of IPs and an accompanying loop unrolling technique were implemented in the SUIF compiler for C programs. Our experiments with automatic unrolling of loops with pointers yielded an improvement of 3–5% for a set of SPEC2000 programs. Experiments with a VLIW IA-64 machine also verified the usefulness of this approach for embedded systems.

Efficacy of prophylactic transfusions using single donor apheresis platelets versus pooled platelet concentrates in AML/MDS patients receiving allogeneic hematopoietic stem cell transplantation

Superiority of single-donor apheresis platelets (SDAP) over pooled platelet concentrates (PPC) transfusions is largely assumed, but unproven. We hypothesized that prophylactic SDAP and PPC transfusions are clinically equivalent after allogeneic hematopoietic stem cell transplants (HSCT). We studied all transfusions administered to 33 patients with AML/MDS during the first 100 days after busulfan-based, myeloablative HSCT. All donor-recipient pairs were ABO identical. Transfusion threshold was a platelet count < or =15 x 10(9)/l. The corrected increment (CCI) was used for all comparisons. Median time to platelet engraftment was 13 days (n=30). PPC transfusions (n=105) were ABO compatible, while 10% of 41 SDAP were not (P=0.006). Median post-transfusion platelet count was 51K/microl (5-118K) after SDAP and 36K/microl (3-115K) after PPC (P=0.0004). Median CCI was 14.178 (SDAP) versus 7.793 (PPC) (P=0.0001). Median time to another transfusion was 3 days (SDAP) and 2 days (PPC; P=0.3). In the week following any given transfusion, the median number of new transfusions was similar (n=2), as well as the need of further transfusion (16 versus 24%, P=0.2). A total of 17% of SDAP and 30% of PPC transfusions were labeled 'ineffective' (P=0.1). There were two non-lethal hemorrhage episodes (6%). SDAP transfusions produced better platelet counts, but SDAP and PPC were equally effective in preventing hemorrhage.

"Prophylactic" Platelet (PLT) Transfusions in the Setting of Allogeneic Hematopoietic Stem Cell Transplantation (alloHSCT): Similar Clinical Efficacy of Single Donor (SDP) and Random Donor Pooled (RDP) Platelet Products.

Superiority of SDP over RDP for PLT transfusions is largely assumed, but unproven. We hypothesized that SDP and RDP used for prophylactic transfusions are clinically equivalent.Methods: In order to minimize the biases imposed by a heterogeneous population, we studied 33 patients (median age 47 years, range, 22–66), which underwent alloHSCT for AML or high-risk MDS with ABO-identical donors. All received intravenous busulfan (BU)-based myeloablative conditioning regimens: 30 patients received BU 130mg/m2 and fludarabine 40mg/m2 for 4 days, and 4 patients were given BU 0.8mg/kg every 6 hours for 4 days with cyclophosphamide 60mg/kg for 2 days. GvHD prophylaxis consisted of tacrolimus and mini-methotrexate. Recipients of unrelated (UD) or one antigen-mismatch related donor transplants received antithymocyte globulin (ATG). Source of stem cells was peripheral blood (n=23) and bone marrow (n=10). Donors were related (n=28) and UD (n=5). Only 3 patients were identified as alloimunized for RBC antigens before tranplant. Transfusions administered for active bleeding were excluded from this analysis. Prophylactic PLT transfusions were administered for PLT counts below 15 x 10e9/l. The corrected increment (CCI) was calculated according to standard formula, using PLT counts performed in samples collected following transfusions. As all patients received both types of products, each transfusion administered during the first 100 days after alloHSCT was evaluated individually. The RDP and SDP were labeled as 'ineffective', according to the CCI: cut-offs of 5.5 for the samples collected in the first hour post transfusion, 5.0 for the samples between 1 and 18 hours and 4.5 for the samples collected 18 hours or later.Results: Median time to PLT engraftment was 13 days (range, 8–51, n=30). Patients received 105 RDP and 41 SDP transfusions. All RDP transfusions were ABO compatible, while 4 out of the 41 SDP (9.75%) were ABO-incompatible (p = 0.006). Median PLT and Hb level before transfusion were similar for both SDP and RDP. Frequency of amphotericin and vancomycin use, and presence of fever on transfusion day was similar on both groups. Median post-transfusion platelet count was 51K/μL (range, 5K-118K) after SDP and 36K/μL (range, 3K–115K) after RDP (p = 0.0004). Median CCI was 14.178 for SDP transfusions versus 7.793 after RDP (p = 0.0001). The difference in post-transfusion PLT counts and CCI favoring the SDP group did not translate into superior clinical efficacy. Median time to another PLT transfusion was 3 days (range, 0–10) after SDP and 2 days (range, 0–10) after RDP (p = 0.3). The median number of new transfusions needed in the following week was similar for both groups (2 transfusions, range 0–7). In the week following any given transfusion, 24% versus 16% of the patients receiving SDP versus RDP did not need other transfusion (p = 0.2); 17% of SDP and 30% of RDP transfusions were labeled 'ineffective' according to CCI (p = 0.1). There were two episodes (6%) of hemorrhage during the study period (none lethal): gastro-intestinal and hemorrhagic cystitis.Conclusion: SDP transfusions produced a greater increment in PLT counts after transfusion, but SDP and RDP were equally effective in preventing hemorrhage.

Hydroxyurea Treated Sickle Disorders Demonstrate Decreased Plasma Hb, Red Cell Vesicles and Thrombolysis.

Free plasma Hb has been recently implicated in the genesis of pulmonary hypertension in sickle cell disorders (SCD) through a putative NO scavenging mechanism. We have recently reported that free plasma Hb is correlated with increased plasma red cell derived vesicles (RBVes) in sickle cell and thalassemia disorders (Westerman, Blood 2004; 104:1671). Since high levels of HbF have been associated with decreased elevation of RBVes in children with SCD (Setty Blood 2000; 96:1119–1124), we hypothesized that patients treated with hydroxyurea (HU) might show a similar normalisation of RBVes. Given our finding of an association between RBVes and free plasma Hb, such treatment might also be predicted to correct increments in free plasma Hb. In this study we have examined whether sickle cell patients treated with HU show evidence of a decrease in free plasma Hb and RBVes compared to untreated SCD patients. RBVes, free plasma Hb, and markers of activation of thrombolysis were quantitated. 35 adult SCD patients, 27 in steady state, untransfused and not receiving HU and 7 patients on long term HU at a dose of 10–30 mg/kg/day. These parameters were also measured in 27 healthy control subjects without SCD. RBVes were significantly higher in untreated SCD (15.59±3.07 x 103/μL of blood) than in control subjects (2.13 ± 0.5)(p=0.001). In HU-treated SCD patients, vesicles were significantly lower (3.97±0.83)(p=0.0371). than in untreated patients and approached levels found in healthy controls. Free plasma Hb was significaly increased in untreated SCD (16.74±3.87) compared with healthy controls (1.77±0.2)(p=0.001); these levels were also corrected in HU treated SCD patients (13.42±4.48). The proportion of RBVes expressing phosphatadyl serine was also lower in HU-treated SCD (37.25± 9.79) than in untreated SCD (52.52±4.74). This was paralleled by a decrease in red cells expressing PS in HU treated patients (11.83± 3.95) compared with untreated patients (42.71±8.45)(p=0.011). This decrease in both RBVes and RBCs expressing PS in HU-treated patients might in principle decrease activation of coagulation. Indeed, plasma Ddimers, which are increased in untreated SCD (480 ±60.14) compared with healthy controls (117.43±38)(p=0.018). are normalised in HU treated patients (190±28.69). These data provide evidence of a link between RBVes and plasma Hb and suggest that PS expression on RBVes and red cells plays a role in the prothrombotic state seen in SCD. As HU treatment appears to correct plasma Hb, long term treatment may be associated with a decreased scavenging of NO and hence the risk of pulmonary hypertension. The correction of the prothrombotic tendency may also be beneficial in this regard. Prospective trials are indicated to confirm whether HU treated patients have evidence of decreased risk of pulmonary hypertension.

Modulation of Idiotypic and Antiidiotypic Immunoglobulin G Responses in an Alloimmune Thrombocytopenic Patient Associated with Extracorporeal Protein A Immunoadsorption

In the present case study, a patient with Non-Hodgkin. Lymphoma underwent combination chemotherapy resulting in severe pancytopenia requiring transfusion support with blood products. The patient became refractory to random donor platelet transfusions and subsequently received five immunoadsorption treatments. The patient's clinical response to immunoadsorption therapy was assessed by monitoring platelet transfusion recovery and survival. In addition, changes in antibody responses were assessed. Early during the course of immunoadsorption therapy, antiplatelet immunoglobulin G (IgG) alloantibody was detected. There was a decline in antiplatelet IgG alloantibody levels by the last immunoadsorption treatment associated with increases to platelet correct count increments after completion of immunoadsorption therapy. In addition, elevated levels of antiidiotypic IgG antibody detected early during the course of therapy were significantly reduced by the last immunoadsorption treatment. This case study suggests that specific alloimmune idiotypic IgG antibody and corresponding antiidiotypic IgG antibody responses may be modulated in association with extracorporeal immunoadsorption employing protein A/silica columns.

Use of 'split' plateletpheresis products for alloimmunized patients.

Single donor platelets obtained using the COBE Spectra were split into two halves and administered to alloimmunized patients with leukemia at two different points in time. The mean platelet yield was 6.83 x 10(11) (n = 63) with 56% of collections having yields of > 6.0 x 10(11) (i.e. twice the current AABB recommendation for an apheresis platelet transfusion). In 58 instances, the two halves were administered to the same patient 24-96 h apart. The differences in the correct increments of the split transfusions administered 24-48 h apart were not statistically significant, although there were decreased increments after 72 and 96 h of storage. In 5 instances when the CCI for first transfusion was unacceptably low, the second half was successfully transfused to another patient. This study proves it is feasible to split apheresis platelets into two transfusions, and discusses approaches to optimally use this strategy for the transfusion support of alloimmunized patients.

Use of 'Split' Plateletpheresis Products for Alloimmunized Patients

Single donor platelets obtained using the COBE Spectra were split into two halves and administered to alloimmunized patients with leukemia at two different points in time. The mean platelet yield was 6.83 x 10^11 (n = 63) with 56% of collections having yields of >6.0x10^11 (i.e. twice the current AABB recommendation for an apheresis platelet transfusion). In 58 instances, the two halves were administered to the same patient 24-96 h apart. The differences in the correct increments of the split transfusions administered 24-48 h apart were not statistically significant, although there were decreased increments after 72 and 96 h of storage. In 5 instances when the CCI for first transfusion was unacceptably low, the second half was successfully transfused to another patient. This study proves it is feasible to split apheresis platelets into two transfusions, and discusses approaches to optimally use this strategy for the transfusion support of alloimmunized patients.

Systematic Use of Leukocyte-Free Blood Components to Prevent Alloimmunization and Platelet Refractoriness in Multitransfused Children with Cancer

A major drawback in the use of platelet transfusions is the development of platelet refractoriness that is usually caused by alloimmunization provoked by leukocytes present in the blood products. We evaluated the development of alloimmunization both by serological demonstration of HLA antibodies and by clinical demonstration of platelet refractoriness in 50 multitransfused children who exclusively received filtered, leukocyte-free blood products. The basic diagnoses included acute leukemia, pediatric solid tumors, and severe aplastic anemia. We also present a reference group of 10 similarly multitransfused children, who either deliberately or inadvertently had received nonfil- tered blood products on some occasions. In the study group of 50 children, none developed platelet refractoriness. The median corrected increment was 11.1 x 10^9/l at the time of initial diagnosis, and 10.4 at the time of the study 8 months later (median). None had detectable HLA antibodies in serum. In contrast, in the reference group 3/10 had HLA antibodies in serum, and 1/10 was clearly refractory to random pooled platelets. We conclude that systematic use of leukocyte-free blood components effectively prevents alloimmunization in heavily transfused children with cancer. Leukocyte depletion to the level of < 1 x 10^6 of contaminating leukocytes per unit is sufficient and seems to prevent alloimmunization totally.

9 DIFERENT THYROID INFILTRATING CELLS AND IMMUNOLOGICAL EXPRESSIN IN JUVENILE CHRONIC LYMPHOCYTIC THRYOIDITIS (CLT) AND GRAVES'DISEASE

Since Hashimoto's description of “struma lymphomatosa” in 1912, immunological disorders were imputed to many thyroid diseases. Close relation between this condition (whose juvenile form is CLT) and Graves' disease were proposed, but it is not clear if they could be or not expressions of a single entity. To elucidate this aspect, thyroid infiltrating cells and immunological markers as well as citological studies, were perfected on thyroid tissue obtained by means of thyroid fine needle aspiration biopsies (TFNAB) in 20 patients (CLT n=10 and GD, n=10). Material and methods: Samples were analyzed according to Hayry and Von Willebrand's method of Corrected Increment (CI). Morphology as well as HLA-DR expression in follicular cells. Interleukine-2 receptor (IL-2/R) B and T cell markers were performed on cytospin smears, either by immunoperoxidase or indirect immunofluoresoenoe. TFNAB were divided in 2 groups, according to patient's thyroid status:Group 1) CLT, n=12 and Group 2) GD, n=14. Results:(in %±SD): Group 1:a:6.9±1.09;B-cells 34.9±12.6;T-cells 60>12.2;CD4:62.7±5.2;CD8:33.2±5.6;ratio:1.9±0.34.HLA-DR was present in 56.4±22.6 of the follicular thyroid cells. IL-2 was present in 11/12 specimens. Group 2:CI:4.5±1.3 (group 2 vs 1, p<0.001);B-cells:59.2±16.0 (p<0.001);T-cells 41.9±16.2(p <0.001)CD4:56.4±8.4(p< 0.05);CD8:41.4±7.8 (p<0.02), ratiol:1.44±0.5(p<0.02). HLA-DR was expressed in 18.8±18 (p< 0.001) of the follicular thyroid cells. IL-2 was present in 3/14. Comments:Significative differences were found between both groups. a)CI vas significantly higher in group 1:CI above 5.3 result to be a sensible indicator of CLT. b)HLA-DR on epithelial thyroid cells as well as IL-2/R were significantly higher in CLT. c) Infiltrating lymphocites showed that 60% were T-cells in CLT while in GD about 60% expressed B-cell markers. These results would suggest a different impact of humoral and cellular immunoresponse in each of these autoimmune thyroid diseases in juvenile patients.

The definition of refractoriness to platelet transfusions.

The relationship between the 1 and 20 h post-transfusion platelet count and three parameters used to define refractory transfusions, namely the corrected increment (CI), platelet increment (PI), and percentage platelet recovery (%REC), was studied in 437 non-HLA matched platelet transfusions given to 102 patients with bone marrow failure. The percentage agreement between common definitions of refractoriness was calculated based on these parameters. As the maintenance of platelet counts above 20 x 10(9)/l is a relevant clinical goal for platelet support, the values of the CI, PI and %REC, which best corresponded to 1- and 20-h post-transfusion counts of 20 x 10(9)/l, were identified. A 1-h post-transfusion CI < 3 (PI < 7 x 10(9)/l or % REC < 8%) corresponded to clinically unsuccessful transfusions with a 1-h platelet count < 20 x 10(9)/l. A 1-h CI > or = 5.5 (PI > or = 12 x 10(9)/l or %REC > or = 14%) corresponded to clinically successful transfusions with a 20-h post-transfusion count of > or = 20 x 10/l. These data tie together the end points reported in the literature for defining refractory transfusions.

Clinical Evaluation of the Effects of Storage Time and Irradiation on Transfused Platelets

Platelet concentrates stored for up to 5 days at room temperature or irradiated with 15 Gy immediately prior to transfusion were evaluated for their ability to increase the platelet count in thrombocytopenic patients. Platelets irradiated with a dose of 15 Gy immediately prior to transfusion achieved corrected increments (CI) at 1 and 20 h after transfusion no different from those achieved by non-irradiated platelets. Storage for 5 days reduced the mean 1-hour CI to 5.7 compared with a mean of 12.3 achieved by platelets transfused after only 1-day storage (p = 0.008). Similarly, the frequency of a repeat transfusion being indicated within 24 h increased with increasing storage time (p = 0.005).

Platelet crossmatching. A direct approach to the selection of platelet transfusions for the alloimmunized thrombocytopenic patient.

Selection of platelets for alloimmunized, thrombocytopenic patients has traditionally been based on HLA matching. This approach is indirect and may not adequately recognize incompatibility between the recipient and the platelet donor. The authors evaluated the usefulness of directly showing donor-recipient compatibility by crossmatching the patient's serum with prospective platelet donors who were not preselected on the basis of their HLA type. Eleven alloimmunized patients were chosen for study, and crossmatching was done by a radiolabeled antiglobulin test. These patients had high levels of HLA alloantibody, and their unusual HLA types made the provision of HLA-matched platelets difficult. When the crossmatch was compatible, the mean one-hour corrected count increment was 18,379 +/- 4,670 (1 standard deviation), n = 22, and at 18-24 hours, 7,318 +/- 3,317. If the crossmatch was positive, the mean one-hour corrected increment was 2,536 +/- 3,057, and at 18-24 hours, 227 +/- 657, n = 16. There were two false negative crossmatches and one false positive crossmatch. One hundred forty-eight crossmatches were done to find 48 potential donors, who, by conventional selection using HLA matching, would not have been considered appropriate donors. These results show that successful platelet transfusions for alloimmunized thrombocytopenic patients can be prospectively selected by platelet crossmatching without the need of doing expensive HLA typing of a large population of platelet donors. Although it may be difficult to find compatible platelets for some patients with broadly reactive HLA antibodies, platelet crossmatching may detect compatible donors who are ordinarily excluded on the basis of their HLA phenotype.

Platelet storage for 7 days in second-generation blood bags.

Plastic storage bags designed to optimize O2 and CO2 transfer to preserve platelets for 7 days prior to transfusion were studied in vivo and in vitro. Platelets stored 7 days in second-generation CLX bags were compared to platelets stored 3 days in standard (CL-3861) 3-day storage bags and platelets transfused within 24 hours of collection. The CLX bags maintained concentrate pH at a mean of 6.85 +/- 0.03 (SEM) after 7 days, while in standard bags after 3 days of storage, the mean pH was 6.46 +/- 0.03. A smaller proportion of platelets stored 7 days in CLX bags were discarded because of a pH less than 6.0 compared to those stored 3 days in CL-3861 bags (10 vs 21%). Poststorage pH showed strong correlation with concentrate platelet count and weak correlation with concentrate white cell count in both bag types. There was no significant difference in the mean corrected platelet count increments between platelets stored 7 days in second generation CLX bags and those stored 3 days in CL-3861 bags (10,000 and 12,200 at 1 hour, and 7000 and 7500 at 24 hours, respectively) following transfusion to 16 thrombocytopenic recipients. However, transfusion of fresh platelets achieved mean corrected increments at both 1 and 24 hours posttransfusion that were higher than seen with either group of stored platelets (20,100 at 1 hour and 10,800 at 24 hours). Platelets can be stored 7 days in second-generation CLX blood bags with results comparable to those of platelets stored 3 days in standard bags.

Therapeutic effectiveness of frozen platelet concentrates for transfusion

Six patients received platelet concentrate transfusions from their HLA- identical siblings. Platelet concentrates were administered either fresh, or after being frozen in 10% dimethylsulfoxide, at a slow controlled rate (1 degree C/min) or rapidly (approximately 8 degrees C/min) in the vapor-phase of a liquid nitrogen refrigerator. The median freeze-thaw loss was 13.5%. The mean 1-hr and 20-hr corrected increments in platelet count were calculated for fresh platelet concentrates transfused before and after transfusion with controlled- rate frozen and vapor-phase frozen platelet concentrates. There was no significant difference among the first and second transfusion of fresh platelet concentrates, nor was the difference observed between fresh and controlled-rate frozen platelet concentrates significant. The difference between fresh and vapor-phase frozen platelet concentrates, and between controlled-rate frozen and vapor-phase frozen platelet concentrates were highly significant (p &lt; 0.01). In vitro tests of aggregation using ristocetin and platelet ultrastructural studies paralleled the transfusion experience. Our results indicate that HLA- identical platelet concentrates can be successfully frozen and thawed for transfusion if a slow, controlled rate of freezing is employed. The use of HLA-identical frozen platelet concentrates may be important in emergency situations for the refractory patient and potentially for the establishment of a platelet concentrate bank.

Therapeutic Effectiveness of Frozen Platelet Concentrates for Transfusion

Six patients received platelet concentrate transfusions from their HLA-identical siblings. Platelet concentrates were administered either fresh, or after being frozen in 10% dimethylsulfoxide, at a slow controlled rate (1 degree C/min) or rapidly (approximately 8 degrees C/min) in the vapor-phase of a liquid nitrogen refrigerator. The median freeze-thaw loss was 13.5%. The mean 1-hr and 20-hr corrected increments in platelet count were calculated for fresh platelet concentrates transfused before and after transfusion with controlled-rate frozen and vapor-phase frozen platelet concentrates. There was no significant difference among the first and second transfusion of fresh platelet concentrates, nor was the difference observed between fresh and controlled-rate frozen platelet concentrates significant. The difference between fresh and vapor-phase frozen platelet concentrates, and between controlled-rate frozen and vapor-phase frozen platelet concentrates were highly significant (p < 0.01). In vitro tests of aggregation using ristocetin and platelet ultrastructural studies paralleled the transfusion experience. Our results indicate that HLA-identical platelet concentrates can be successfully frozen and thawed for transfusion if a slow, controlled rate of freezing is employed. The use of HLA-identical frozen platelet concentrates may be important in emergency situations for the refractory patient and potentially for the establishment of a platelet concentrate bank.

Unbiased sampling from a falling stream of particulate material

A sample must be unbiased. Unbiased samples can be obtained only by means of correct sampling devices (a sampler is said to be correct when it gives all particles an equal probability of being selected). To be correct a sampler must take into account various conditions concerning each of the three logical steps of the sampling process, i.e., integration, increment delimitation, and increment extraction. The conditions of correct integration and correct increment delimitation have been well defined (ref. 1). The purpose of this study is to ascertain the conditions of correct increment extraction from a falling stream of particulate material. Theoretical and experimental approaches to this problem are followed by a discussion of the experimental method, a description of the testing plant layout, a discussion of the measurement accuracy and a description of the tests. Then follows the analysis and interpretation of the test results. This analysis leads to the statement of three conditions concerning the critical cutter characteristics (the value of a parameter is said to be critical when its effect on the increment extraction borders between correct and incorrect) and one condition describing the economical optimum (correct increment extraction at lowest possible cost). The first condition states that for materials over 3 mm the critical cutter width is equal to three times the diameter of the coarsest particles in the material to be sampled, whereas under 3 mm the critical width is 10 mm irrespective of the diameter of the coarsest particles. The actual cutter width must always be larger than or equal to the critical width if an unbiased sample is to be obtained. The second condition states that, irrespective of the diameter of the coarsest particles, if the actual cutter width is equal to the critical width, then the critical cutter speed is equal to 0.6 m/s. The actual cutter speed must always be smaller than or equal to the critical speed if an unbiased sample is to be obtained. The third condition states that when the actual cutter width is n times larger than the critical width, the critical cutter speed is equal to 0.3 (1 + n) m/s. The actual cutter speed must always be smaller than or equal to the critical speed if an unbiased sample is to be obtained. The fourth condition states that an economical optimum is attained when the actual cutter width is equal to the critical width and if the actual cutter speed is equal to the critical speed. When observing this rule, a correct and unbiased sample at the lowest possible cost will be obtained