1 proposed an extrapolation chart   , which was based on a referenced mathematical formula . since the publication , two comments or concerns have been received in personal communications . the colleague expressed concern that the working of the reference range had used the value of serum proteins in g / dl . a second person emailed to express delight on the work , and enquired whether the formula has been reviewed for suitability to determine wbv at low shear rate . in response to the two concerns , this work sets out to compare the outcomes of using different units - converted - modifications of the extrapolation and their suitability for determination of wbv at high and low shear rate . it is known that low wbv , which is anaemia related , complicates low shear rate and constitutes part of abnormalities that are associated with decreased vasodilating response to endothelial mechanical stimulation . changes in wbv are measured at high and low shear rates and there has been interest in determining percentage increase in both , especially after haemodialysis . therefore , it would be logical that any formula that provides the values of wbv at both high and low shear rates , regardless of anaemia is appropriate . the objective is to develop a position statement regarding the combination of units of haematocrit and serum proteins that are most appropriate to be employed on the mathematical extrapolation formula . to our knowledge , the actual fractional contribution of haematocrit or serum proteins to wbv by this extrapolation method has yet to be reviewed . it may provide additional basis to discern a most appropriate combination of units for the formula . it was supported materially by the albury south west pathology  a unit of western pathology cluster of nsw health australia . ten years of de - identified archived clinical pathology data for the period of january 1999 to december 2008 constitute the research database . in a 10-year period , the pathology referred only ten cases for wbv determination , of which five cases that were selected for this evaluation . the pair of haematocrit ( hct ) and serum total protein ( tp ) values was used in various units to derive four units - converted - extrapolations of the same formulae for : high shear rate : wbv ( 208 sec ) = ( 0.12  hct ) + 0.17(tp - 2.07 ) low shear rate : wbv ( 0.5 sec ) = ( 1.89  hct ) + 3.76(tp - 78.42 ) 
 extrapolation 1 : according to the units employed in developing the chart , which converted the units for serum total protein only : where hct = haematocrit ( % ) and tp = serum total proteins ( g / l)extrapolation 2 : based on units ( tp g / dl ; hct % ) in referenced material .extrapolation 3 : based on  prot g / dl and  hct fraction. that is , both units of hct and tp from the referenced formula were converted.extrapolation 4 : wbv 208 sec based on prot g / l and  hct fraction. that is , only the hct has been modified . extrapolation 1 : according to the units employed in developing the chart , which converted the units for serum total protein only : where hct = haematocrit ( % ) and tp = serum total proteins ( g / l ) extrapolation 2 : based on units ( tp g / dl ; hct % ) in referenced material . prot g / dl and  hct fraction. that is , both units of hct and tp from the referenced formula were converted . extrapolation 4 : wbv 208 sec based on  prot g / l and  hct fraction. that is , only the hct has been modified . the fractional contribution of haematocrit or serum proteins to wbv were worked out , in percentages , according to the following formulae 
 haematocrit ( hct % ) contribution = ( 0.12  hct)/((0.12  hct ) + 0.17(prot  2.07))protein ( tp % ) contribution = 0.17(prot 2.07)/((0.12  hct ) + 0.17(prot  2.07 ) ) 
  haematocrit ( hct % ) contribution = ( 0.12  hct)/((0.12  hct ) + 0.17(prot  2.07 ) ) protein ( tp % ) contribution = 0.17(prot the outcomes of the modifications for wbv at high shear rate are presented ( table 1 ) . numeric values of results from all 4-modifications for all cases figure 1 shows the differences in fractional or percentage contribution of haematocrit and serum proteins to the wbv value due to the different four units - converted - extrapolations . disparity in contributions of hct and tp to wbv in different units - converted - extrapolations . hct : haematocrit , tp : serum total protein , wbv : whole blood viscosity level ( cps ) at high shear rate ( 208 sec ) , ext 1 : extrapolation formula 1 , ext 2 : extrapolation formula 2 , ext 3 : extrapolation formula 3 , and ext 4 : extrapolation formula 4 . determination of wbv at low shear rate ( 0.5 sec ) using the formula to derive four units - converted - extrapolations yielded negative values , except in results from extrapolations 1  4 for wbv at low shear rate ( 0.5 sec ) in comparing the outcomes of the different units - converted - modifications of the extrapolation formula , attempt has been made to consider the impact of haematocrit and serum proteins to the wbv value . on one hand , it is determined that extrapolation 2 model attributes more to haematocrit than serum proteins . for instance , in case 1 who has anaemia and hyperproteinaemia ( table 1 ) , serum total proteins have contributed less than 30% to hyperviscosity ( fig . 1 ) . in our opinion , this is not in agreement with current scientific understanding , whereby the impact of total proteins to viscosity in certain diseases associated with hyperproteinaemia underpins the concept of assessing plasma viscosity in place of wbv . on the other hand , it is determined that extrapolations 3 modification attribute only about 5% effect to haematocrit in wbv of a healthy individual who has hct at the upper normal range ; and much less by  ext-4 modification . that is , a question of where is the essence of managing or monitoring polycythemia with wbv measurement if the impact of haematocrit is ignorable ? it also raises the question of potential difference in reference values based on gender differences in haematocrit . this is an issue that has actually being deliberated for more than four decades [ 68 ] . in our opinion , attribution of insignificant contribution to haematocrit tantamount to no gender differences , and contradicts its inclusion in the formula . therefore , we submit that the combination of units employed on extrapolation  ext-1 as used in developing the chart is most appropriate . from the comparison of different units - converted - modifications of the extrapolation formula for the assessment of wbv at low shear rate ( table 2 ) , it is observed that the contribution by haematocrit is grossly infinitesimal , while that of total proteins default to negative at any value below 78.42 g / l . in our opinion , this is unthinkable ; especially as it would mean that only people with hyperproteinaemia have measurable blood viscosity . might have missed this observation since they excluded extreme haematocrit and total protein values in their study protocol . indeed , assuming normoproteinaemia , blood viscosity level may not be zero even when the haemoglobin concentration is very low . perhaps at this juncture , it is pertinent to acknowledge the notion of a critical haematocrit level below which measurement of whole blood viscosity may be invalid . that is , wbv may be too low to be measureable or valid for man or woman who has concomitant anaemia and hypoproteinaemia . the cases reviewed in this study do not include any concomitant anaemia and hypoproteinaemia to enable such observation ( table 1 ) . nevertheless , results in table 2 does show that only by extrapolation 1 modification can wbv at low shear rate be determined . haematocrit ( % ) and serum total proteins ( g / l) is most appropriate in the formula . comparative statement is that extrapolation formula using units of haematocrit in [ % ] and serum total proteins in [ g / use of other units may render the method not able to assess wbv at low shear rates or at protein levels below 78
background : a series has recently been done on whole blood viscosity . the first on the series proposed extrapolation chart with conventional reference range . since the publication 
 , two concerns have been received in personal communications . the first expressed concern over the use of serum proteins values in 
 g / l instead of  g / dl that was contained in the referenced material . 
 the second enquired on suitability of the formula for determination of blood viscosity at low shear rate.aim:this work sets out to compare different units - converted - modifications of the extrapolation with a view to develop a statement of comparison and suitability of units.materials and methods : the values of haematocrit and serum proteins were used in different unit - conversions on the mathematical formula to derive four modifications , which were compared . 
 five clinical cases that were specifically tested for whole blood viscosity , and had results for haematocrit and serum proteins were evaluated . 
 the appropriateness of modifications for determination of viscosity at low shear rate was reviewed.results:except as modified and used in the series , determination of whole blood viscosity at low shear rate using other unit conversions on the formula yields negative values for all five cases.conclusion:given that it is unexpected for blood viscosity level to be zero let alone less , it is logical that negative values are invalid . 
 a formula that gives the least invalid results may be most appropriate . 
 therefore , extrapolation modification used in the series is most appropriate .