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similar results. Their study experimentation with a collapsible indicate whether they thought of either speed or volume for
tube was set up vertically to check the effects of area reduction flow, as there may be an opportunity for improved clarity by
on flow rate; they subsequently checked their measurements surveying opinions and by later refining instruction of the skill
with the use of mathematical equations, and they confirmed of bleeding assessment. In a 2007 study of tourniquet use as
the effect of arterial luminal reduction on blood flow in dogs. assessed with the use of plethysmography, investigators puz-
Mann and coauthors found similar results by reducing luminal zled why tourniquets may increase blood flow velocity when
area in two ways: external compression and internal blockage. occlusion was not attained, and the present study results,
They found that flow was affected little until area reduction collapsible tube science, and the Venturi effect can plausibly
was severe, like the key finding of our study. Mann and co- explain why it was so. If caregivers or investigators do not
14
authors found that: “The area of the lumen may be reduced understand well the metric of performance (velocity of flow
50 per cent without any change in blood flow, and it can be or volume of flow) that they use in assessment, then their as-
reduced as much as 90 per cent before a 50 per cent reduction sessment may be incomplete or biased, resulting in suboptimal
in blood flow occurs.” Results of the present study and of care to the patient.
10
Mann and coauthors’ study are coherent in their applicability
to inorganic tubes and living mammals. In other words, the In the 20th century, collapsible tube science was used in at-
phenomena described are not specific to blood flow or even to tempts to develop bleeding control interventions. It was funded
biology, as fluid mechanics applies generally. by the US government. Funds were granted to several institu-
tions whose investigators developed knowledge and interven-
Collapsible tube science can aid in the selection of bleeding tions (Table 2). Few such interventions were eventually tried
control interventions for further preclinical study such as with in care, but the funding eventually stopped and evidently did
manikins, cadavers, or animals or by down-selection of un- not flow again. During the decade we have been involved in
promising candidate interventions. Such studies may improve the management of bleeding control research, potential fund-
our capacity to reduce the number of animals required for ing for such development has not come up in discussion until
later studies of bleeding control by abandoning poorly per- late 2016, when we reported to managers the results of the
forming candidate interventions or refining power analyses present study. Current costs of such research are mostly in the
through better understanding of treatment effect sizes. Mann man-hours of skilled investigators because the materials are
and coauthors used animals, and knowledge generated from relatively inexpensive. The lines of potential work in applying
this study of tubes could reduce the number needed for future collapsible tube science to first aid control of bleeding appear
studies. 10 to be legitimate scientific topics and appear to be a frugal out-
lay offering a good return on investment. Organizations that
Mann and coauthors also pointed out that the clinicians they may conduct such work include civilian programs of biome-
spoke with thought that the bleeding was most reliably as- chanical engineering involving professors/instructors and their
sociated with the artery’s external wall diameter, its internal students at the level of a master’s or doctoral degree. The US
(lumen) diameter, or its cross-sectional area of the lumen, government may reconsider its funding of such programs.
and clinicians were unsure about which area was most reli-
ably associated with flow. Although that awareness gap has TABLE 2 Past Funding for Research Related to Collapsible
10
been studied over ensuing decades since Mann and coauthors’ Tube Science
1938 publication, the gap remains commonly felt even today National Heart Institute Grant Veterans Administration
by caregivers with whom we speak periodically. Among such H-720 Hospital and Department
of Medicine, Georgetown
US Public Health Service
individual caregivers, we have occasionally detected strategies University Medical Center
for interventions like tourniquet use, and their particular strat- National Institutes of Health Department of Surgery,
egies were rooted in their personal intuitions regarding bleed- Grant HE-02038 University of Virginia Medical
ing. Such differing strategies led them to focus on particular Center
metrics of performance such as blood volume lost or time to National Science Foundation New York University
stop bleeding. Different focuses affect various outcomes differ- Grant GP 27209
ently; for example, emphasizing minimal blood loss may most National Science Foundation Cornell University
improve casualty survival but it may inadvertently increase the Grant GP 20528
time a user and patient are at risk during care under fire. In US Army Medical Research Department of Surgery,
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the present study, we measured volumetric flow rate and in- and Development Command, University of Virginia Medical
ferred flow velocity such as by the Venturi effect, but when we Research contract 17-67-C-7039 Center
ask caregivers, most initially talk of flow as volume per time. Study Limitations
Few mention flow velocity (speed), and almost none mention
both volume and velocity unless given clues during follow-on One limitation is the setup, which examines flow through only
discussion. Most caregivers believe that a half-closed artery one tube, rather than as a vascular network, which could bet-
has about half its normal flow (an incorrect intuition), and ter mimic bleeding. However, understanding the effects of re-
this postulation is further confusing to caregivers because of duced luminal area and of compressed lengths on individual
the fact that speed and volume differ: for most of the spectrum tubes may inform the development of complexly realistic mod-
of closure by compression, the former is increased while the els for understanding phenomena like limb flow in parallel.
latter remains the same. Speed and volume do not increase Another limitation is that the tube was unsupported in that
and decrease together as some caregivers thought. Therefore, normally surrounding tissues were absent. A supported tube
“flow,” whether as written in a document or as spoken in a might not buckle downstream, as was observed in this study.
first aid class, is ambiguous because its two meanings—speed A supported tube may have different outcomes than observed
and volume—are neither interchangeable nor understood presently regarding lengths of compression. If that is the case,
uniformly by caregivers. To us, first reactions of caregivers the length of the compression might have a significant effect
Collapsible Tube Model of Bleeding Control | 51

