21. Cerebrovascular time constant
Thanks to Dr.M.Kasprowicz
What is cerebrovascular time constant ?
 time to fill cerebral arterial bed with blood volume after a
sudden change in ABP during one cardiac cycle
ABP
τ = Ca  CVR [s]
CBFV
EtCO2
CaBV
Sa  AmpCaBV
Amp ABP
meanABP
meanCBFV  Sa
Kim DJ, Kasprowicz M, Carrera E, Castellani G, Zweifel C, Lavinio A,
Czosnyka M, Piechnik S, Richards HK, Kirkpatrick P,
Smielewski P, Sutcliffe MP, Pickard JD, Czosnyka M.
Smielewski P, Pickard JD.
The monitoring of relative changes in compartmental compliances of Contribution of mathematical modelling to the interpretation of bedside tests of
brain.
cerebrovascular autoregulation.
Physiol Meas. 2009 Jul;30(7):647-59
J Neurol Neurosurg Psychiatry. 1997, 63(6):721-31
Thanks to Dr.M.Kasprowicz
• Volunteers (35 young normals- students’ project)
Thanks to Dr.M.Kasprowicz
Carotid Artery stenosis study: Material
1. 25 patients with ICA stenosis
(20 males and 5 females, median age: 62 years)
• 16 patients with unilateral ICA stenosis
(median stenosis 84.5%, range 50-100% on one side)
• 9 patients with bilateral ICA stenosis
(median stenosis 95%, range 50-100% on both sides)
2. 11 healthy volunteers
(8 males and 3 females, median age: 21 years)
Thanks to Dr.M.Kasprowicz
Thanks to Dr.M.Kasprowicz
Response to changes in CO2
normal subject
[mmHg]
ABP
mmHg
cm/s
[cm/s]
FV
kPa
[kPa]
EtCO2
s
[s]
TAU
CVRCa
CVR Ca
Thanks to Dr.M.Kasprowicz
Response to changes in CO2
unilateral ICA stenosis
ANOVA, p<0.002
ANOVA, p<0.009
p<0.006
0.28
0.28
p<0.003
p<0.0007
0.26
0.24
0.24
0.22
0.22
 [s]
 [s]
0.26
0.20
0.20
0.18
0.18
0.16
0.16
0.14
normocapnia
hypocapnia
hypercapnia
ipsilateral side
p<0.03
0.14
normocapnia
hypocapnia
hypercapnia
contralateral side
Thanks to Dr.M.Kasprowicz
Response to changes in CO2
unilateral ICA stenosis
p<0.004
p<0.001
p=0.001
0.28
0.26
0.26
0.24
0.24
0.22
0.22
 [s]
 [s]
0.28
0.20
0.20
0.18
0.18
0.16
0.16
0.14
normocapnia
hypocapnia
hypercapnia
ipsilateral side
0.14
normocapnia
hypocapnia
hypercapnia
contralateral side
Thanks to Dr.M.Kasprowicz
Response to changes in CO2
bilateral ICA stenosis
ANOVA, p=0.00002
0.28
p<0.00005
0.26
0.24
 [s]
0.22
0.20
0.18
0.16
0.14
0.12
p<0.00002
0.10
normocapnia
hypocapnia
hypercapnia
Thanks to Dr.M.Kasprowicz
Baseline: comparison of patients &controls
0.28
ANOVA, p=0.011
0.26
0.24
p=0.009
 [s]
0.22
0.20
0.18
0.16
p=0.035
0.14
p=0.003
0.12
controls
contra
ipsi
unilateral stenosis
bilateral
stenosis
Thanks to Dr.M.Kasprowicz
 and degree of stenosis
0.28
0.26
 [s]
0.24
0.21
0.19
0.18
0.16
0.14
0.12
0.10
0.08
R=-0.62 p<0.001
0.06
40
50
60
70
80
90
degree of stenosis [%]
100
110
Experimenta study: Increase in PaCO2
TAU: CVRa=CPP/FV
ABP
FV
CPP
ICP
Ca
CVR
CVRa
TAU
TAUa
TAUa: CVRa= ABP/FV
Change in PaCO2 (at normal ICP and normal ABP), 0- hypocania, 1-normocapnia 2hypercapnia. How ‘primary variables react to PaCO2?
Reduction of ABP
ABP
FV
CPP
ICP
Ca
CVRa
TAUa
Haemorrhagic hypotension
ABP
FV
Ca
CVRa
TAUa
Arterial hypertension
ABP
FV
Ca
CVRa
TAUa
TAU2: CVRa=CPP/FV
ABP
FV
TAUa: CVRa= ABP/FV
CPP
ICP
Ca
CVR
CVRa
TAU
TAUa
Controlled increase in ICP
SUMMARY LOOKS LIKE THAT:
ABP
: TAU
(CVR
ICP
: TAU
(CVR
PaCO2
: TAU
(CVR
, Ca
, Ca
, Ca
)
)
)
Thanks to Dr.M.Kasprowicz
HI –ABP drop - 
T-test, dependent samples p=0.000003
106
104
Mean
±SE
T-test, dependent samples p=0.89
±0.95 Conf. Interval
102
100
0.19
98
ABP [mm Hg]
96
±SE
Mean
94
92
±0.95 Conf. Interval
0.18
90
88
86
84
0.17
82
80
76
ABP baseline
ABP decrease
T-test, dependent samples p=0.000005
90
Mean
±SE
±0.95 Conf. Interval
 [sec]
78
0.16
0.15
85
0.14
CPP [mm Hg]
80
75
0.13
70
b
0.12
65
baseline
60
55
baseline
ABP drop
ABP drop
c
Arterial hypotension- TBI
ABP
FV
CPP
ICP
Ca
CVR
CVRa
TAU
TAUa
Thanks to Dr.M.Kasprowicz
HI -Hypocapnia - 
T-test, dependent samples p=0.000075
0.180
0.175
0.170
0.165
 [sec]
0.160
0.155
0.150
0.145
0.140
b
0.135
c
0.130
baseline
hypocapnia
Thanks to Dr.M.Kasprowicz
Plataeu waves-
Friedman Anova p<0.62
0.22
0.21
 [sec]
0.20
0.19
0.18
0.17
0.16
Plataeu wave
0.15
baseline
a
b
c
b
baseline
a
c
Individual tracing: plateau wave
ABP CPP
FV
ICP
Ca
CVR
CVRa
TAU
TAUa
Stroke- Freiburg
• 44 patients tested 1st day after recanalization
and day 5th after recanalization (2)
• NIH score, infarct volume, outcome (mRelkin
score)
Thanks to Dr. M.Reinhard
Thanks to Dr. M.Reinhard
Thanks to Dr. M.Reinhard
Thanks to Dr. M.Reinhard
Thanks to Dr.M.Kasprowicz
SAH study: Material
1. 13 patients with vasospasm after SAH
(7 males and 6 females, median age: 48 years)
2. cerebral vasospasm was detected by TCD
mean CBFV in MCA>120 [cm/s]
Lindegaard ratio (CBFVMCA/CBFVICA)>3
and confirmed by angiography
3. all patients received triple-H therapy
Thanks to Dr.M.Kasprowicz
Thanks to Dr.M.Kasprowicz
Thanks to Dr.M.Kasprowicz
Messages to take home:
•TAU conceptually shows how fast brain arterial blood volume settles after step change
in ABP
•It has units! Therefore comparison between patients is possible
•TAU decreases with hypercapnia and increases with hypocapnia
•TAU increases in arterial hypotension
•TAU decreases during vasospasm
•TAU is longer in diabetic patients?
•TAU increases with infarct size in patients after stroke?