SME
Human Anatomy & Physiology
Nervous system
Use this for “Sensory and motor axons are 1 m each and conduct at 60 m/s, with two 0.5 ms synapses. How long is the reflex?”
Diagram
t
=
1,000L
v
+
kδ
=
33.33
+
2
×
0.5
t = 34.33 ms
Each synapse adds its delay while the signal crosses the cleft as a chemical; the axons carry it the rest of the way.
This is an example. Type your own values to start a new problem.
Lₛ
Sensory axon length
example · m
Lₘ
Motor axon length
example · m
v
Conduction speed
example · m/s
k
Synapses
example
δ
Delay per synapse
example · ms
t
Reflex time
calculated · ms
L
Path length
worked out (not typed) · m
tc
Conduction time
worked out (not typed) · ms
Formulas
L
=
Lₛ
+
Lₘ
2 = 1 + 1
tc
=
L
v
×
1,000
33.3333
=
2
60
×
1,000
t
=
tc
+
k
×
δ
34.3333 = 33.3333 + 2 × 0.5
Assumptions
•
The impulse runs up the sensory axon to the spinal cord and back down the motor axon, both at speed v.
•
k counts the synapses in the spinal cord: 1 in the knee-jerk reflex, 2 with one interneuron between.
•
Each synapse adds a delay δ of about 0.5 ms while the transmitter crosses the gap.
•
Myelinated axons conduct at about 10–120 m/s, thin bare ones at 0.5–2 m/s; time in the receptor and muscle is left out.
Step-by-step
WE KNOW
Lₛ = 1 m, Lₘ = 1 m, v = 60 m/s, k = 2, δ = 0.5 ms
FIND
path length (L), conduction time (tc), reflex time (t)
Step 1 · Find path length (L)
Use L = Lₛ + Lₘ
The impulse travels in to the spinal cord and back out to the muscle.
L
=
1
+
1
L
=
2
m
Step 2 · Find conduction time (tc)
Use tc = L ÷ v × 1,000
Distance
speed
is
the
time
in
seconds;
1,000
times
that
is
the
time
in
ms.
tc
=
2
60
×
1,000
tc = 0.03333 × 1,000
tc = 33.3333 ms
Step 3 · Find reflex time (t)
Use t = tc + k × δ
Add the delay at each synapse to the time on the axons.
t
=
33.3333
+
2
×
0.5
t
=
33.3333
+
1
t
=
34.3333
ms
Check
Put the numbers back in. Both sides should match.
2 = 1 + 1 ✓
33.3333
=
2
60
×
1,000
✓
34.3333 = 33.3333 + 2 × 0.5 ✓
Topic check
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