2. Introduction
Anesthesia has significant influences on the heart and blood pressure.
The rationale for cardiovascular monitoring during anesthesia stems
from the realization that it may blunt appropriate autonomic responses
associated with procedural stresses.
Furthermore, if anesthesia is inadequate, the patient may respond with
potentially detrimental autonomic responses such as tachycardia and
hypertension.
Early detection of these cardiovascular changes may lead the
practitioner to intervene earlier and thus reduce the risk of
complications from these changes.
Published guidelines strongly agree that monitoring heart rate and
blood pressure decrease the likelihood of adverse outcomes related to
anesthesia.
3. What all do we monitor?
Pulse Rate and Heart Rate
Arterial Blood Pressure
Central Venous Pressure
Pulmonary Artery Catheter Monitoring
Cardiac Output
Electrocardiography
4. Pulse And Heart Rate
The distinction between heart rate and pulse rate is the difference
between electrical depolarization with systolic contraction of the heart
(heart rate) and a detectable peripheral arterial pulsation (pulse rate).
Many monitors report heart rate and pulse rate separately, the former
from the ECG trace and the latter from the pulse oximeter
plethysmograph or arterial blood pressure monitor.
In addition to indicating the pulse rate, this waveform may also provide
supplementary diagnostic clues to cardiovascular function.
Although monitoring both heart rate and pulse rate may seem
redundant, such redundancy is intentional, improves accuracy, and
reduces measurement errors and false alarms.
5. Arterial Blood Pressure
Monitoring
Like heart rate, arterial blood pressure is a fundamental cardiovascular
vital sign included in the mandated standards for basic anesthetic
monitoring.
Blood pressure is usually measured either by indirect cuff devices or
direct arterial cannulation with pressure transduction.
These techniques measure different physical signals and differ in their
degree of invasiveness.
The techniques can be broadly classified as
ā¦ Indirect
ā¦ Direct
6. Indirect Arterial Blood Pressure
Monitoring
Most indirect methods of arterial blood pressure measurement use a
sphygmomanometer, first described by Riva-Rocci in 1896.
A. Palpation
ā¦ SBP can be determined by locating a palpable peripheral pulse, inflating a
blood pressure cuff proximal to the pulse until flow is occluded, releasing
cuff pressure by 2 or 3 mm Hg per heartbeat, and measuring the cuff
pressure at which pulsations are again palpable.
ā¦ Tends to underestimate systolic pressure
ā¦ Does not provide a diastolic pressure or MAP.
7. B. Auscultation
ā¦ Detecting both systolic and diastolic pressure became possible with the
description of the auscultatory method of blood pressure measurement by
Korotkoff in 1905.
ā¦ The Korotkoff sounds are a complex series of audible frequencies produced by
turbulent flow beyond the partially occluding cuff.
ā¦ The pressure at which the first Korotkoff sound is heard is considered the systolic
pressure (phase I). The sound character progressively changes (phases II and III),
becomes muffled (phase IV), and is finally absent (phase V).
ā¦ DBP is recorded at phase IV or V (i.e., significant muffling or disappearance of the
sounds altogether).
ā¦ A well-fitted cuff has a bladder that extends to 40% of arm circumference and
80% of length of the upper arm. The cuff should be applied snugly and contain no
residual air, with the bladder centered over the artery.
ā¦ Although too large a cuff often provides acceptable results, the use of a cuff that
is too small usually results in falsely high readings.
8.
9. C. Doppler Probe
ā¦ When a Doppler probe is substituted for the anesthesiologistās finger, arterial
blood pressure measurement becomes sensitive enough to be useful in
obese patients, pediatric patients, and patients in shock.
ā¦ A Doppler probe transmits an ultrasonic signal that is reflected by underlying
tissue.
ā¦ As red blood cells move through an artery, a Doppler frequency shift will be
detected by the probe.
ā¦ The difference between transmitted and received frequency causes the
characteristic swishing sound, which indicates blood flow.
ā¦ Note that only systolic pressures can be reliably determined with the
Doppler technique.
10.
11. D. Oscillometry
ā¦ First described by Marey in 1876.
ā¦ Arterial pulsations cause oscillations in cuff pressure. These oscillations are
small if the cuff is inflated above systolic pressure. When the cuff pressure
decreases to systolic pressure, the pulsations are transmitted to the entire
cuff , and the oscillations markedly increase.
ā¦ Maximal oscillation occurs at the MAP, after which oscillations decrease.
Because some oscillations are present above and below arterial blood
pressure, a mercury or aneroid manometer provides an inaccurate and
unreliable measurement.
ā¦ Automated blood pressure monitors electronically measure the pressures at
which the oscillation amplitudes change. A microprocessor derives systolic,
mean, and diastolic pressures using an algorithm.
12.
13. ā¦ In general, automated NIBP measurements closely approximate directly
measured arterial pressure, especially at mean pressures of 75 mm Hg and
lower.
ā¦ Oscillometric methods often underestimate systolic and overestimate
diastolic measurements, significantly underestimating pulse pressure
calculations.
ā¦ These devices also tend to underestimate mean values during periods of
hypertension and overestimate during hypotension, potentially biasing
clinical decisions in unstable patients.
ā¦ Nonetheless, the speed, accuracy, and versatility of oscillometric devices
have greatly improved, and they have become the preferred noninvasive
blood pressure monitors worldwide.
14. E. Arterial Tonometry
ā¦ Arterial tonometry measures beat-to-beat arterial blood pressure by sensing
the pressure required to partially flatten a superficial artery that is supported
by a bony structure (eg, radial artery).
ā¦ A tonometer consisting of several independent pressure transducers is
applied to the skin overlying the artery. The contact stress between the
transducer directly over the artery and the skin reflects intraluminal
pressure.
ā¦ Continuous pulse recordings produce a tracing very similar to an invasive
arterial blood pressure waveform. Limitations to this technology include
sensitivity to movement artifact and the need for frequent calibration.
15.
16.
17. Direct Arterial Blood Pressure
Monitoring
Intra-arterial blood pressure (IABP) measurement is often considered to be
the gold standard of blood pressure measurement. Whilst not without risk,
it has a number of advantages over non-invasive blood pressure
measurement (NIBP):
ā¦ It allows continuous beat-to-beat pressure measurement, useful for the close
monitoring of patients whose condition may change rapidly, or those who require
careful blood pressure control; for example those on vasoactive drugs
ā¦ The waveforms produced may be analyzed, allowing further information about
the patientās cardiovascular status to be gained (pulse contour analysis)
ā¦ It may also be useful where NIBP measurement is difficult e.g. burns or obesity
ā¦ It reduces the risk of tissue injury and neuropraxias in patients who will require
prolonged blood pressure measurement
ā¦ It allows frequent arterial blood sampling
ā¦ It is more accurate than NIBP, especially in the extremely hypotensive or the
patient with arrhythmias.
18.
19. BASIC PRICIPLES
The commonly used IABP measuring systems consist of a column of
fluid directly connecting the arterial system to a pressure transducer
(hydraulic coupling).
The pressure waveform of the arterial pulse is transmitted via the
column of fluid, to a pressure transducer where it is converted into an
electrical signal.
This electrical signal is then processed, amplified and converted into a
visual display by a microprocessor.
20.
21. COMPONENTS OF AN IABP
MEASURING SYSTEM
Intra-arterial cannula
The arterial system is accessed using a short, narrow, parallel sided
cannula made of polyurethane or Teflonā¢ to reduce the risk of arterial
thrombus formation. Although non-ported venous cannulas can be
used, (non-ported to reduce the risk of inadvertent injection) there are
a number of specially designed arterial cannulas available.
The risk of arterial thrombus formation is directly proportional to the
diameter of the cannula, hence small-diameter cannulas are used (20-
22g), however, this may increase damping in the system.
The radial artery is the most commonly used site of insertion as it
usually has a good collateral circulation and is easily accessible.
22.
23. Fluid filled tubing
This is attached to the arterial cannula, and provides a column of
non-compressible, bubble free fluid between the arterial blood
and the pressure transducer for hydraulic coupling.
Ideally, the tubing should be short, wide and non-compliant (stiff)
to reduce damping ā extra 3-way taps and unnecessary lengths of
tubing should be avoided where possible. This tubing should be
color coded or clearly labelled to assist easy recognition and
reduce the risk of intra-arterial injection of drugs.
A 3-way tap is incorporated to allow the system to be zeroed and
blood samples to be taken.
24.
25. Transducer
Fluid in the tubing is in direct contact with a flexible diaphragm, which
in turn moves strain gauges in the pressure transducer, converting the
pressure waveform into an electrical signal.
26. Infusion/flushing system
A bag of either plain 0.9% saline or heparinized 0.9% saline is
pressurized to 300mmHg and attached to the fluid filled tubing via a
flush system.
This allows a slow infusion of fluid at a rate of about 2-4ml/hour to
maintain the patency of the cannula.
A flush system will also allow a high-pressure flush of fluid through the
system in order to check the damping and natural frequency of the
system (see below) and to keep the tubing clear.
27. Signal processor, amplifier and display
The pressure transducer relays its electrical signal via a cable to a
microprocessor where it is filtered, amplified, analyzed and displayed on
a screen as a waveform of pressure vs. time.
Beat to beat blood pressure can be seen and further analysis of the
pressure waveform can be made, either clinically, looking at the
characteristic shape of the waveform, or with more complex systems,
using the shape of the waveform to calculate cardiac output and other
cardiovascular parameters.
28.
29. PHYSICAL PRINCIPLES
Sine Waves
A wave is a disturbance that travels through a medium, transferring
energy but not matter. One of the simplest waveforms is the sine wave
(Fig. 1). These may be thought of as the path of a point travelling round
a circle at a constant speed and are defined by the function y = sin x.
30. Sine waves may be described in terms of their
ā¦ amplitude ā their maximal displacement from zero,
ā¦ Frequency, which is the number of cycles per second (expressed as Hertz or
Hz),
ā¦ their wavelength, which is the distance between two points on the wave
which have the same value (e.g. two crests or troughs)
ā¦ their phase, which is the displacement of one wave as compared with
another ā expressed as degrees from 0 to 360.
Sine waves are of particular importance as any waveform may be
produced by combining together sine waves of differing frequency,
amplitude and phase. Another way of looking at this is that any complex
wave can be broken down into a number of different sine waves.
31. Fourier Analysis
The arterial waveform is clearly not a simple sine wave as described above, but it can be
broken down into a series of many component sine waves.
The arterial pressure wave consists of a fundamental wave (the pulse rate) and a series of
harmonic waves. These are smaller waves whose frequencies are multiples of the
fundamental frequency (e.g. if the fundamental frequency is 1Hz, you would see harmonic
waves with frequencies of 2Hz, 3Hz, 4Hz and so on.).
The process of analysing a complex waveform in terms of its constituent sine waves is
called Fourier Analysis.
In the IABP system, the complex waveform is broken down by a microprocessor into its
component sine waves, then reconstructed from the fundamental and eight or more
harmonic waves of higher frequency to give an accurate representation of the original
waveform.
The IABP system must be able to transmit and detect the high frequency components of
the arterial waveform (at least 24Hz) in order to represent the arterial pressure wave
precisely. This is important to remember when considering the natural frequency of the
system.
32.
33. Natural Frequency & Resonance
Every material has a frequency at which it oscillates freely. This is called its natural
frequency.
If a force with a similar frequency to the natural frequency is applied to a system, it
will begin to oscillate at its maximum amplitude. This phenomenon is known as
resonance.
If the natural frequency of an IABP measuring system lies close to the frequency of
any of the sine wave components of the arterial waveform, then the system will
resonate, causing excessive amplification, and distortion of the signal. In this case, an
erroneously wide pulse pressure and elevated systolic blood pressure would result.
It is thus important that the IABP system has a very high natural frequency ā at least
eight times the fundamental frequency of the arterial waveform (the pulse rate).
Therefore, for a system to remain accurate at heart rates of up to 180bpm, its natural
frequency must be at least: (180bpm x 8) / 60secs = 24Hz.
34. The natural frequency of a system is determined by the properties of its
components. It may be increased by:
ā¦ Reducing the length of the cannula or tubing
ā¦ Reducing the compliance of the cannula or diaphragm
ā¦ Reducing the density of the fluid used in the tubing
ā¦ Increasing the diameter of the cannula or tubing
Most commercially available systems have a natural frequency of around
200Hz but this is reduced by the addition of three-way taps, bubbles, clots
and additional lengths of tubing. The natural frequency of a system may be
measured in the clinical setting using the āfast flushā test.
The system is flushed with high-pressure saline via the flush system. This
generates an undershoot and overshoot of waves, resonating at the natural
frequency of the system. This frequency may be calculated by dividing the
paper or screen speed by the wavelength.
35.
36. Damping
Anything that reduces energy in an oscillating system will reduce the
amplitude of the oscillations. This is termed damping.
Some degree of damping is required in all systems (critical damping), but if
excessive (overdamping) or insufficient (underdamping) the output will be
adversely effected.
In an IABP measuring system, most damping is from friction in the fluid
pathway. There are however, a number of other factors that will cause
overdamping including:
ā¦ Three way taps
ā¦ Bubbles and clots
ā¦ Vasospasm
ā¦ Narrow, long or compliant tubing
ā¦ Kinks in the cannula or tubing
37. These may be a major source of error, causing an under-reading of systolic
blood pressure (SBP) and overreading of diastolic blood pressure (DBP)
although the mean blood pressure is relatively unaffected.
Damping also causes a reduction in the natural frequency of the system,
allowing resonance and distortion of the signal.
Whilst care must be taken to avoid overdamping, underdamping may also
pose problems. In an underdamped system, one sees an overshoot of the
pressure waves ā with excessively high SBP and low DBP, as in a resonant
signal. A compromise between over and under-damping must be therefore
be found.
If a brief burst of energy is applied to a critically damped system, for
example quickly flushing an IABP system, after displacement, the wave
returns to the baseline, without any overshoot. Critical damping is therefore
defined as the minimal amount of damping required to prevent any
overshoot. The damping co-efficient in a critically damped system is 1.
However, this does result in a system that is relatively slow to respond.
38.
39.
40. Transducers
A transducer is any device that converts energy from one form into another
and are usually used for measurement or monitoring. Pressure transducers
are used in IABP systems. These convert the arterial pressure waveform into
an electrical signal that can then be measured, processed and displayed.
The arterial pulse pressure is transmitted via the column of fluid in the
tubing to a flexible diaphragm, displacing it. This displacement can then be
measured in a number if different ways. The commonest method is with a
strain gauge.
Strain gauges are based on the principle that the electrical resistance of
wire or silicone increases with increasing stretch. The flexible diagram is
attached to wire or silicone strain gauges and then incorporated into a
Wheatstone bridge circuit in such a way that with movement of the
diaphragm the gauges are stretched or compressed, altering their
resistance.
41. The Wheatstone Bridge
The Wheatstone bridge is a circuit designed to measure unknown
electrical resistance.
42. Newer Wheatstone bridge setups use strain gauges in all four positions.
The diaphragm is attached in such a way that when pressure is applied
to it, gauges on one side of the Wheatstone bridge become
compressed, reducing their resistance, whilst the gauges on the other
side are stretched, increasing their resistance.
The bridge then becomes unbalanced and the potential difference
generated is proportional to the pressure applied. This setup of four
strain gauges has the advantage that it is four times more sensitive than
a single gauge Wheatstone bridge.
It also compensates for any temperature change as all of the strain
gauges are affected equally.
43. Zeroing
For a pressure transducer to read accurately, atmospheric pressure
must be discounted from the pressure measurement.
This is done by exposing the transducer to atmospheric pressure and
calibrating the pressure reading to zero.
At this point, the level of the transducer is not important. A transducer
should be zeroed several times per day to eliminate any baseline drift.
44.
45. Levelling
The pressure transducer must be set at the appropriate level in relation
to the patient in order to measure blood pressure correctly. This is
usually taken to be level with the patientās heart, at the 4th intercostal
space, in the mid-axillary line.
Failure to do this results in an error due to hydrostatic pressure (the
pressure exerted by a column of fluid ā in this case, blood) being
measured in addition to blood pressure.
This can be significant ā every 10cm error in levelling will result in a
7.4mmHg error in the pressure measured; a transducer too low over
reads, a transducer too high under reads.
46. SELECTION OF ARTERY FOR
CANNULATION
The radial artery is commonly cannulated because of its superficial
location and substantial collateral flow. Allenās test is a simple, but not
reliable, method for assessing the safety of radial artery cannulation.
Other sites are :
ā¦ Ulnar artery
ā¦ Brachial artery
ā¦ Femoral artery
ā¦ Dorsalis pedis artery
ā¦ Posterior tibial artery
ā¦ Axillary artery.
49. The bedside monitor displays values for the peak systolic and
end-diastolic nadir pressures. MAP is dependent on the algorithm
used by the monitor. In simplest terms, MAP is equal to the area
beneath the arterial pressure curve divided by the beat period,
averaged over multiple cardiac cycles.
As the pressure wave travels from the central aorta to the
periphery, the arterial upstroke becomes steeper, the systolic
peak increases, the dicrotic notch appears later, the diastolic
wave becomes more prominent, and end-diastolic pressure
decreases.
As a result, compared with central aortic pressure, peripheral
arterial waveforms have higher systolic, lower diastolic, and
wider pulse pressures.
50.
51.
52.
53. Aortic stenosis
It produces a fixed obstruction to ejection resulting in reduced stroke volume and a
slowed rate of ejection. As a result, the waveform is small in amplitude (pulsus parvus),
and has a slowly rising systolic upstroke on the arterial pressure waveform and a
delayed peak in systole (pulsus tardus)
54. Aortic regurgitation
The arterial pressure wave displays a sharp increase, wide pulse pressure, and
decreased diastolic pressure owing to the runoff of blood into both the left ventricle
and the periphery during diastole. The arterial waveform may have two systolic peaks
(bisferiens pulse), with the first peak resulting from antegrade ejection and the second
from a reflected wave originating in the periphery
55. Hypertrophic cardiomyopathy
The arterial pressure waveform assumes a peculiar bifid shape termed a spike-and-
dome configuration. After an initial sharp blood pressure increase resulting from rapid,
early systolic ejection, arterial pressure plummets as left ventricular outflow
obstruction in mid-systole impedes ejection. This is finally followed by a second, late-
systolic increase associated with arrival of reflected waves from the periphery
56. Systolic left ventricular failure
Pulsus alternans is a pattern of alternating beats of larger and smaller pulse pressures
that also vary with the respiratory cycle although its underlying mechanism remains
poorly understood
57. Cardiac tamponade
Pulsus paradoxus is exaggerated variation in arterial pressure (<10 to 12 mm Hg) during
quiet breathing. It is highly characteristic, almost universal, in patients with cardiac
tamponade but may also develop with pericardial constriction, severe airway
obstruction, bronchospasm, dyspnea, or any condition that involves large swings in
intrathoracic pressure.
58.
59. Central Venous Pressure Monitoring
Cannulation of a central vein and direct measurement of central venous pressure (CVP)
are frequently performed in hemodynamically unstable patients and those undergoing
major operations.
The central venous pressure (CVP) measures the filling pressure of the right ventricular
(RV); it gives an estimate of the intravascular volume status and is an interplay of the
ā¦ (1) circulating blood volume
ā¦ (2) venous tone and
ā¦ (3) right ventricular function.
Central venous cannulation involves introducing a catheter into a vein so that the
catheterās tip lies with the venous system within the thorax.
Generally, the optimal location of the catheter tip is just superior to or at the junction of
the superior vena cava and the right atrium. When the catheter tip is located within the
thorax, inspiration will increase or decrease CVP, depending on whether ventilation is
controlled or spontaneous.
Measurement of CVP is made with a water column (cm H2O), or, preferably, an electronic
transducer (mm Hg). The pressure should be measured during end expiration.
60.
61.
62. The sites and techniques for placing central venous catheters are numerous.
Cannulation of internal jugular vein (IJV) was first described by English et al
in 1969. Since then, it has steadily increased in popularity to its present
position as one of the methods of choice for CVP/RAP monitoring.
The reason for this popularity relates to its landmarks; itās short, straight
(right IJV), valveless course to the superior vena cava (SVC) and right atrium
(RA); and its position at the patientās head, which provides easy access by
anesthetists in more intra operative settings. Further, the success rate for its
use exceeds 90% in most series of adults and children.
For accurate measurement of CVP/RAP and also to aid aspiration of air in
venous air embolism, the catheter tip is positioned ideally at the SVC-RA
junction, SVC, or high up in the RA, away from the tricuspid valve.
Cannulation of the IJV is relatively safe and convenient and various
approaches exist for its cannulation.
63.
64.
65. CVP Recording
CVP is usually recorded at the mid-axillary line where the manometer
arm or transducer is level with the phlebostatic axis. This is where the
fourth intercostal space and mid-axillary line cross each other allowing
the measurement to be as close to the right atrium as possible.
For example, in this fig,the paper speed is 25mm/sec and the wavelength of the resonant waves is 1mm so the natural frequency is 25/1 = 25Hz ā just acceptable.
The 1st figure is a trace from an overdamped IABP system. The damping coefficient is >1. This system will not oscillate freely and detail such as the dichrotic notch will be lost. It will not overshoot but will tend to under-read SBP and over-read DBP. It will be slow to respond to change due to the frictional drag in the system.
The 2nd figure is a trace from an underdamped IABP system. The damping coefficient is <0.7. This system will be quick to respond but will tend to overshoot and oscillate around its resting point, over-reading SBP and under-reading DBP.
The 3rd figure is a trace from an optimally damped system. The damping co-efficient will be around 0.7, which provides the best balance between speed of response and accuracy.
The damping co-efficient of a system can also be measured clinically using the fast flush test. Following a system flush, the amplitude ratio of two consecutive resonant waves are calculated by dividing the smaller ratio by the larger. The respective damping co-efficient is then taken from the chart shown. In the example shown, the amplitude ratio is 0.31 (2.5/8), giving a damping co-efficient of 0.36, meaning that this system is underdamped.
Classically, these were arranged with three resistors of known resistance and one of variable resistance (the strain gauge). When the ratio of the resistors on the known side of the circuit (R2/R1) equals the ratio on the other side of the circuit (R3/Rx) the bridge is balanced, no current will flow and no potential difference will be measured by the galvanometer (VG).
When the resistance of the strain gauge (Rx) changes due to pressure applied to the attached diaphragm, the two sides of the bridge become unbalanced and a current flows. The resulting potential difference is measured by the galvanometer and is proportional to the magnitude of the pressure applied.
In this test, the patient exsanguinates his or her hand by making a fist. While the operator occludes the radial and ulnar arteries with fingertip pressure, the patient relaxes the blanched hand. Collateral flow through the palmar arterial arch is confirmed by flushing of the thumb within 5 sec after pressure on the ulnar artery is released. Delayed return of normal color (5ā10 s) indicates an equivocal test or insufficient collateral circulation (>10 s). The Allenās test is of questionable utility.
Alternatively, blood flow distal to the radial artery occlusion can be detected by palpation, Doppler probe, plethysmography, or pulse oximetry. Unlike Allenās test, these methods of determining the adequacy of collateral circulation do not require patient cooperation.
A : Proper positioning and palpation of the artery are crucial. Supination and extension of the wrist provide optimal exposure of the radial artery. After skin preparation, local anesthetic is infiltrated with a 25-gauge needle.
B: A 20- or 22-gauge catheter is advanced through the skin at a 45Ā° angle.
C: Flashback of blood signals entry into the artery, and the catheterā needle assembly is lowered to a 30Ā° angle and advanced 1ā2 mm to ensure an intraluminal catheter position.
D: The catheter is advanced over the needle, which is withdrawn.
E: Proximal pressure with middle and ring fingers prevents blood loss, while the arterial tubing Luer-lock connector is secured to the intraarterial catheter.
The systemic arterial pressure waveform results from ejection of blood from the left ventricle into the aorta during systole, followed by peripheral runoff during diastole.
The systolic waveform components consist of a steep pressure upstroke, peak, and ensuing decline, and immediately follow the ECG R wave. The downslope of the arterial pressure waveform is interrupted by the dicrotic notch, continues its decline during diastole after the ECG T wave, and reaches its nadir at end diastole
As the pressure wave travels from the central aorta to the periphery, the arterial upstroke becomes steeper, the systolic peak increases, the dicrotic notch appears later, the diastolic wave becomes more prominent, and end-diastolic pressure decreases. As a result, compared with central aortic pressure, peripheral arterial waveforms have higher systolic, lower diastolic, and wider pulse pressures.
*= in these cases, the internal jugular vein on the contra lateral side should be considered. It should be remembered that the thoracic duct lies in close proximity
to the left IJV11 and that laceration of the left brachio-cephalic vein or superior vena cava by the catheter is more likely with the left-sided IJV approach to the central circulation.
Mechanical events during the cardiac cycle are responsible for the sequence of waves seen in a typical CVP trace. The CVP waveform consists of five phasic events: three peaks (a, c, v) and two descents (x, y).