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1 Biophysics Laboratory, Institute of Physics, Academia Sinica, Nankang, Taipei, Taiwan 11529, ROC 2 Electrical Engineering Department, National Taiwan University, Taipei, Taiwan, ROC 3 Department of Electrical Engineering, Yuan Ze University, Taoyuan, Taiwan, ROC 4 Department of Physics, National Taiwan Normal University, Taipei, Taiwan, ROC
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Abstract |
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(Received 13 July 2005;
accepted after revision 3 October 2005; first published online 6 October 2005)
Corresponding author Y. Y. L. Wang: Biophysics Laboratory, Institute of Physics, Academia Sinica, Nankang, Taipei, Taiwan 11529, ROC. Email: yuhying{at}phys.ntnu.edu.tw
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Introduction |
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Resonance theory
The pattern of harmonic components of the arterial-bed-specific pulse spectrum might be suitable for analysing the behaviour of the vascular bed. According to resonance theory (Wang et al. 1991; Yu et al. 1994; Jan et al. 2003), each arterial bed in the vascular system is forced to oscillate by pressure waves at its own resonant frequency. As the physical properties of an arterial bed change, its resonant frequencies will also vary. However, the same resonance harmonics will be maintained by the heart rate (HR) control system to minimize energy loss (Jan et al. 2003). The amplitudes of the resonance harmonics change more than other harmonics. Since the pulse spectrum is the combined result of the influence from all arterial beds, we may therefore deconstruct it into components that relate to specific arterial beds.
Evidence for arterial-bed-specific harmonic components of the pulse spectrum
Farrow & Stacy (1961) found that clamping the femoral artery produced large variations in only the third harmonic of the pressure wave, and Wiener et al. (1966) reported that the pulmonary circulation had the strongest effect on the fourth harmonic. Wang et al. (1989) and Young et al. (1989, 1992) reported that ligating the renal, gastric, splenic or superior mesenteric artery for a very short duration (less than 3 s) caused specific changes to individual harmonics. Young et al. (1989) further proved that the organ ligation effects were linearly additive; ligating two different arterial beds simultaneously (the renal artery and the superior mesenteric artery) changed the pulse spectrum in a similar manner to the direct addition of the two spectra resulting from individual ligations. This suggests that these linearly additive organ ligation spectra can be used as independent parameters to elucidate the physical status of specific vascular beds.
Organ ligation spectra and regional drug selectivity
The regional drug selectivity of different vascular beds is an important issue in pharmaceutics. Traditional methods of evaluation require both blood pressure and flow data. Often this involves highly invasive surgery in order to place several probes on different arteries of the test subject, which certainly disturbs the circulatory system. However, the artefacts may be greatly reduced if the regional selectivity could be revealed by performing pressure measurements only. Since the effect of ligation can be regarded as a huge increase in the resistance of the ligated vascular bed, increase in vascular resistance during vessel constriction can be considered to be equal to ligating the arterial bed by a certain amount. The potential of using variations in organ ligation spectra as reference parameters to study the regional selectivity of vasoconstrictors was examined in this study.
Simulation method
The chemical ligation effects of two potent vasoconstri-ctors, arginine vasopressin (AVP) and angiotensin II (Ang II), were studied. These two vasoconstrictors reportedly exhibit different selectivities between the renal and mesenteric vascular beds (Hellebrekers et al. 1990; Jackson & Herzer, 2001). We simulated the drugs that affected pulse spectra by combining the effects of renal artery ligation and superior mesenteric artery ligation in different ratios. The best ratio (with the least mean square difference) was obtained by computer analysis, and the associated regional drug selectivity was compared with results obtained by traditional methods (Hellebrekers et al. 1990; Jackson & Herzer, 2001).
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Methods |
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The investigation conforms with the "Guide for the Care and Use of Laboratory Animals" published by the US National Institute of Health. Male Wistar rats weighing between 240 and 320 g were obtained from the Experimental Animal Center of National Taiwan University, Taipei, Taiwan. The animals were housed in our animal care facility with a 12 h:12 h light–dark cycle for at least 1 week before experiments were conducted. They received water and food ad libitum (Labdiet 5001 Rodent diet, PMI Nutrition International, Brentwood, MO, USA) prior to the experiments.
The rats were divided into three experimental groups: AVP infusion (5 pmol min–1, n = 14), Ang II infusion (20 pmol min–1, n = 10) and saline infusion (control group, 5 µl min–1, n = 9). Both drugs were dissolved in saline, with the doses chosen so that the two drugs would induce the same increase in DP after 1 h of continuous infusion at a rate of 5 µl min–1. AVP and Ang II were purchased from Sigma (St Louis, MO, USA).
The rats were anaesthetized with urethane only (1.1 g kg–1 2 ml–1 in saline, I.P.) (Sigma, St Louis, MO, USA) with a heat pad to keep the body temperature. The femoral vein was exposed through an inguinal incision and a polyethylene cannula (PE-10, PE-10 I.D. 0.28 mm, O.D. 0.61 mm) was inserted. Drugs were infused through the polyethylene tubing at the doses mentioned above, at a rate of 5 µl min–1 using a pump (Gilson minipuls 2, Gilson Medical Electronics, Middleton, WI, USA). The tail artery was cannulated with an intravenous catheter (Angiocath Plus, 22 GA needle size, 1.00 IN needle length, 0.9 x 25 mm, Becton-Dickinson, Seoul Korea) filled with physiological saline and heparin 1.5 kg g–1 2 ml–1 in saline, which was then connected to a pressure transducer (P10EZ, Ohmeda, Singapore). The cannulation opening on the tail artery was about 1 cm from the anus. The aortic blood pressure pulse then passed through the catheter tip (25 mm from the opening) to the pressure transducer.
After all recording procedures had been completed, the rats were killed by overdose urethane.
Recording procedure
The pressure signal was sent to a preamplifier (Universal amplifier, Gould Instrument Systems, Valley View, OH, USA) and then to a 16 bit A–D converter PC interface card (AX5621, Axiom Technology, Hsin Tien, Taiwan) for data analysis.
After all of the operations were completed, at least 3 h was allowed for stabilization. A 1 s data sequence (5–8 pulses) was sampled every minute, with 20 data sequences (about 140 pulses) being recorded over 20 min as self-controlled data. Three criteria were employed to ensure that the control data sampling was sufficiently accurate, representative and stable: the coefficients of variance (CV, S.D./mean) of the HR, the DP and the amplitudes of the first two harmonics of the pressure wave were all required to be less than 2%. Where the CV values exceeded this limit, the animal was considered unstable and data were discarded.
After the control period, drug or saline was infused continuously into the femoral vein at a rate of 5 µl min–1 (AVP at 5 pmol min–1, Ang II at 20 pmol min–1) for 1 h. The effects during and 1 h after drug infusion (two sets of 60 1 s pulse sequences) were recorded.
Data analysis
Since we were mainly interested in the relative amplitudes of each harmonic in the blood pressure spectrum, only the pulsatile parts of the pressure waves were calculated. We separated each pulse in a pressure wave sequence at its two lowest points (the place where two neighbouring SP waves started). Every isolated pulse was then Fourier transformed into the frequency domain. For each pressure pulse, the amplitude An (for harmonics n = 1–6) was normalized by the mean level of the pulse A0, and the harmonic proportions (HPs) for each harmonic Cn were calculated as percentages using Cn = 100(An/A0).
The entire experiment was divided into seven time periods, each with 20 1 s pulse sequences: the self-controlled period (from –20 to 0 min), three drug-infusion periods (0–20, 20–40 and 40–60 min) and three after-drug periods (60–80, 80–100 and 100–120 min). We defined the drug effect as the percentage difference in the proportion of the nth harmonic:
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Since the amplitudes decreased rapidly with the harmonic number, we considered only the first six harmonics (i.e. n = 1–6).
Statistical analysis
Student's paired t test was used for statistical comparisons. The drug effects on the HP, DP, SP and HR during and after drug infusion were compared with the control values. The drug effects were considered to be significantly different from the control values if P < 0.001. For HP, the averaged %Diff_HP values were considered to be significantly different from zero if P < 0.001.
Analyses of variance were not performed because differences between groups were not of interest in this study.
Chemical ligation simulation
The superior mesenteric artery ligation effects (%Diff_HP)m and the single-side renal artery ligation effects (%Diff_HP)r reported by Young et al. (1989) were combined at different ratios (Rr and Rm) to simulate the effects of AVP and Ang II, respectively, according to the following equation:
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The summation of the square of the difference (SSD) between (%Diff_HP)drug and (%Diff_HP)combined was calculated for the first to the sixth harmonic as:
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The best simulation effect was obtained by computer searching for the minimum value of SSD with both Rr and Rm ranging from 0 to 10 in 0.01 increments.
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Results |
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Angiotensin II caused significant decreases in C3, C4 and C5 during the three drug-infusion periods. These effects diminished soon after the drug infusion was stopped. It is also evident that the effect on C2 increased with the infusion time. The effects became significantly different from zero from the 40–60 min time period until the end of the experiments. The characteristics of the variations in the spectrum faded after the infusion of vasoconstrictors.
In Fig. 4, the experimental effect of drugs and the simulated chemical ligation effects are plotted against the blood pressure spectrum; the two curves are similar. %Diff_HP decreases with the harmonic number for Ang II curves, whereas a relative peak at the third harmonic and a minimum at the fifth harmonic are evident for AVP.
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Discussion |
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This study demonstrates that variations in the harmonics of the pulse spectrum can be used to identify the vasoconstrictor affected internal organs. Using only the pressure spectrum, we found that the effects of Ang II can be attributed to renal artery ligation (Young et al. 1989, 1992; Wang Lin et al. 1991; Jan et al. 2003), whereas AVP is more likely to affect both the renal and superior mesenteric arteries (Young et al. 1992). The best-fit ligation ratio for Ang II (Fig. 4) indicates that it induced a resistance change of about 20% from each kidney but had little effect on the superior mesenteric vascular resistance. In contrast, AVP induced a resistance change of about 50% from each kidney as well as 4.7 % in the superior mesenteric bed.
In this preliminary study, we minimized the anaesthetic dosage and avoided possible surgical interference to the blood pressure spectrum. We did not measure the local vascular resistance, but instead compared our data with the distinct regional vascular selectivity studies on AVP and Ang II by Jackson & Herzer (2001). They reported that intravenous infusion of AVP caused similar increases in the vascular resistance in renal, mesenteric, carotid, hindquarter and other tissues. Angiotensin II, however, caused a noticeable increase in renal vascular resistance, with lesser effects on mesenteric vascular resistance, little effect on carotid vascular resistance, and no effect on hindquarter or other tissue vascular resistance. Similar effects in dogs have been reported by Hellebrekers et al. (1990). These reports coincide well with our data and support our claim that the effects of vasoconstrictors on regional vascular selectivity can be determined using only measurements of the blood pressure spectrum.
Influences from blood pressure and heart rate changes
Young et al. (1989, 1992) found that the changes in HR and mean blood pressure during organ ligation were insignificant. A very short duration of ligation (less than 3 s) avoided possible physiological reflexive responses; variations in the pulse spectrum due to organ ligation were only related to the intrinsic physical properties of each organ.
In the present study, however, both vasoconstrictors significantly changed the mean blood pressure and the HR. The autoregulatory effect due to the increase in blood pressure (Hellebrekers et al. 1990; Jackson & Herzer, 2001) and the influence of shifts in harmonics due to HR changes can be summarized as follows.
First, both drugs caused very similar changes in the blood pressure and HR, suggesting that the influence of blood pressure and HR on variations in the pulse spectrum should be about the same. Hence, the distinct drug-affected variations should be related mainly to the regional drug selectivity.
Second, the kidney reportedly has the highest autoregulatory capability, and so the autoregulatory effect initiated by the increase in blood pressure might account for the smaller decrease in C2 elicited by both drugs.
Third, the effects of AVP and Ang II on the harmonic components of the pulse spectrum should be less than the 10–20% changes in HR evident in Fig. 1. For a periodical signal such as a pressure pulse, most of its energy is concentrated into its harmonic bands (Jan et al. 2003). Therefore, the frequency-dependent behaviour of the vascular system should be related to the harmonics of the HR rather than the intrinsic resonant frequencies to ensure optimal energy usage. When AVP or Ang II changes the physical properties of the affected vascular beds, thus changing their resonant frequencies, the heart should adjust its pumping rate to keep the pressure energy focused at the new harmonic bands, and so the specific relationships between the organs and the harmonics should be maintained. Therefore, despite the changes in the frequency of each harmonic, we may still compare the two pulse spectra on the basis of the harmonic components due to the maintained relationship between the organs and the harmonics.
Influences of flow changes
Changes in the input flow to the vascular bed during drug infusion would have had little effect on our analyses for the following reasons.
First, the amplitude of each harmonic in the pressure pulse was normalized by the mean level of the pulse, which avoids any possible cardiac influence.
Second, the pulse spectra were compared on the basis of harmonics rather than their actual frequencies. Therefore, the comparisons are related to the resonance status of the vascular system and not to the vascular impedance or the input flow. In this study, the ligation profile or the drug effect profile describes how the vascular resistance changes, and not how the impedance changes.
Influences from the occluded tail artery
To avoid possible surgical interference on the blood pressure spectrum, we chose fluid-filled catheters rather than micromanometers for the pressure measurements. Compared with other surgical techniques, opening the tail artery was considered to have the least influence on the vascular system, and the self-control design of the study minimized the possible influence from tail artery occlusion as well as the damping effect.
Further improvements
First, our method provides relative vasoconstrictor selectivity information from the ligation data of two vascular beds. The calculations only account for the two largest arterial beds, since there are few experimental data on the smaller arterial beds. Further experimental data should therefore be collected.
Second, the vascular reactivity may differ with the animal species or anaesthetic used (Faber, 1989). Different experimental set-ups may also affect the results (Lappe & Brody, 1984; Gardiner et al. 1988, 1989). Quantitative comparisons performed under similar conditions between the regional vascular resistances and the ligation ratios may further improve the similarity.
Possible applications
This study forms part of a series aimed at proving that the blood pressure waveform can be used as the sole parameter to determine the blood circulatory condition of the arterial bed (Wang et al. 1989, 1996; Young et al. 1989, 1992; Wang et al. 1991, 2000; Lu et al. 1996; Jan et al. 2003; Hsu et al. 2003; Lin Wang et al. 2004). It is easy to obtain pulse information in humans non-invasively from the radial artery or several other points on the body. The pulse analysis method has the potential to be developed as a non-invasive quantitative monitoring tool (Lu et al. 1996; Hsu et al. 2003; Kizilova, 2003). To achieve this, the frequency characteristics of more human vascular beds must be determined. The potential clinical relevance is presently limited by the need for training data sets. The applicability of the method is as follows.
First, the resonance theory is based on large arterial beds, such as the major internal organs, having unique shapes, sizes and structures, which results in each bed having its own resonant frequency that causes its own specific ligation profile (Wang et al. 1989; Wang et al. 1991, 2000; Jan et al. 2003; Lin Wang et al. 2004). We have presented the specific frequency characteristics of six large arterial beds in the Introduction, each of which has a distinct profile (Farrow & Stacy, 1961; Wiener et al. 1966; Wang et al. 1989; Young et al. 1989, 1992). There is also indirect evidence supporting these suggestions from drug studies (Wang et al. 1995, 1997, 2003; Hsu et al. 2003) and clinical observations (Chen et al. 1993; Wang et al. 1996; Lu et al. 1996).
Second, the application of the law of linear superposition to the pressure spectral pattern is another key aspect of our method. Milnor (1989) stated that many findings support the conclusion that the arterial system is approximately linear (up to 98%) with respect to impedance. So the linearity of the pressure spectral pattern for most major arterial beds is expected. We have also observed that the pressure spectra were approximately linear in our previous herbal studies (Wang et al. 1995, 1997, 2003).
Third, the ligation data can only mimic the increases in local vascular resistance, because both events (ligation and vasoconstriction) cause the vascular system to deviate from its original state in a similar way. Conceptually, it is not adequate to consider ligation as negative vasodilatation on a resonance basis, and hence this ligation-data method is limited to vasoconstrictors. We therefore need other pulse analysis parameters that mimic the decreases in vascular resistance to evaluate the effects of vasodilators.
Conclusions
Many studies have shown that the blood pressure wave contour may reveal more valuable internal physiological information than that of SP and DP alone. The present study strengthens this concept by demonstrating that pressure-wave spectrum analysis reveals not only which arterial bed is vasoconstictor affected but also the magnitude of the change. We were able to detect the changing ratios of the vascular resistance, and so the regional AVP and Ang II selectivity, from distinctive changes in the blood pressure spectrum.
Conventional investigations of vascular resistance provide detailed data on regional blood flow and pressure by placing multiple monitoring probes inside the body via surgical approaches. The proposed non-invasive pulse analysis method provides a complementary macroscopic summary of regional selectivity.
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