Nonparametric Block-Structured Modeling of Lung Tissue Strip Mechanics

Very large amplitude pseudorandom uniaxial perturbations containing frequencies between 0.125 and 12.5 Hz were applied to five dog lung tissue strips. Three different nonlinear block-structured models in nonparametric form were fit to the data. These models consisted of (1) a static nonlinear block followed by a dynamic linear block (Hammerstein model); (2) the same blocks in reverse order (Wiener model); and (3) the blocks in parallel (parallel model). Both the Hammerstein and Wiener models performed well for a given input perturbation, each accounting for greater than 99% of the measured stress signal variance. However, the Wiener and parallel model parameters showed some dependence on the strain amplitude and the mean stress. In contrast, a single Hammerstein model accounted for the data at all strain amplitudes and operating stresses. A Hammerstein model featuring a fifth-order polynomial static nonlinearity and a linear impulse response function of 1 s duration accounted for the most output variance (99.84% ± 0.13%, mean ± standard deviations for perturbations of 50% strain at 1.5 kPa stress). The static nonlinear behavior of the Hammerstein model also matched the quasistatic stress–strain behavior obtained at the same strain amplitude and operating stress. These results show that the static nonlinear behavior of the dog lung tissue strip is separable from its linear dynamic behavior. © 1998 Biomedical Engineering Society. PAC98: 8745Bp, 8710+e     

An analysis of muscle spindle behavior using randomly applied stretches

The behavior of mammalian muscle spindles to relatively large amplitude randomly applied stretches is compared to the linear behavior elicited by small amplitude sinusoidal stretches. The results disclose two apparently independent sources of nonlinear behavior. One is a static nonlinearity affecting both primary and secondary endings in which the sensitivity decreases with stretch amplitude up to about 1% stretch. The other is a ‘dynamic’ nonlinearity affecting only primary endings that is manifest as a charge in the ratio of rate to proportional sensitivity depending on the duration of an applied stretch.     

The influence on the breathing pattern in man of moderate levels of continuous positive and negative airway pressure and of positive end-expiratory pressure during air and CO2 inhalation

The purpose of this study was to determine in man the effect on the breathing pattern of continuous positive (CPAP), continuous negative (CNAP) and positive end-expiratory (PEEP) airway pressure during air breathing and CO₂ inhalation. Six subjects were exposed to CPAP, CNAP and PEEP 0.5 kPa, while five subjects were exposed to CPAP and CNAP 0.8 kPa. End-expiratory lung volume increased during CPAP 0.8 kPa and decreased during CNAP 0.8 kPa. CPAP induced more extensive changes in the ventilatory pattern, and the changes in each parameter were larger than observed during CNAP and PEEP at the same pressure level. In contrast to previous reports we found the effect of CO₂ inhalation combined with the effect of pressure breathing to be not stronger than additive. Even moderate CPAP induced alveolar hyperventilation with marked reduction in arterial PCO₂ (PaCO₂) when breathing air. With increasing fraction of CO₂ in the inspiratory gas, the difference in PaCO₂ between CPAP and no CPAP disappeared. PEEP also affected the breathing pattern in that it induced an increase in mean inspiratory flow and mean expiratory flow and a reduction in inspiratory duration. Occurrence of ventilatory pauses depended on whether mouthpiece or facemask was used. CPAP and CNAP did not influence the occurrence of pauses, while PEEP prolonged post-expiratory pauses. We conclude that CPAP, CNAP and PEEP induce active ventilatory responses in man and that strong mechanisms are involved during CPAP since PaCO₂ is markedly reduced.     

Separable least squares identification of nonlinear Hammerstein models: application to stretch reflex dynamics

The Hammerstein cascade, consisting of a zero-memory nonlinearity followed by a linear filter, is often used to model nonlinear biological systems. This structure can represent some high-order nonlinear systems accurately with relatively few parameters. However, it is not possible, in general, to estimate the parameters of a Hammerstein cascade in closed form. The most effective method available to date uses an iterative approach, which alternates between estimating the linear element from a crosscorrelation, and then fitting a polynomial to the nonlinearity via linear regression. This paper proposes the use of separable least squares optimization methods to estimate the linear and nonlinear elements simultaneously in a least squares framework. A separable least squares algorithm for the identification of Hammerstein cascades is developed and used to analyze stretch reflex electromyogram data from two experimental subjects. The results show that in each case the proposed algorithm produced a better model, in that it predicted the systems response to novel inputs more accurately, than did models estimated using the traditional iterative algorithm. Monte-Carlo simulations demonstrated that when the input is a non-Gaussian, nonwhite signal, as is often the case experimentally, the traditional iterative identification approach produces biased models, whereas the separable least squares approach proposed in this paper does not. © 2001 Biomedical Engineering Society. PAC01: 8719Ff, 8719Nn, 8710+e     

New oscillometric method for indirect measurement of systolic and mean arterial pressure in the human finger. Part 1: Model experiment

To analyse the mechanism of the occurrence of the maximum volume pulsation in an artery during the application of counterpressure, the static, and dynamic pressure-volume (P-V) relationship was measured in excised arterial segments placed in a compression chamber. Teh volume change caused by perfusing the segment with a sinusoidal pump was detected by an infrared photoelectric plethysmograph during the application of counterpressure. It was revealed that the characteristic change in the amplitude of volume pulsation in response to the gradual change in the counterpressure was due to the nonlinearity of the P-V relation of the artery, and that the value of the counterpressure showing the maximum pulsation amplitude was coincided with the mean arterial pressure. From this evidence it was concluded that the maximum volume pulsation occurs when the transmural pressure was equal to zero, i.e. the arterial wall isunloaded. Based on the results a new oscillometric method for the indirect measurement of systolic and mean arterial pressure in an arterial segment was designed. Through the comparison of data with the actual pressure produced by perfusing the segment, it was demonstrated that systolic and mean arterial pressure can be indirectly measured by this technique within ±3 mm Hg error.     

A dynamic nonlinear lumped parameter model for skeletal muscle circulation

A dynamic nonlinear lumped parameter model of the circulation of skeletal muscle for constant vasoactive state is presented. This model consists of four compartments that represent the large arteries, the arterioles, the capillaries and venules, and the veins, respectively. The first compartment consists of a linear compliance (C₁) and resistance (R₁). The third compartment possesses no compliance and is represented by a linear resistance (R₃). The second and fourth compartments each consist of a nonlinear pressure-volume relation, resulting in a pressure dependent compliance (C₂, C₄, respectively) and nonlinear resistance (R₂, R₄, respectively). The eleven model parameters were collected in a complementary way: they were partly obtained from a priori knowledge including, information at the microscopic level, and partly determined by means of an estimation algorithm. Estimated values of the compliances (in cm³·kPa⁻¹·100 g⁻¹, 1kPa=7.5 mmHg) and resistances (in kPa·s·cm⁻³·100 g) at an (arterial) inflow pressure of 10 kPa and a (venous) outflow pressure of 0 kPa were: C₁: 0.014; R₁: 6.6; C₂: 0.565; R₂: 84.6; R₃: 37.9; C₄: 1.044; R₄: 24.5. The model (with the nonlinear pressure-volume relations) is able to predict the static and dynamic instantaneous (i.e., for constant vasomotor tone) pressure-flow relation and the instantaneous zero flow pressure intercept. These phenomena are therefore not necessarily the result of the rheological properties of blood. The secondary or delayed dilatation upon a positive inflow pressure step (or negative step in venous pressure) is predicted by the model implying that delayed dilatation is not necessarily related to changes in vasomotor tone. Venous outflow delay, upon a positive inflow pressure step (starting from zero flow), is also predicted by the model.     

Harmonic distortion from nonlinear systems with broadband inputs: Applications to lung mechanics

We present a simple index, extended harmonic distortion (k _d ), to represent the degree of system nonlinearity under sparse pseudorandom noise inputs (SPRN). The frequencies in a SPRN waveform are neither harmonics nor sums or differences of the other component frequencies. Expressed by percentage, thek _d is the square root of the ratio of output power at non-input frequencies to the total output power. We evoke three simple corrections to recover the truek _d under imperfect SPRN inputs. Simulations on two block-structured nonlinear models (Wiener and Hammerstein) demonstrate the necessity and effectiveness of these corrections especially for the Wiener-type nonlinearity. By applyingk _d to pressure-flow data of dog lungs, we found that the nonlinear harmonic interactions from a lung arise primarily from its tissues most likely the processes governing the tissue stiffness. This nonlinearity, assessed fromk _d , is stronger at higher tidal volumes and enhanced (but to a lesser degree) during bronchoconstriction. We conclude that since thek _d approach avoids the necessity for multiple-input measurements and lengthy data records, it may be useful for tracking the dynamic variations in nonlinearities of a physiological system.     

Nonlinear and Frequency-Dependent Mechanical Behavior of the Mouse Respiratory System

The assessment of the mechanical properties of the respiratory system is typically done by oscillating flow into the lungs via the trachea, measuring the resulting pressure generated at the trachea, and relating the two signals to each other in terms of some suitable mathematical model. If the perturbing flow signal is broadband and not too large in amplitude, linear behavior is usually assumed and the input impedance calculated. Alternatively, some researchers have used flow signals that are narrow band but large in amplitude, and invoked nonlinear lumped-parameter models to account for the relationship between flow and pressure. There has been little attempt, however, to deal with respiratory data that are both broadband and reflective of system nonlinearities. In the present study, we collected such data from mice. To interpret these data, we first developed a time-domain approximation to a widely used model of respiratory input impedance. We then extended this model to include nonlinear resistive and elastic terms. We found that the nonlinear elastic term fit the data better than the linear model or the nonlinear resistance model when amplitudes were large. This model may be useful for detecting overinflation of the lung during mechanical ventilation. © 2003 Biomedical Engineering Society. PAC2003: 8719Rr, 8719Uv     

一种非线性呼吸力学模型及其参数估计

本文报道了一个非线性呼吸力学模型,该模型可以反映深呼吸过程中呼吸气体流率、跨肺压力及肺容积变化之间的动态关系。模型参数分别反映气道阻力状态及肺弹性特性。敏感度分析表明,该模型肺弹性参数估计值的准确度高于气道阻力。实验测定了10名被试者的呼吸气体流率、食道压力及肺容积。参数估计结果表明,动、静态肺弹性参数之间存在显著差异(P<0.01)。我们认为肺组织及肺泡表面活性物质的应力松驰机制是造成这种差异的主要原因。     

Volume and flow dependence of respiratory mechanics in mechanically ventilated COPD patients

Volume and flow dependencies of respiratory mechanics are examined in 10 COPD patients under mechanical ventilation (MV) at 3 levels of externally applied PEEP (PEEPe). Airways pressure (Paw), flow (V') and volume (V) data are analyzed according to (1) the linear and (2) a non-linear model, accounting for volume dependence of elastance and for flow and volume dependence of resistance. The models' fitness to data is assessed by the regression errors. Non-linear modelling fits significantly better to data, while the difference of fitness decreases with PEEPe. Linear mechanics are not significantly different between the 3 levels of PEEPe. A positive volume dependence of elastance observed at 0, decreases at 5 and increases again at 10 hPa of PEEPe. A seriously negative volume dependence of resistance at 0 turned to positive with PEEPe. These dependencies of respiratory mechanics during COPD under MV, show that the present non-linear respiratory mechanical monitoring may help for better and less risky adjustment of PEEPe.     

High tidal volume ventilation in infant mice

Infant mice were ventilated with either high tidal volume (V(T)) with zero end-expiratory pressure (HVZ), high V(T) with positive end-expiratory pressure (PEEP) (HVP), or low V(T) with PEEP. Thoracic gas volume (TGV) was determined plethysmographically and low-frequency forced oscillations were used to measure the input impedance of the respiratory system. Inflammatory cells, total protein, and cytokines in bronchoalveolar lavage fluid (BALF) and interleukin-6 (IL-6) in serum were measured as markers of pulmonary and systemic inflammatory response, respectively. Coefficients of tissue damping and tissue elastance increased in all ventilated mice, with the largest rise seen in the HVZ group where TGV rapidly decreased. BALF protein levels increased in the HVP group, whereas serum IL-6 rose in the HVZ group. PEEP keeps the lungs open, but provides high volumes to the entire lungs and induces lung injury. Compared to studies in adult and non-neonatal rodents, infant mice demonstrate a different response to similar ventilation strategies underscoring the need for age-specific animal models.     

Dynamic manipulation of the subharmonic scattering of phospholipid-coated microbubbles

In this paper, the influence of a dynamic variation in the ambient pressure on the subharmonic response of phospholipid-coated microbubbles was investigated. The ambient pressure in water was modulated by a 2.5 kHz acoustic wave with a peak amplitude of 15 kPa. We investigated the fundamental and subharmonic emissions at two driving frequencies: 5 and 10 MHz. The modulation of the bubble radius induced by the dynamic variation in the liquid ambient pressure subsequently causes modulations of the scattered acoustic pressure at the fundamental and subharmonic frequencies (half the fundamental frequency). As a first result, we measured that the variation in the ambient pressure of 15 kPa can modulate the subharmonic amplitude up to 10 dB as compared to the static atmospheric pressure condition. As a second result, we noticed that the relative subharmonic amplitude modulation as a function of the LF acoustic pressure was symmetrical for the 5 MHz driving frequency but asymmetric for 10 MHz. In the latter case, the subharmonic amplitude was more enhanced for an ambient overpressure than reduced for an ambient depression of the same amplitude likely due to the buckling of the lipid shell. However, the fundamental amplitude was symmetrically modulated during bubble compression and expansion. Moreover, subharmonic and fundamental amplitude modulations were found to be either in phase or out of phase with the low-frequency acoustic pressure. Numerical simulations showed that this behavior can be obtained depending on the bubbles' diameter. The highest subharmonic amplitude was measured when microbubbles were insonified at 10 MHz. This fact together with the asymmetry observed in the subharmonic modulation suggests that smaller bubbles with a buckling shell are excited at 10 MHz compared to 5 MHz. These results present new potentials for in vitro characterization of contrast agent microbubbles and possibly a new imaging modality.     

激波载荷下绵羊胸部动力学响应的数学模型

本文利用单自由度非线性单腔模型描述激波作用下机体胸部动力学响应,并建立其数学模型,通过测定激波作用下的绵羊胸壁内向运动的位移、速度和加速度,检验这一模型的预测效果。实验结果表明,该模型基本上反映了激波作用下绵羊胸壁运动过程,但有待于发展和完善。     

Effect of using several levels of positive end-expiratory pressure over barotrauma's induced lung injury in a model of isolated and perfused rabbit lungs

The use of Positive end-expiratory pressure (PEEP) as a strategy of mechanical ventilation offers its advantages, such as improved oxygenation, without causing alveolar overstretching and barotrauma. We aim to investigate the effect of several levels of PEEP on barotrauma and, whether an optimal level of PEEP exists. Forty-eight New Zealand rabbits (2.5-3.5 kg) were divided into four groups with PEEP settings of 0, 4, 8 and 12 cmH2O, at increasing levels of inspiratory volume (IV). This was done in blood perfused rabbit lungs and in lungs perfused with a Buffer-Albumin Solution. We observed that lungs ventilated with PEEP 0 cmH2O suffered pulmonary rupture at high IV (300cc), with significant increases of Pap (Pulmonary artery pressure) and FFR (Fluid filtration rate). Lungs ventilated with PEEP 8 and 12 suffered pulmonary rupture at lower IV (200cc and 150cc vs. 300cc respectively) On the other hand, lungs ventilated with PEEP 4 cmH2O reached the highest IV (400cc), in addition, they showed the lowest elevations of Pap and FFR. The acellular lungs ventilated with PEEP 4, 8 and 12 showed pulmonary rupture at lower IV when compared with cellular ones (300cc vs. 400cc: 100cc vs. 200cc and 100cc vs. 150cc respectively). We concluded that an optimal PEEP exists, which protects against barotrauma, however, excess of PEEP could enhance its development. The blood could contain some mediators which attenuate the damage induced by barotrauma.     

Full-field deformation of bovine cornea under constrained inflation conditions

The viscoelastic response of bovine corneas was characterized using in vitro inflation (bulge) experiments combined with spatially-resolved deformation mapping via digital image correlation. A complex fixture conforming to the limbal annulus was developed to hold the attached sclera rigid while allowing deformation only in the cornea. A statistical set of experiments was performed for a pressure range of 3.6-8 kPa (27-60 mmHg), representing nominal bovine intraocular pressure (IOP) to acute glaucoma conditions. A broader pressure range of 0-32 kPa (0-240 mmHg) was also examined to characterize the nonlinear finite deformation behavior of the tissue. Results showed that for pressures near and above IOP, the majority of the deformation was localized in the limbus and peripheral regions, which left the central cornea largely undeformed. This observation was consistent with the known preferred circumferential alignment of collagen fibrils outside of the central cornea. In general, the inflation experiments observed viscoelastic behavior in the form of rate-dependent hysteresis in the pressure-deformation response of the apex of the cornea, creep in the apex deformation at a constant inflation pressure, and relaxation in the pressure response at a constant inflation volume. The 3.6-8 kPa (27-60 mmHg) pressure range produced small viscoelastic deformations and a nearly linear pressure-deformation response, which suggests that for physiological pressure ranges, the cornea can be approximated as a linear viscoelastic or linear pseudo-elastic material.     

Pulmonary clearance of inhaled [99Tcm]DTPA: effects of ventilation pattern

While a rise in lung volume is known to increase the pulmonary clearance of technetium-99m-labelled dietylene triamine pentaacetate ([99Tcm]DTPA), little interest has been focused on the effects of changes in ventilation frequency, tidal volume and airway pressure. We studied adult, anaesthetized and intubated rabbits during three ventilation patterns (VP) using pressure controlled ventilation (ServoVentilator 900C). VP was either deep slow (f = 20 min-1, tidal volume (VT) = 30 +/- 4 ml kg-1 and positive end-expiratory pressure (PEEP) = 0.2 kPa [VP 20/0.2, n = 8]) or rapid shallow (f = 80 min-1, VT = 11 +/- 2 ml kg-1 and PEEP = 0.2 or 0.4 kPa [VP 80/0.2, n = 6 and VP 80/0.4, n = 6]). The mean airway pressure was similar at VP 20/0.2 and VP 80/0.4. During administration of [99Tcm]DTPA aerosol all animals were ventilated under the same conditions (f = 40 min-1 and PEEP = 0.2 kPa). The pulmonary clearance rate expressed as the half-life time (T1/2) of [99Tcm]DTPA was at VP 80/0.2 = 113 +/- 31 min, at VP 80/0.4 = 70 +/- 24 min (P less than 0.01 compared to VP 80/0.2) and at VP 20/0.2 = 36 +/- 18 min (P less than 0.001 compared to VP 80/0.2 and P less than 0.01 compared to VP 80/0.4). We conclude that the pulmonary clearance of [99Tcm]DTPA increases (1) during rapid shallow ventilation when PEEP is increased from 0.2 to 0.4 kPa; (2) during deep slow ventilation relative to rapid shallow ventilation even when the mean airway pressure is similar.     

Myoelectric response of the human triceps brachii to displacement-controlled oscillations of the forearm

Summary The dynamic relations between the surface myoelectric activity in tonically contracting triceps brachii and the forearm rotation (proportional to triceps stretch) were measured by imposing small, sinusoidal, displacement-controlled perturbations on the forearm position. Three normal, adult, male subjects participated in these experiments. The amplitude of the forearm rotation, the driving frequency, and the tonic contraction level were all carefully regulated. The mean rectified triceps EMG (the output) showed a strong harmonic at the driving frequency, and the frequency-response characteristics were computed directly by comparing the amplitude and phase of this harmonic to that of the forearm flexion angle (the input). The (electrical) reflex gain is defined as the amplitude ratio of output to input. The system response was measured from 2 to 18 Hz, at two tonic contraction levels and two forearm rotation amplitudes, about a mean position of 90° forearm flexion. The results show clearly that the system response is nonlinear: the reflex gain decreases with forearm rotation amplitude. (This gain also increases with tonic contraction level for sufficiently low values of the latter variable.) The measured frequency-response characteristics of the system can be modeled approximately as a second order linear lead filter with a single time delay, followed by a saturating nonlinearity. Both model independent estimates and least-squares model fitting, yielded values of the time delay of the order of 25 ms, suggesting that a segmental mechanism mediates reflex activity. Simplified calculations and limited measurements are presented to show that a nonlinear system of the type we have identified with constant displacement driving may appear linear under constant torque driving. Our directly-measured frequency-response characteristics differ from those reported by investigators employing random, rather than periodic, driving; possible reasons for these apparent discrepancies are discussed.     

Shaker K+ channels contribute early nonlinear amplification to the light response in Drosophila photoreceptors

We describe the contribution of rapidly inactivating Shaker K+ channels to the dynamic membrane properties of Drosophila photoreceptors. Phototransduction was measured in wild-type and Shaker mutant (Sh14) Drosophila photoreceptors by stimulating with white noise-modulated light contrast and recording the resulting intracellular membrane potential fluctuations. A second-order Volterra kernel series was used to characterize the nonlinear dynamic properties of transduction in the two situations. First-order kernels were indistinguishable in wild-type and Sh14 photoreceptors, indicating that the basic light transduction machinery was always intact. However, second-order kernels of Shaker mutants lacked a large, early amplification, indicating a novel role for Shaker K+ channels in amplifying and accelerating the voltage response of wild-type photoreceptors. A cascade model of two nonlinear static components surrounding one linear dynamic component was able to partially reproduce the experimental responses. Parameters obtained by fitting the model to the experimental data supported the hypothesis that normal Shaker K+ channels contribute an early, positive nonlinearity that partially offsets a later attenuating nonlinearity caused by membrane shunting.     

Effects of dynamic and static handgrip exercises on hand and wrist volume

It is not known how the mode of exercise, dynamic and static exercises, affects the limb volume. Therefore, the purpose of this study was to investigate hand and wrist volume (HWV) after dynamic and static handgrip exercise. Nine healthy subjects (age 31.8 ± 7.3 years; height 172.0 ± 5.7 cm; body mass 66.9 ± 8.1 kg, mean ± SD) volunteered for this study. HWV was measured with a hand and wrist volumeter before and immediately after dynamic and static exercises. Initially during rest, HWV was measured after the hand was passively hung for 5 min. Handgrip exercises with an ergonomic hand exerciser were performed at 20% of maximum voluntary contraction in right and left hands by static and dynamic exercises, respectively. Both dynamic and static handgrip exercises consisted of six sets of 30-s contractions with 10-s rest intervals between exercise bouts. The dynamic handgrip exercise was performed by repetitive contraction and relaxation of the hand at a maximum frequency. In order to determine intensity of handgrip exercises, maximum isometric handgrip strength of the right and left hand was measured with a handgrip dynamometer. Data are presented as mean ± SD. After dynamic and static handgrip exercises, HWV increased significantly, and these increases represent 2.2 ± 0.7% (P < 0.001) and 1.4 ± 0.8% (P < 0.001) of resting HWV, respectively. The elevation of HWV after dynamic exercise was significantly higher than that after static exercise (P < 0.05). These results suggest that the higher HWV after dynamic exercise may be caused by higher increased interstitial fluid volume, capillary volume and venous volume in hand and wrist tissues.