Isometric muscle length-tension curves do not predict angle-torque curves of human wrist in continuous active movements

In this study we tested the hypothesis that during steady contractions of human wrist extensors or flexors, the torque-angle relationship during movements imposed about the wrist is predicted by the classical isometric muscle length-tension curve, with ascending, descending and ascending limbs. Angle-torque relationships were measured during steady muscle activation (10% of maximal voluntary contraction: MVC), elicited either by electrical stimulation or voluntary regulation of the electromyogram (EMG). Flexion-extension movements of constant speed (+/-10 degrees /s) were imposed on the subjects' hands with a servo actuator, either through the full physiological range of motion +/-50 degrees, or through +/-10 degrees. During extensor contractions, angle-torque curves in +/-50 degrees movements had ascending, descending and ascending limbs, as in isometric contractions. However, in +/-10 degrees movements, torque always increased with increasing muscle length and decreased with decreasing length, even over angles corresponding to the descending limb of isometric curves. For flexor activation, angle-torque curves had similar properties, though descending limbs were less obvious or absent. During imposed movements, hysteresis was observed in the angle-torque curves. This was attributed to non-linearities of the active muscles. Hysteresis reached a maximum at intermediate wrist angles and declined at maximal muscle length, contradicting the recent hypothesis that sarcomere non-uniformity is responsible for the hysteresis. We conclude that the classical isometric length-tension curve, with its prominent descending limb, does not predict angle-torque curves of human wrist muscles in continuous movements. A more appropriate model is one in which stiffness about the wrist is always positive and hysteresis is a significant factor.     

Mechanics of the compression wood response: I. Preliminary analyses

Righting of two tilted white pine (Pinus strobus L.) stem leaders by compression wood formation was followed for 16 weeks. The natural curves and three deflection curves under added end loads were determined from weekly field photographs. Data for self-loading and cross sectional diameters were interpolated from original estimated and final measurements. A mechanical-mathematical model was developed to predict curves under zero gravity for each stem each week. The model estimated stiffness of the leaders independently for each week, and the stiffnesses were consistent throughout the experiment. A second model was developed to simulate the deflection curves assumed when the zero gravity curves were subjected to different end loads. These predicted curves were nearly identical to the observed curves from the photographs, thus verifying the assumptions in the first model. Data from this study will be used to investigate the mechanical aspects of compression wood induction and action as the stem is bent upward toward the vertical.     

Mathematical models of the kinetics of glucose and insulin in plasma

On the assumption that plasma glucose and IRI curves are essentially non-periodic in character, two simple, linear, lumped-parameter mathematical models have been investigated, one consisting of a single compartment and the other of two compartments between which glucose exchanges. The two-compartment model has the stronger appeal in that it admits more readily of a variable hepatic output of glucose. Estimation of many of the rate constants involved has been effected by conforming the theoretical functions to data from intravenous glucose tolerance tests. Numerical values obtained for the rate constants associated with the two-compartment model are satisfactory, but some confusion still remains concerning the turnover time of insulin in plasma.     

Altered baroreflex function after tail suspension in the conscious rat

Experiments were performed on conscious chronically instrumented rats to determine the contribution of peripheral V2-vasopressinergic receptors in any alteration of baroreceptor reflex (BRR) sensitivity on release from 1 wk of 30 degrees head-down tilt resulting from tail suspension. Initial experiments determined changes in plasma volume (PV) occurring over this period by use of the Evans Blue dye dilution technique. PV was determined immediately before tail suspension and on day 7 of the stimulus. PV, erythrocyte volume, and total blood volume were all significantly diminished on day 7, whereas hematocrit was unchanged. Other rats were instrumented with pulsed Doppler flow probes on the ascending aorta for determination of cardiac output and with arterial and venous catheters 7-10 days before study. Immediately before tail suspension, control cardiac output, mean arterial blood pressure, and heart rate values were determined. In addition, BRR sensitivity was estimated both before and after intravenous administration of a V2-receptor antagonist by assessing the slope of the pulse interval-mean arterial blood pressure relationship in response to a series of pressor doses of phenylephrine. BRR sensitivity was determined on the last day of head-down tilt, 1 min after release from tail suspension, and 10 min after administration of a specific V2-vasopressinergic antagonist. BRR sensitivity tended to fall on day 7 of tail suspension compared with control and was significantly increased after release. However, BRR sensitivity was not altered by intravenous V2 antagonist administration either before tail suspension or after release.(ABSTRACT TRUNCATED AT 250 WORDS)     

Respiration and measurement of cardiac output by thermodilution and central or peripheral dye dilution.

Cardiac output as measured by indicator dilution methods during artificial ventilation shows differences up to +/- 35%. We studied the influence of spontaneous breathing on measurement of cardiac output by thermodilution (TD) and central (CDD) and peripheral dye dilution (PDD) in seven anesthetized dogs. Injection of indicator was timed at one of five chosen moments in a respiratory cycle. The indicator for TD was also used as solvent for indocyanine green. Results were normalized by the value obtained with injection at inspiratory onset. Results of the central dilution methods showed a slight but not significant difference between values measured with injection at 25 and 75% of the respiratory cycle: 105.7 and 98.0%, respectively, (TD) and 102.3 and 97.2% (CDD). Mean cardiac output determined by TD, CDD, or PDD was not significantly different. We conclude that 1) a reasonable estimate of cardiac output may be obtained by means of a single indicator-dilution curve and 2) the choice of the dilution method may be determined by practical considerations.     

Effect of Extended CT Perfusion Acquisition Time on Ischemic Core and Penumbra Volume Estimation in Patients with Acute Ischemic Stroke due to a Large Vessel Occlusion

Background and Purpose

It has been suggested that CT Perfusion acquisition times <60 seconds are too short to capture the complete in and out-wash of contrast in the tissue, resulting in incomplete time attenuation curves. Yet, these short acquisitions times are not uncommon in clinical practice. The purpose of this study was to investigate the occurrence of time attenuation curve truncation in 48 seconds CT Perfusion acquisition and to quantify its effect on ischemic core and penumbra estimation in patients with acute ischemic stroke due to a proximal intracranial arterial occlusion of the anterior circulation.

Materials and Methods

We analyzed CT Perfusion data with 48 seconds and extended acquisition times, assuring full time attenuation curves, of 36 patients. Time attenuation curves were classified as complete or truncated. Ischemic core and penumbra volumes resulting from both data sets were compared by median paired differences and interquartile ranges. Controlled experiments were performed using a digital CT Perfusion phantom to investigate the effect of time attenuation curve truncation on ischemic core and penumbra estimation.

Results

In 48 seconds acquisition data, truncation was observed in 24 (67%) cases for the time attenuation curves in the ischemic core, in 2 cases for the arterial input function and in 5 cases for the venous output function. Analysis of extended data resulted in smaller ischemic cores and larger penumbras with a median difference of 13.2 (IQR: 4.3–26.0)ml (P<0.001) and; 12.4 (IQR: 4.1–25.7)ml (P<0.001), respectively. The phantom data showed increasing ischemic core overestimation with increasing tissue time attenuation curve truncation.

Conclusions

Truncation is common in patients with large vessel occlusion and results in repartitioning of the area of hypoperfusion into larger ischemic core and smaller penumbra estimations. Phantom experiments confirmed that truncation results in overestimation of the ischemic core.     

Examination of stimulation mechanism and strength-interval curve in cardiac tissue

Understanding the basic mechanisms of excitability through the cardiac cycle is critical to both the development of new implantable cardiac stimulators and improvement of the pacing protocol. Although numerous works have examined excitability in different phases of the cardiac cycle, no systematic experimental research has been conducted to elucidate the correlation among the virtual electrode polarization pattern, stimulation mechanism, and excitability under unipolar cathodal and anodal stimulation. We used a high-resolution imaging system to study the spatial and temporal stimulation patterns in 20 Langendorff-perfused rabbit hearts. The potential-sensitive dye di-4-ANEPPS was utilized to record the electrical activity using epifluorescence. We delivered S1-S2 unipolar point stimuli with durations of 2-20 ms. The anodal S-I curves displayed a more complex shape in comparison with the cathodal curves. The descent from refractoriness for anodal stimulation was extremely steep, and a local minimum was clearly observed. The subsequent ascending limb had either a dome-shaped maximum or was flattened, appearing as a plateau. The cathodal S-I curves were smoother, closer to a hyperbolic shape. The transition of the stimulation mechanism from break to make always coincided with the final descending phase of both anodal and cathodal S-I curves. The transition is attributed to the bidomain properties of cardiac tissue. The effective refractory period was longer when negative stimuli were delivered than for positive stimulation. Our spatial and temporal analyses of the stimulation patterns near refractoriness show always an excitation mechanism mediated by damped wave propagation after S2 termination.     

Hemodynamics of conscious unrestrained baboons, including cardiac output

A method is described for comprehensive hemodynamic study of undisturbed baboons (Papio hamadryas) that incorporates cardiac output measurement by thermodilution. Instrumentation includes arterial, aortic, and central venous catheterization by a surgical technique that does not require entry to peritoneal or thoracic cavities. It provides a means for right atrial indicator delivery with aortic temperature recording of thermodilution curves. Accuracy was confirmed by comparison to measurement by Swan-Ganz catheters. Diurnal variations of systemic arterial pressure in long-term study of conscious baboons were shown to result from significant increases in cardiac output by day (P less than 0.001), despite concomitant falls in systemic vascular resistance. The cardiac output values obtained were 0.13 l.min-1.kg-1 at night and 0.16 l.min-1.kg-1 by day. Comparison of these results to previous reports of cardiac output in baboons highlights the inadequacies of methods that require physical restraint or anesthesia. This technique also leaves the baboons intact for subsequent breeding or experimental use after catheter removal without the need for further surgery.     

Reconstruction of the human gastrocnemius force-length curve in vivo: part 2-experimental results

For a physiologically realistic range of joint motion and therefore range of muscle fiber lengths, only part of the force-length curve can be used in vivo; i.e., the section of the force-length curve that is expressed can vary. The purpose of this study was to determine the expressed section of the force-length relationship of the gastrocnemius for humans. Fourteen male and fourteen female subjects aged 18-27 performed maximal isometric plantar flexions in a Biodex dynamometer. Plantar flexion moments were recorded at five ankle angles:-15 degrees , 0 degrees , 15 degrees , 30 degrees , and 40 degrees , with negative angles defined as dorsiflexion. These measurements were repeated for four randomly ordered knee angles over two testing sessions 4 to 10 days apart. The algorithm of Herzog and ter Keurs (1988a) was used to reconstruct the force-length curves of the biarticular gastrocnemius. Twenty-four subjects operated over the ascending limb, three operated over the descending limb, and one operated over the plateau region. The variation found suggests that large subject groups should be used to determine the extent of normal in vivo variability in this muscle property. The possible source of the variability is discussed in terms of parameters typically used in muscle models.     

A heterogeneous tissue model for measurement of regional blood perfusion in the myocardium using inert gas isotopes

Inert gas isotopes are finding increasing application in the measurement of blood perfusion in the capillary beds of muscle, especially the myocardium. When measuring blood perfusion of the myocardium, washout curves are first produced by precordial monitoring of isotope activity following intracoronary artery injection of an inert gas isotope dissolved in saline. The washout curve data are then applied to a mathematical model to yield blood perfusion rate. Present models for this purpose either ignore any diffusive effects of gas movement (Kety-Schmidt model), or diffusive effects are accounted for by weighting the calculated perfusion value (Zierler's height-over-area technique). A new model is described here for convective and diffusive movement of an inert, nonpolar gas in myocardial tissue. A digital computer simulation of the model equations is used both to simply the model and to show agreement between the model response and experimental ¹³³Xe washout curves from normal and infracted canine hearts. The model assumes that the tail of the washout curves (portion after roughly 1.5 minutes) is caused by a heterogeneous, diffusion-limited tissue structure. The model provides two parameters which can be adjusted to washout curve data using model-matching techniques. These are perfusion rate, and a parameter which is an index of the diffusive nature of the particular myocardial area under study.     

Estimation of cardiac output from dynamic contrast multispiral tomographic data

OBJECTIVE: To describe and apply a method for programmatically calculating central hemodynamic parameters from the data of dynamic contrast X-ray computed tomography (CT). MATERIAL AND METHODS: A procedure is proposed to calculate cardiac output (CO) on the basis of the tracer dilution method as a ratio of the injected dose of a contrast agent (Urografin, Shering AG, Austria) to the area under the concentration-time curve derived for one of the cardiac chambers: [see text]. The blood concentration of the agent was estimated from the blood iodine (I) concentration-X-ray density (XD) regression dependence: [XD] = 0.49+22.07 x [I]. Thirty-three patients were studied on a multispiral X-ray Somatom Sensation 4 computed tomograph (Siemens), by injecting 15-20 ml of Urografin. The calculating method was realized as a software package for processing dynamic contrast CT data. RESULTS: The proposed method could exactly determine the values of cardiac output: the correlation with the results of the reference technique (Doppler echo measurement) was highly significant (r = 0.95; p < 0.001) in the whole range of values. Moreover, the data on XD could accurately determine the blood concentration of both iodine (I): [XD] = 0.49+22.07 x [I] and gadolinium as a component of the contrast paramagnetic Gd-DTPA for which the solution concentration-XR dependence was as follows: XD 1.2+33.6 x [Gd]. CONCLUSIONS: Thus, dynamic spiral CT may be also used for the estimation of cardiac output by the tracer dilution method.     

Simulation of Dilated Heart Failure with Continuous Flow Circulatory Support

Lumped parameter models have been employed for decades to simulate important hemodynamic couplings between a left ventricular assist device (LVAD) and the native circulation. However, these studies seldom consider the pathological descending limb of the Frank-Starling response of the overloaded ventricle. This study introduces a dilated heart failure model featuring a unimodal end systolic pressure-volume relationship (ESPVR) to address this critical shortcoming. The resulting hemodynamic response to mechanical circulatory support are illustrated through numerical simulations of a rotodynamic, continuous flow ventricular assist device (cfVAD) coupled to systemic and pulmonary circulations with baroreflex control. The model further incorporated septal interaction to capture the influence of left ventricular (LV) unloading on right ventricular function. Four heart failure conditions were simulated (LV and bi-ventricular failure with/without pulmonary hypertension) in addition to normal baseline. Several metrics of LV function, including cardiac output and stroke work, exhibited a unimodal response whereby initial unloading improved function, and further unloading depleted preload reserve thereby reducing ventricular output. The concept of extremal loading was introduced to reflect the loading condition in which the intrinsic LV stroke work is maximized. Simulation of bi-ventricular failure with pulmonary hypertension revealed inadequacy of LV support alone. These simulations motivate the implementation of an extremum tracking feedback controller to potentially optimize ventricular recovery.     

A compartmental capillary, convolution integration model to investigate nutrient transport and metabolism in vivo from paired indicator/nutrient dilution curves.

Thirty-three paired indicator/nutrient dilution curves across the mammary glands of four cows were obtained after rapid injection of para-aminohippuric acid (PAH) plus glucose into the external iliac artery. For the measurement of extracellular volume and kinetics of nutrient uptake from indicator dilution curves, several models of solute dispersion and disappearance have been proposed. The Crone-Renkin models of exchange in a single capillary assume negligible washout of solutes from the extracellular space and do not describe entire dilution curves. The Goresky models include a distribution of capillary transit times to generate whole system outflow profiles but require two indicators to parametize extracellular behavior. A compartmental capillary, convolution integration model is proposed that uses one indicator to account for the extracellular behavior of the nutrient after a paired indicator/nutrient injection. With the use of an iterative approach to least squares, unique solutions for nonexchanging vessel transit time t(mu) and its variance sigma were obtained from all 33 PAH curves. The average of heterogeneous vascular transit times was approximated as 2sigma = 8.5 s. The remainder of indicator dispersion was considered to be due to washout from a well-mixed compartment representing extracellular space that had an estimated volume of 5.5 liters or 24% of mammary gland weight. More than 99% of the variation in the time course of venous PAH concentration after rapid injection into the arterial supply of the mammary glands was explained in an unbiased manner by partitioning the organ into a heterogeneous nonexchanging vessel subsystem and a well-mixed compartmental capillary subsystem.     

Environmental factors influencing the relationship between optical density and cell count for Listeria monocytogenes

AIMS: The effect of temperature (2-30 degrees C), pH (4.8-7.4) and water activity (0.946-0.995) on the relationship between optical density (OD) at 600 nm and the plate count (CFU ml(-1)) was investigated for Listeria monocytogenes. METHODS AND RESULTS: Calibration curves, relating OD with plate counts, were collected by measuring the OD of consecutive one-half dilution series, before determining the cell density by classic plate count methods. The calibration curves were observed to be shifting in a parallel way, with increasing stress levels. Especially pH influenced the curve in a great extent, while the other variables were showing more synergetic effects. The reason for the shift was investigated by a microscopic viability test, showing a viability decrease with increasing stress levels, causing the shift of the calibration curve. In a last step a model was made describing the effect of environmental factors on the calibration curve, with different data transformations being tested. A polynomial equation was fitted to the data, taking into account a set of constraints to incorporate microbiological knowledge in the black box model. Hence, illogical interpolation results and overfitting of the data could be avoided. CONCLUSIONS: Different stress factors are affecting the relationship between the OD and the cell count of L. monocytogenes by lowering the cell viability. These effects could be modelled using a constrained polynomial model. SIGNIFICANCE AND IMPACT OF THE STUDY: The observed phenomena are important when calculating growth parameters, like growth rate and lag phase, based on OD data.     

Effects of anthropogenic disturbance on plant diversity and community structure of a sacred grove in Meghalaya, northeast India

This study analyses the effects of anthropogenic disturbance on plant diversity and community attributes of a sacred grove (montane subtropical forest) at Swer in the East Khasi Hills district of Meghalaya in northeast India. The undisturbed, moderately disturbed and highly disturbed stands were identified within the sacred grove on the basis of canopy cover, light interception and tree (cbh 15 cm) density. The undisturbed forest stand had >40% canopy cover, >50% light interception and a density of 2103 trees per hectare, whereas the highly disturbed stand had <10% canopy cover, <10% light interception and 852 trees per hectare. The moderately disturbed stand occupied the intermediate position with respect to these parameters. The study revealed that the mild disturbance favoured species richness, but with increased degree of disturbance, as was the case in the highly disturbed stand, the species richness markedly decreased. The number of families of angiosperms was highest (63) in the undisturbed stand, followed by the moderately (60) and highly disturbed (46) stands. The families Rubiaceae, Asteraceae and Poaceae were the dominant families in the sacred forest. Rubiaceae was represented by 11, 14 and 10 species in the undisturbed, moderately disturbed and highly disturbed stands, respectively, whilst the family Asteraceae had 16 species in the moderately disturbed stand and 14 species in the highly disturbed stand. The number of families represented by a single species was reduced significantly from 33 in the undisturbed stand to 23 in the moderately and 21 in the highly disturbed stand. The similarity index was maximum (71%) between the undisturbed and moderately disturbed stand and minimum (33%) between the undisturbed and highly disturbed stands. The Margalef index, Shannon diversity index and evenness index exhibited a similar trend, with highest values in the moderately disturbed stand. In contrast, the Simpson dominance index was highest in the highly disturbed stand. There was a sharp decline in tree density and basal area from the undisturbed (2103 trees ha^–1 and 26.9 m² ha^–1) to the moderately disturbed (1268 trees ha^–1 and 18.6 m² ha^–1) and finally to the highly disturbed (852 trees ha^–1 and 7.1 m² ha^–1) stand. Density–girth curves depicted a successive reduction in number of trees in higher girth classes from the undisturbed to the moderately and highly disturbed stands. The log-normal dominance–distribution curve in the undisturbed and moderately disturbed stands indicated the complex and stable nature of the community. However, the short-hooked curve obtained for the highly disturbed stand denoted its simple and unstable nature.     

Estimation of cardiac output by analysis of respiratory gas exchange.

Cardiac output is estimated by least squares fitting of a model of pulmonary gas exchange to measurements of respiratory gas composition obtained with a mass spectrometer during a rebreathing maneuver. This new technique estimates cardiac output on spontaneously breathing subjects at rest and requires neither central venous nor arterial blood samples. Principal features of the technique are the use of multiple gases simultaneously in the analysis, the use of a mathematical model for breath-to-breath evaluation of gas exchange, and simultaneous estimation of gas exchange and alveolar gas tensions with the same instrumentation. The technique is compared with thermal dilution estimates in dogs before and during hemorrhagic shock. Two-thirds of these estimates were within 20% of one another. The standard deviation of replication was 15%. Shortcomings, possibilities for improvement, and possible applications are discussed.     

Tail autotomy works as a pre‐capture defense by deflecting attacks

Caudal autotomy is a dramatic antipredator adaptation where prey shed their tail in order to escape capture by a predator. The mechanism underlying the effectiveness of caudal autotomy as a pre‐capture defense has not been thoroughly investigated. We tested two nonexclusive hypotheses, that caudal autotomy works by providing the predator with a “consolation prize” that makes it break off the hunt to consume the shed tail, and the deflection hypothesis, where the autotomy event directs predator attacks to the autotomized tail enabling prey escape. Our experiment utilized domestic dogs Canis familiaris as model predator engaged to chase a snake‐like stimulus with a detachable tail. The tail was manipulated to vary in length (long versus short) and conspicuousness (green versus blue), with the prediction that dog attacks on the tail should increase with length under the consolation‐prize hypothesis and conspicuous color under the deflection hypothesis. The tail was attacked on 35% of trials, supporting the potential for pre‐capture autotomy to offer antipredator benefits. Dogs were attracted to the tail when it was conspicuously colored, but not when it was longer. This supports the idea that deflection of predator attacks through visual effects is the prime antipredator mechanism underlying the effectiveness of caudal autotomy as opposed to provision of a consolation prize meal.     

Kinetics of mineralization of organic compounds at low concentrations in soil.

The kinetics of mineralization of 14C-labeled phenol and aniline were measured at initial concentrations ranging from 0.32 to 5,000 ng and 0.30 ng to 500 micrograms/g of soil, respectively. Mineralization of phenol at concentrations less than or equal to 32 ng/g of soil and of aniline at all concentrations began immediately, and the curves for the evolution of labeled CO2 were biphasic. The patterns of mineralization of 4.0 ng of 2,4-dichlorophenol per g of soil and 20 ng of nitrilotriacetic acid per g of soil were similar to the patterns for phenol and aniline. The patterns of mineralization of 1.0 to 100 ng of p-nitrophenol and 6.0 ng of benzylamine per g of soil were also biphasic but after a short apparent lag period. The curves of CO2 evolution from higher concentrations of phenol and p-nitrophenol had increasing apparent lag phases and were S-shaped or linear. Cumulative plots of the percentage of substrate converted to CO2 were fit by nonlinear regression to first-order, integrated Monod, logistic, logarithmic, zero-order, three-half-order, and two-compartment models. None of the models of the Monod family provided the curve of best fit to any of the patterns of mineralization. The linear growth form of the three-half-order model provided the best fit for the mineralization of p-nitrophenol, with the exception of the lowest concentrations, and of benzylamine. The two-compartment model provided the best fit for the mineralization of concentrations of phenol below 100 ng/g, of several concentrations of aniline, and of nitrilotriacetic acid. It is concluded that models derived from the Monod equation, including the first-order model, do not adequately describe the kinetics of mineralization of low concentrations of chemicals added to soil.     

Kinetics of mineralization of organic compounds at low concentrations in soil

The kinetics of mineralization of 14C-labeled phenol and aniline were measured at initial concentrations ranging from 0.32 to 5,000 ng and 0.30 ng to 500 micrograms/g of soil, respectively. Mineralization of phenol at concentrations less than or equal to 32 ng/g of soil and of aniline at all concentrations began immediately, and the curves for the evolution of labeled CO2 were biphasic. The patterns of mineralization of 4.0 ng of 2,4-dichlorophenol per g of soil and 20 ng of nitrilotriacetic acid per g of soil were similar to the patterns for phenol and aniline. The patterns of mineralization of 1.0 to 100 ng of p-nitrophenol and 6.0 ng of benzylamine per g of soil were also biphasic but after a short apparent lag period. The curves of CO2 evolution from higher concentrations of phenol and p-nitrophenol had increasing apparent lag phases and were S-shaped or linear. Cumulative plots of the percentage of substrate converted to CO2 were fit by nonlinear regression to first-order, integrated Monod, logistic, logarithmic, zero-order, three-half-order, and two-compartment models. None of the models of the Monod family provided the curve of best fit to any of the patterns of mineralization. The linear growth form of the three-half-order model provided the best fit for the mineralization of p-nitrophenol, with the exception of the lowest concentrations, and of benzylamine. The two-compartment model provided the best fit for the mineralization of concentrations of phenol below 100 ng/g, of several concentrations of aniline, and of nitrilotriacetic acid. It is concluded that models derived from the Monod equation, including the first-order model, do not adequately describe the kinetics of mineralization of low concentrations of chemicals added to soil.