Local Density Random Walk Model Research Articles

Model-Based Characterization of the Transpulmonary Circulation by Dynamic Contrast-Enhanced Magnetic Resonance Imaging in Heart Failure and Healthy Volunteers

Novel quantitative measures of transpulmonary circulation status may allow the improvement of heart failure (HF) patient management. In this work, we propose a method for the assessment of the transpulmonary circulation using measurements from indicator time intensity curves, derived from dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) series. The derived indicator dilution parameters in healthy volunteers (HVs) and HF patients were compared, and repeatability was assessed. Furthermore, we compared the parameters derived using the proposed method with standard measures of cardiovascular function, such as left ventricular (LV) volumes and ejection fraction. In total, 19 HVs and 33 HF patients underwent a DCE-MRI scan on a 1.5 T MRI scanner using a T1-weighted spoiled gradient echo sequence. Image loops with 1 heartbeat temporal resolution were acquired in 4-chamber view during ventricular late diastole, after the injection of a 0.1-mmol gadoteriol bolus. In a subset of subjects (8 HFs, 2 HVs), a second injection of a 0.3-mmol gadoteriol bolus was performed with the same imaging settings. The study was approved by the local institutional review board.Indicator dilution curves were derived, averaging the MR signal within regions of interest in the right and left ventricle; parametric deconvolution was performed between the right and LV indicator dilution curves to identify the impulse response of the transpulmonary dilution system. The local density random walk model was used to parametrize the impulse response; pulmonary transit time (PTT) was defined as the mean transit time of the indicator. λ, related to the Péclet number (ratio between convection and diffusion) for the dilution process, was also estimated. Pulmonary transit time was significantly prolonged in HF patients (8.70 ± 1.87 seconds vs 6.68 ± 1.89 seconds in HV, P < 0.005) and even stronger when normalized to subject heart rate (normalized PTT, 9.90 ± 2.16 vs 7.11 ± 2.17 in HV, dimensionless, P < 0.001). λ was significantly smaller in HF patients (8.59 ± 4.24 in HF vs 12.50 ± 17.09 in HV, dimensionless, P < 0.005), indicating a longer tail for the impulse response. Pulmonary transit time correlated well with established cardiovascular parameters (LV end-diastolic volume index, r = 0.61, P < 0.0001; LV ejection fraction, r = -0.64, P < 0.0001). The measurement of indicator dilution parameters was repeatable (correlation between estimates based on the 2 repetitions for PTT: r = 0.94, P < 0.001, difference between 2 repetitions 0.01 ± 0.60 second, for λ: r = 0.74, P < 0.01, difference 0.69 ± 4.39). Characterization of the transpulmonary circulation by DCE-MRI is feasible in HF patients and HVs. Significant differences are observed between indicator dilution parameters measured in HVs and HF patients; preliminary results suggest good repeatability for the proposed parameters.

An Inflection Point Method for the Determination of Pulmonary Transit Time From Contrast Echocardiography.

Indicator-dilution curves (IDCs) for the estimation of pulmonary transit times (PTTs) can be generated noninvasively using contrast echocardiography. Currently, these IDCs are analyzed by manual inspection, which is not feasible in a clinical setting, or fit to a statistical model to derive parameters of interest. However, IDCs generated from patients are frequently subject to significant low-frequency noise and recirculation artifacts that obscure the first-pass signal and render model fitting impractical or inaccurate. Thus, the objective of this paper was to develop alternative computational methods to determine PTT using noisy clinical data in which the signal decay is not adequately visible. We report on a method that uses a model fit to the rise portion of the IDCs to determine the signal inflection point. Additionally, a signal truncation algorithm was developed that enables automated analysis of the IDCs. We compare PTTs derived from our inflection point method to those obtained by manual inspection in 25 patients (R(2) = 0.86) and to those obtained by mean transit time calculation following fitting to a local density random walk model (R(2) = 0.80) in a subset of this cohort. Combined with a signal truncation algorithm, the inflection point method provides robust, automated determination of PTT from noisy IDCs containing recirculation artifacts. The inflection point method addresses the need for computational analysis of IDCs obtained from contrast echocardiograms that are not amenable to first-pass model fitting.

Comparison and evaluation of indicator dilution models for bolus of ultrasound contrast agents

Dynamic contrast-enhanced ultrasound (DCE-US) imaging is a promising diagnostic method, which enables the evaluation of tissue perfusion via different parameters. The mean transit time and time-to-peak parameters are the main time parameters and their values depend on the model used for the approximation of the noisy perfusion curves. In this paper, we described a new comparison of different perfusion models using a tissue mimicking phantom. The following models were compared: log-normal, lagged, Erlang, Gamma and the local density random walk model. We discovered that the mean-square error is not the best criterion for model evaluation. More important is the comparison between the estimated time perfusion parameters and the physical parameters of the developed tissue mimicking phantom. Based on the statistical analysis, we can suggest that for the DCE-US perfusion analysis more models should be used, excluding the log-normal model, which gives the highest error of mean transit time value.

Comparison of four mathematical models to analyze indicator-dilution curves in the coronary circulation

While several models have proven to result in accurate estimations when measuring cardiac output using indicator dilution, the mono-exponential model has primarily been chosen for deriving coronary blood/plasma volume. In this study, we compared four models to derive coronary plasma volume using indicator dilution; the mono-exponential, power-law, gamma-variate, and local density random walk (LDRW) model. In anesthetized goats (N = 14), we determined the distribution volume of high molecular weight (2,000 kDa) dextrans. A bolus injection (1.0 ml, 0.65 mg/ml) was given intracoronary and coronary venous blood samples were taken every 0.5–1.0 s; outflow curves were analyzed using the four aforementioned models. Measurements were done at baseline and during adenosine infusion. Absolute coronary plasma volume estimates varied by ~25% between models, while the relative volume increase during adenosine infusion was similar for all models. The gamma-variate, LDRW, and mono-exponential model resulted in volumes corresponding with literature, whereas the power-model seemed to overestimate the coronary plasma volume. The gamma-variate and LDRW model appear to be suitable alternative models to the mono-exponential model to analyze coronary indicator-dilution curves, particularly since these models are minimally influenced by outliers and do not depend on data of the descending slope of the curve only.

Contrast-Ultrasound Diffusion Imaging for Localization of Prostate Cancer

Prostate cancer is the most prevalent form of cancer in western men. An accurate early localization of prostate cancer, permitting efficient use of modern focal therapies, is currently hampered by a lack of imaging methods. Several methods have aimed at detecting microvascular changes associated with prostate cancer with limited success by quantitative imaging of blood perfusion. Differently, we propose contrast-ultrasound diffusion imaging, based on the hypothesis that the complexity of microvascular changes is better reflected by diffusion than by perfusion characteristics. Quantification of local, intravascular diffusion is performed after transrectal ultrasound imaging of an intravenously injected ultrasound contrast agent bolus. Indicator dilution curves are measured with the ultrasound scanner resolution and fitted by a modified local density random walk model, which, being a solution of the convective diffusion equation, enables the estimation of a local, diffusion-related parameter. Diffusion parametric images obtained from five datasets of four patients were compared with histology data on a pixel basis. The resulting receiver operating characteristic (curve area = 0.91) was superior to that of any perfusion-related parameter proposed in the literature. Contrast-ultrasound diffusion imaging seems therefore to be a promising method for prostate cancer localization, encouraging further research to assess the clinical reliability.

On the physical and stochastic representation of an indicator dilution curve as a gamma variate

The analysis of intravascular indicator dynamics is important for cardiovascular diagnostics as well as for the assessment of tissue perfusion, aimed at the detection of ischemic regions or cancer hypervascularization. To this end, indicator dilution curves are measured after the intravenous injection of an indicator bolus and fitted by parametric models for the estimation of the hemodynamic parameters of interest. Based on heuristic reasoning, the dilution process is often modeled by a gamma variate. In this paper, we provide both a physical and stochastic interpretation of the gamma variate model. The accuracy of the model is compared with the local density random walk model, a known model based on physics principles. Dilution curves were measured by contrast ultrasonography both in vitro and in vivo (20 patients). Blood volume measurements were used to test the accuracy and clinical relevance of the estimated parameters. Both models provided accurate curve fits and volume estimates. In conclusion, the proposed interpretations of the gamma variate model describe physics aspects of the dilution process and lead to a better understanding of the observed parameters, increasing the value and credibility of the model, and possibly expanding its diagnostic applications.

Videodensitometric Methods for Cardiac Output Measurements

Cardiac output is often measured by indicator dilution techniques, usually based on dye or cold saline injections. Developments of more stable ultrasound contrast agents (UCA) are leading to new noninvasive indicator dilution methods. However, several problems concerning the interpretation of dilution curves as detected by ultrasound transducers have arisen. This paper presents a method for blood flow measurements based on UCA dilution. Dilution curves are determined by real-time densitometric analysis of the video output of an ultrasound scanner and are automatically fitted by the Local Density Random Walk model. A new fitting algorithm based on multiple linear regression is developed. Calibration, that is, the relation between videodensity and UCA concentration, is modelled by in vitro experimentation. The flow measurement system is validated by in vitro perfusion of SonoVue contrast agent. The results show an accurate dilution curve fit and flow estimation with determination coefficient larger than 0.95 and 0.99, respectively.