Hemodynamic Simulations Workbench:
A JavaScript Web Framework Towards an Open Source Platform


Graph vs Simulation: Why Simulations Are Essential for Hemodynamic Research

Traditional graph drawing, while effective in providing a clear visual representation of data, often falls short in addressing the dynamic and complex nature inherent in systems like hemodynamics. This is precisely where the power of simulations, especially hemodynamic models, becomes evident. Unlike static graphs, which display a fixed dataset, simulations of hemodynamic models offer a dynamic platform that enables researchers to interact with the model, adjust parameters, and observe how these changes influence the system in real-time. This level of interactivity is pivotal for understanding the impact of various physiological conditions on blood flow and heart function, offering insights that are both detailed and predictive.

Simulations excel in their predictive capabilities, allowing researchers to forecast cardiovascular behaviors under conditions that have not been previously observed. This is particularly invaluable in medical fields, where accurately predicting outcomes can guide the planning of surgical interventions or the design of therapeutic devices. Moreover, hemodynamic simulations can integrate complex fluid dynamics and biological interactions through advanced computational methods, providing a depth of realism and detail far surpassing what can be achieved through simple graph drawing. This includes modeling responses to physical activities, drug interactions, or therapeutic measures, thereby not only describing but also predicting physiological responses.

The interactivity offered by simulations supports experimental design and testing within a controlled virtual environment, which can dramatically reduce the costs, time, and ethical concerns associated with direct physical experimentation. In contrast, traditional graphs, once created, do not allow for modifications to test different scenarios or predict the outcomes of variable changes, limiting their utility in dynamic and complex areas such as cardiovascular health.

Adding to the clinical relevance, hemodynamic models help bridge the gap between clinical issues and theoretical models through effective visualization. For instance, the development of logistic-based equations for estimating Pulmonary Artery Pressure (PAP), based on hemodynamic models (Frank, 2018), illustrates how simulations can turn complex equations into accessible insights for clinicians. Such tools are essential not only for their ability to simulate but also for their user-friendliness in allowing clinicians to derive meaningful interpretations from complex data. Therefore, while traditional graph drawing remains useful for straightforward presentations, simulations are indispensable for deeper understanding, innovation, and advancement in dynamic and complex fields like hemodynamics, enhancing both the exploration and explanation of intricate medical phenomena.



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Table of Contents nGeneHemodynamicSimulation:

nGeneHemodynamicSimulation.js: A Base JavaScriptv Class for Simulation Development

→ nGeneHemodynamicSimulation_LBSM.js: Class Inheritance for LBSM (Roh, 2018)

→ nGeneHemodynamicSimulation_deLavalNozzle.js: Class Inheritance for Nozzle Model


BASE: nGeneHemodynamicSimulation.js


LBSM: nGeneHemodynamicSimulation.js



nGeneHemodynamicSimulation: Base JavaScript Class for Simulation Development index

This nGeneHemodynamicSimulation class serves as the base JavaScript class structure from which subsequent classes will inherit. This facilitates and accelerates the development of JavaScript simulation implementations.



Yellow Slope 0.30 Blue Slope 0.70
X: 0 Y: 0
Canvas not supported

nGeneHemodynamicSimulation_LBSM: Class Inheritance for LBSM (Roh, 2018) index

Based on a base javascript class for simulation development, nGeneHemodynamicSimulation, this class nGeneHemodynamicSimulation_LBSM is inhereited from nGeneHemodynamicSimulation for simulating PAP and PAcT with respect to variable factors. This kind of method to employ class inheritance is to help making web-based hemodynamic simulation.



α   7.25 L   310000 γr 1.90
ET 0.36 R   8790000 γl 4.25
Ap 0.00059 C   3.30e-8 γ   6.10
As 0.00038 β   3.00
Canvas not supported

nGeneHemodynamicSimulation_deLavalNozzle: Class Inheritance for Nozzle Model index


A*   5.0 k   10 k'   10
γ   1.3 pe   3 p    30
T   3500
A: 0.000 M: 0.000 V: 0.000
Canvas not supported

Equation \( Velocity = f(x) \)

To determine the gas velocity \( V \) as a function of the axial distance \( x \) along the nozzle from the throat, where \( x \) is zero at the throat:

(1) Nozzle Geometry \( A(x) \):

(2) Area-Velocity Relationship:

The relationship between area and velocity in a de Laval nozzle is governed by compressible flow dynamics:

\( V(x) = M(x) \cdot \gamma \cdot R \cdot T(x) \)

where \( M(x) \) is the local Mach number which can be derived from:

\( M(x) = \sqrt{\frac{2}{\gamma-1} \left[ \left(\frac{A(x)}{A^*}\right)^{\frac{2}{\gamma-1}} \left(1 - \left(\frac{p_e}{p_0}\right)^{\frac{\gamma-1}{\gamma}} \right) \right]} \)

\( T(x) = T_0 \left(1 + \frac{\gamma - 1}{2} M(x)^2\right)^{-1} \)

\( T(x) = T_0 \left(1 + \frac{\gamma - 1}{2} \left(\sqrt{\frac{2}{\gamma-1} \left[ \left(\frac{A(x)}{A^*}\right)^{\frac{2}{\gamma-1}} \left(1 - \left(\frac{p_e}{p_0}\right)^{\frac{\gamma-1}{\gamma}} \right) \right]}\right)^2\right)^{-1} \)

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