Prehospital Transport and Whole-Body Vibration

By Salam Rahmatalla

Prehospital Transport and Whole-body Vibration helps medical transport professionals and vehicle and equipment designers understand the concepts of human response to whole body vibration in order to shed light on the ongoing debate on the effectiveness of current immobilization systems. Written for anyone working with patients who have been medically transported, such as emergency medicine physicians, medics, ER nurses, and those researching and studying whole-body vibration (medical students, ergonomists, human factor researchers, engineers, system developers), this book takes an informative look at situations that occur in the air, on the sea and in ground medical vehicles en route to a hospital.

The transport of supine humans under these conditions may lead to severe involuntary motions of body segments, which can generate discomfort, pain and secondary injuries, especially when the patient has a suspected spinal cord injury. This book will help medical transport professionals and vehicle and equipment designers understand the basic concepts of human response to whole body vibration and shed light on the ongoing debate on the effectiveness of current immobilization systems.

• Provides readers the information needed to create efficient systems that ensure the safety and wellbeing of patients in transport
• Offers measurements and biodynamic metrics to professionals in the field so they can conduct vibration testing on their own
• Includes basic information that will not be affected by regulatory updates

• Language: English
• Publisher: Academic Press
• Release date: Sep 14, 2021
• ISBN: 9780323901048

Salam Rahmatalla

Dr. Salam Rahmatalla is a professor of structural mechanics and biomechanics. His research focuses on the positive and negative effects of vibration on humans and structures. Dr. Rahmatalla has authored and coauthored more than 20 peer-reviewed journal articles and participated in many national and international conferences in the area of human response to vibration. His present research interests are: multi-body dynamics, whole body vibration, structural health monitoring, damage detection and human movement. Dr. Rahmatalla is an active member of the International Organization for Standardization (ISO) in the area of human response to vibration.

Book preview

Chapter 1

Fundamentals of motion and biomechanics

Abstract

This chapter presents the basis for understanding motion fundamentals and biomechanics that are utilized in the rest of the book. The chapter covers basic concepts in linear algebra, complex numbers, forces and motions of particles, rigid bodies (with examples on human models), basic statistics (including the meaning of the p-value and confidence intervals), and time and frequency analysis. It concludes with an introduction to vibration that includes vibration fundamentals, random vibration, and equivalent systems, including examples of supine humans. One point that should be taken from this chapter is that complicated motions and systems, such as the human body, can be simplified, and simplification can be a very powerful tool.

Keywords

Velocity; acceleration; forces; vibration; human models; equivalent system; statistics; frequency analysis; supine human

1.1 Introduction

The human body is a complex system that comprises many segments, namely, the head, neck, chest, abdomen, pelvis, arms, and legs, connected by muscles, tendons, ligaments, soft tissues, and blood vessels, among other things. On the other hand, vibration or shaking is generally a random and unpredictable motion with characteristics that can generate different types of forces that, when combined with sudden impacts (shocks), can be severe. Therefore putting humans in a vibration environment and studying their response is considered a very challenging task. Due to the complexity of the subject matter, the goal here is to present basic concepts to readers from different backgrounds. Readers with engineering backgrounds may skip the majority of the materials presented in the chapter; however, the materials present a summary of basic concepts in motion, statistics, and vibration, and readers may find it a good opportunity to review or learn these concepts before reading the rest of the chapters.

This chapter introduces fundamental concepts in motion and vibration with an emphasis on human response to vibration. The goal of this chapter is to familiarize the reader with the concepts of motion and forces and their effects on different systems, including the human body. In order to reach the point where the reader can understand the effect of vibration on the human body, a step-by-step process is introduced in this chapter to help readers with different backgrounds understand these concepts. This chapter also introduces some fundamental metrics in statistics and vibration that will help the reader understand the materials in the following chapters.

The chapter starts with a description of the motion of one particle without considering the effect of its mass or the forces applied to it (this is called kinematics of motion). Although a particle represents an idealized form of objects because it does not have dimensions, Newton’s second law, which is considered the fundamental law of motion, is based on the concept of particles. This chapter introduces the concept of a particle to describe motion in terms of position, displacement, velocity, and acceleration. The need for establishing a reference coordinate system as an essential part of defining the motion of any object is also explained. Because the motion of any object can have magnitude and direction, for example, a velocity of 30 km/h north, the concept of vectors is introduced. As motion variables can change with time, their magnitude and direction can also change, so the chapter introduces schemes for vector differentiation and integration. The magnitude and direction of forces that can result in different forms based on the coordinate system used are then introduced, and the concept of a particle is extended to an object, where dimensions become important. With objects, the motion becomes more complicated because objects can not only translate like particles, but they can also rotate. Newton’s second law is then extended to deal with objects, and examples illustrate the implementation of the established formulas.

The chapter then introduces the concept of vibration as well as different types of vibration. These include simple forms of deterministic free, damped, and forced systems. As with particles and motions, the introduction of simple vibratory systems with a single mass and one degree of freedom should help readers understand what can happen to complicated systems like the human body. While random vibration is mostly the norm in real-life applications, including transport, different fundamental concepts and metrics are introduced and explained, including the definition of transfer functions that relate the output motion to the input motion of the system. Understanding these concepts will help readers quantify and assess vibrations in the environments where they work. More detailed models are presented toward the end of the chapter to illustrate the degree of complexity that can be involved in predicting the involuntary motion of humans inside a vibration environment.

1.2 Basic vector algebra

Scalars, such as mass, are quantities that can be described by a single number with standardized units such as kilograms (kg) in the SI system, pound mass (lbm) in the British system, and slug in the United States customary system. Vectors, on the other hand, are mathematical representations of any physical property that has a magnitude and a direction. Velocity and acceleration are vectors because they are described by their magnitudes and directions; for example, a wind with a velocity of 30 kilometers per hour (km/h) in the northeast direction will have a different effect than a 30 km/h wind in the northwest direction.

Vectors are normally presented with arrows. The head of the arrow points in the direction of the vector, and the length of the arrow reflects its length or magnitude. Fig. 1.1A shows a schematic representation of a vector. Normally, a vector is described within a coordinate system, and a Cartesian coordinate system is used in many applications. The Cartesian coordinate system has three perpendicular, or orthogonal, axes, representing the space surrounding us or the space that we live in. They are normally represented as x, y, and z using the right-hand rule description. In the right-hand rule (Fig. 1.1B), the thumb of the right-hand points to one axis, such as the z-axis, and the curled fingers of the right hand represent a rotation starting from the x-axis and pointing to the y-axis.

Figure 1.1 (A) Schematic representation of a vector showing its magnitude and direction; (B) the right-hand rule between orthogonal axes.

Any vector in the Cartesian coordinate system can be represented by its components along the axes (x, y, and z). The x, y, and z components are independent, meaning that analysis can be conducted in each axis direction independent of what is happening in other axes. The collection of these components at any location will result in the vector. It should be noted that the vector magnitude will be the same regardless of the use of any coordinate system.

The vector in Fig. 1.2 shows the position of a point P with coordinates 4, 2, and 6. In this representation, the vector has 4 units in the x-direction, 2 units in the y-direction, and 6 units in the z-direction.

Figure 1.2 Position of a point P in the Cartesian coordinate system, showing a unit vector (e) in the direction of the vector (r) and a unit vector perpendicular to it (n).

This vector can be represented using the following mathematical form:

where i, j, and k are unit vectors. A unit vector is a vector that has a length of one unit. The unit vectors i, j, and k are always pointing in the directions of x, y, and z, respectively. Other types of unit vectors can be developed to point in any direction. Vectors can be represented in different forms depending on the coordinate systems they are used in. For example, in the polar (two-dimensional) or cylindrical (if the z-axis is included to become three-dimensional) coordinate system, any vector can be represented by its length and the angle it makes with the coordinate axes.

In the case shown in Fig. 1.2, point P can also be described by the coordinates and , indicating the distance that P is from the center or origin of the coordinate system and the angle it is making with the x-axis. The vector can be written in terms of its magnitude and direction as follows:

(1.1)

where the magnitude or the length of the vector ,

and is a unit vector pointing in the direction of and can be calculated as follows:

It can be seen that the magnitude or length of the unit vector is

Let us take another example and look at the meaning of the unit vector in a plane (x, y).

Let us have

where

and

As shown in Fig. 1.3, the component of the unit vector in the x-direction (0.8) represents the cosine of the angle it is making with the x-axis, that is,

and the component of the unit vector in the y-direction (0.6) represents the cosine of the angle it is making with the y-axis, that is,

Figure 1.3 The component of the unit vector in the x- and y-directions as a function of the cosine of the angles.

So the components of the unit vector are the cosines of the angle it is making with the coordinate system.

1.2.1 Vector addition and subtraction

Vectors like scalar quantities can be added and subtracted as shown in the following example. If

and

then

and

As shown in the example, the components in each similar direction (i, j, and k) are added together.

1.2.2 Vector multiplication

The multiplication of vectors can be done in different ways, including inner or dot and cross product. In the dot product of two vectors (Fig. 1.4), the result is a scalar. That is why the dot product is sometimes called a scalar product. The mathematical formula for the dot product is as follows:

(1.2)

where is the angle between the two vectors, and and are the magnitudes of the vectors.

Figure 1.4 Vectors in the Cartesian system.

When the two vectors become perpendicular to each other, that is, when , the dot product result will be zero because . The dot product can also be done by multiplying each component of by its corresponding component in each direction in as follows.

Let

and

then

When the dot product is conducted on the vector itself, the result of this multiplication represents the norm or the length of the vector as follows:

(1.3)

The dot product can also be used to determine the angle between two vectors and as follows:

(1.4)

This relationship is sometimes used to check whether two vectors are perpendicular to each other; in this case, if the dot product between the two vectors is zero, that is, , then the vectors are orthogonal, or perpendicular, to each other. One implication of this is the orthogonality of the unit vectors in the Cartesian coordinate system (Fig. 1.2), where .

1.2.3 Projection of a vector in a certain direction

The dot product can be used to project a vector in any desired direction. This can be done by conducting a dot product between the vector with a unit vector in the intended projected direction.

Example:

The vector projection of in the direction of another vector can be done as follows.

1. Find a unit vector in the direction of the vector

.

2. Find the magnitude of the projection (d) of v on the vector a (Fig. 1.5).

Figure 1.5 Projection of a vector v in the direction of another vector a.

3. Multiply the magnitude of projection d in step 2 by to create a vector in the direction of a.

1.2.4 Geometric representation of vectors

One interesting representation of a vector is the geometrical representation. A main advantage of this representation is the ability to represent a vector in the n-dimensional space, with the vector having many components in many directions, for applications that cannot be represented by the Cartesian space or coordinate system, which only has three independent axes (x, y, and z).

In the geometrical form, the vector can be written as or .

The vector is the transpose of the vector . If is a row vector, then is a column vector and vice versa. The dot product of a vector by itself can be written as