Two-compartment models do a good job of accounting for the behavior of the normal lung over a modest range of ventilation frequencies or stress-adaptation time scales. Of course, these models do not come close to representing the structural complexities of a real lung, so one can easily imagine that a model with more than two compartments might provide an improved account of lung mechanical behavior. This is particularly true for behavior pertaining to extended scales of time or frequency, or when the lungs become heterogeneous in disease. In principle, there is no limit to the number of compartments such a model could possess. Dealing with such models might sound like a daunting prospect, given the algebraic machinations presented in the previous chapter for models with only two compartments. Fortunately, the tools of linear systems theory, and the fast Fourier transform (FFT) in particular, come to the rescue. These tools apply so long as the lung can be considered to behave as a collection of linear compartments, each behaving like the model in Fig. 3.1. In this chapter, we examine the principal tools of linear systems theory and see how they apply to the study of lung mechanics.

Linear systems theory

A system is a set of components that have some kind of collective identity. Systems interact with their environments by receiving inputs and producing outputs. The relationships between these inputs and outputs are determined by processes within the system.

Measurement theory

The usefulness and validity of any model of lung mechanics rest entirely on the experimental data upon which it is based. An appreciation for these data and an understanding of how they were obtained are therefore vital for a complete understanding of the model itself.

The experimental data required for the construction of models of lung mechanics usually consist of gas pressures, flows, and volumes. These variables can be measured at a variety of sites around the body. By far the most common measurement site is at the entrance to the airways (this is the nose and mouth in an intact subject, but may be the entrance to the trachea in experimental animals or patients receiving mechanical ventilation). However, other sites have been used, such as at the body surface, inside the esophagus, and even within individual alveoli. Generally speaking, increasing the number of simultaneous measurement sites allows for an increase in the complexity of the possible models that can be identified from the resulting data. Of course, this has to be balanced against practical and ethical considerations.

The measurement of a variable such as pressure occurs in a sequence of steps, as depicted in Fig. 2.1, beginning with the variable itself and ending with the recorded data. First, the pressure is allowed to impinge on a pressure transducer, which is a device that converts the pressure signal into a corresponding voltage signal.

Viewing the lungs as a mechanical system has intrigued engineers, physicists, and mathematicians for decades. Indeed, the field of lung mechanics is now mature and highly quantitative, making wide use of sophisticated mathematical and computational methods. Nevertheless, most books on lung mechanics are aimed primarily at physiologists and medical professionals, and are therefore somewhat lacking in the mathematical treatment necessary for a rigorous scientific introduction to the subject. This book attempts to fill that gap. Accordingly, some familiarity with the methods of applied mathematics, including basic calculus and differential equations, is assumed. The material covered is suitable for a first-year graduate course in bioengineering. I hope, however, it will also be accessible to motivated biologists and physiologists.

This book focuses on inverse models of lung mechanics, and is organized around the principle that these models can be arranged in a hierarchy of complexity. Chapter 1 expands on this concept and introduces the adjunct notion of forward modeling. It also sets the scene with a brief overview of pulmonary physiology in general. Chapter 2 attends to the fact that all the mathematical modeling skill in the world is for nought without good experimental data. Accordingly, this chapter is devoted to the key experimental methodologies that have provided the data on which the models described in subsequent chapters are based. It can thus be skipped without loss of continuity and referred back to when issues related to experimental validation of models arise.

We now come back to the general question of how the single-compartment linear model can be extended to provide a more realistic representation of the lung. Even this simple model has proven extremely useful for describing the behavior of the lung (Chapters 3 and 4). It does even better when extended to include nonlinearities related to flow and volume (Chapters 5 and 6). Nevertheless, a model with only one alveolar compartment just seems too simplistic. It is obvious from considerations of anatomy that a real lung can never be perfectly homogeneous, even when healthy. Structural asymmetries in the airway tree alone make it easier for inspired air to reach some alveolar regions than others. It is also hard to imagine that any disease process affecting mechanical function would strike the lung in a geographically uniform manner. It is therefore natural to think that a realistic model of lung mechanics should account for regional differences in mechanical properties. Indeed, one does not have to look far to find examples of significant departure from single-compartment behavior in the lung.

Passive expiration

One source of experimental evidence for the presence of more than one compartment in the lung comes from passive expiration. Here, the lungs are inflated to some volume V0 above functional residual capacity, and then suddenly allowed to exhale solely under the influence of the elastic recoil forces of the respiratory tissues.

Many common diseases of the lung involve alterations in lung mechanics. Being able to characterize these alterations is thus of great importance. Most research involving the model-based estimation of lung mechanics involves nothing more than what has just been described in the previous chapter. That is, the lung is assumed to behave like a single linear compartment characterized by only two parameters, resistance (RL) and elastance (EL). These two parameters are typically evaluated first under baseline or control conditions and then following whatever intervention is being investigated. This raises the question of how to interpret R and E, and their changes, in physiological terms. In this chapter we consider what these two parameters can tell us about events happening within the lungs.

We saw in the previous chapter (Fig. 3.4) that RL is made up of two distinct components – one from the airways (Raw) and one from the lung tissues (Rt). This raises questions about how these two components arise. How, for example, could the airway tree, with all its structural complexity, give rise to a particular value of Raw? Why is it that when energy is imparted to the tissues during lung inflation, some portion of this energy is dissipated to give rise to Rt while the remainder is stored to be reflected in the value of EL? Answering these questions is clearly important in being able to assign Raw, Rt, and EL their appropriate physiological interpretations.

This ends our tour through the inverse modeling world of lung mechanics, but it is only the tour that has ended. The inverse modeling world itself is limitless in extent, and its known borders continue to be extended by the synergistic forces of advancing experimental methods and increasing computational power. Nevertheless, the landscape we have covered in this book already exhibits widely varying terrain, and so it is easy to lose sight of the fact that all the different regions of this landscape are part of a single inverse modeling world. A brief overview will help bring it all together.

We began by pointing out in Chapter 1 that inverse models of lung mechanics can be usefully grouped into a hierarchy of increasing complexity (Fig. 1.6). The first level of complexity is represented by the single-compartment linear model, consisting of an elastic tissue compartment served by a single flow-resistive airway (Fig. 12.1). This model, which comprises the standard conception of lung mechanics, was explored in Chapter 3 and is characterized by the two parameters lung resistance (RL) and lung elastance (EL). Evaluation of RL and EL can be achieved by applying multiple linear regression to measurements of the independent variables volume (V) and flow () together with the dependent variable transpulmonary pressure (Ptp). Confidence intervals about the estimated values of RL and EL can be determined according to classical regression theory under the assumptions that the noise in the data arises only in Ptp and that this noise is random, uncorrelated, and normally distributed.

LEARNING OBJECTIVES

After reading this chapter, you should:

• Understand the types of chemical bonds that hold atoms together in molecules.

• Understand the difference between polar and nonpolar molecules, and the important role that polarity plays in interactions of biological molecules.

• Understand the basic concepts of biochemical energetics, including the role of adenosine-5′-triphosphate (ATP) in the transformation of energy into biochemical work.

• Understand the concepts of acids, bases, pH, and buffering.

• Know the major classes of biological polymers: proteins, polysaccharides, and nucleic acids.

• Understand the chemical structure of polysaccharides as polymers of monosaccharides, including the simple sugars glucose, galactose, and fructose.

• Understand the basic structure of nucleic acids as polymers of nucleotides and how that structure is different in deoxyribonucleic acid (DNA) and ribonucleic acid (RNA) polymers.

• Understand the basic structure of proteins, which are polymers of amino acids, and how the diversity of amino acid structure influences protein three-dimensional structure and function.

• Understand how the chemical structure of phospholipids contributes to the properties of biological membranes.

• Understand the basic features of biological membranes, which are lipid bilayers that are decorated with proteins and carbohydrates.

• Understand the mechanisms of diffusion and osmotic pressure generation.

Prelude

Biomedical engineers are engaged in a great diversity of activities: Chapter 1 described many of the fields in which biomedical engineers make significant contributions. This chapter, together with Chapters 3 and 4, reviews fundamental chemistry concepts that are important for understanding human physiology and biomedical engineering (BME).

LEARNING OBJECTIVES

After reading this chapter, you should:

• Understand the role of the excretory systems in eliminating wastes and toxins and maintaining body balances.

• Understand the concept of biotransformation and the role of the liver in accomplishing the removal of compounds by both direct excretion (through the biliary system) and biotransformation.

• Understand the basic anatomy of the kidney and its functional unit, the nephron.

• Understand the basic processes that underlie kidney function: filtration, reabsorption, and secretion.

• Understand the biophysical processes responsible for filtration and regulation of filtration in the glomerulus.

• Understand the concept of clearance and be able to calculate clearances for typical solutes.

• Understand how proteins in the membrane of tubular epithelial cells—such as channels, active transporters, co-transporters, and exchangers—are responsible for reabsorption and secretion of compounds.

• Understand the role of osmotic pressure as a driving force for water reabsorption in the tubules.

Prelude

Each person ingests a large number of molecules per day with meals and snacks (Figure 9.1). A similarly large number of molecules enters the body through respiration (Figure 9.2). Body processes—such as building proteins, producing energy, and replenishing lost nutritional stores—use many of these molecules (recall Table 7.1). But a sizeable number of ingested chemicals are either not usable or not needed by the body, and therefore must be eliminated. In addition, metabolic processes generate waste products that are toxic if they accumulate in body tissues. These molecules must also be eliminated.

LEARNING OBJECTIVES

After reading this chapter, you should:

• Understand the concept of affinity of a ligand for its associated receptor.

• Understand the principle of signal transduction, and how signals can be activated by ligand binding to a receptor.

• Understand the role of action potentials in signaling within the nervous system.

• Understand how protein and steroid hormones provide circulating signals in the endocrine system.

• Understand the diverse roles of signaling within the immune system.

Prelude

Chapter 5 provided background on the structure and function of human cells, which are the main functional units of the body. Most cells are fully independent living entities, capable of consuming nutrients, growing, and functioning autonomously. The human body is a collection of trillions of cells and, amazingly, these units act in a coordinated fashion, so that people can walk (usually without bumping into walls), breathe (without consciously motivating each breath), and kill invading pathogens (without knowing that they are there). How is the operation of all of these cells coordinated? This chapter reviews how cells communicate with each other directly and through signaling molecules to relay signals from outside and inside the cell (Figure 6.1).

Cells communicate with each other directly or indirectly via molecules called ligands. In direct cell–cell communication, the ligands are bound to the surface of the cell. Soluble, diffusible ligands are used for communication between cells that are not physically connected or are separated by long distances.

LEARNING OBJECTIVES

After reading this chapter, you should:

• Understand the importance of deoxyribonucleic acid (DNA) in storing genetic information in cells.

• Know the chemical structures of DNA and ribonucleic acid (RNA), and how these chemical structures are related to the functions of these biological macromolecules.

• Understand the mechanism of DNA replication and its importance in cell division.

• Understand the central dogma of molecular biology and the concepts of biological transcription and translation.

• Understand that RNA exists in different forms in the cell, with each form contributing uniquely to the processes of transcription and translation.

• Recognize the importance of gene cloning and how recombinant DNA technology has revolutionized biology and biomedical engineering (BME).

• Understand the technique of the polymerase chain reaction (PCR) and how it is used to synthesize DNA.

• Know the common gene delivery vectors that are used in human cells, as well as their advantages and disadvantages.

Prelude

One of the most fascinating and well-known stories in science is that of the discovery of the structure of DNA, which was accomplished by James Watson and Francis Crick in 1953, when both were young men working at Cavendish Laboratory in Cambridge, England. Watson's autobiographical book, The Double Helix, describes that period of accomplishment, but it retains its popularity because it deals directly with a more general theme. It might be the best description for modern readers of the magical quality of science and its appeal for young people seeking adventure, mystery, and fame.

LEARNING OBJECTIVES

After reading this chapter, you should:

• Understand the magnitude of the problem of cancer in modern society.

• Develop an elementary understanding of the biology of cancer cells and be able to describe some of the methods for characterizing the progression of tumors in cancer patients.

• Know some of the ways that ionizing radiation interacts with biological tissues and understand the use of radiation in treatment of solid tumors.

• Understand the role of surgery in diagnosis and treatment of tumors and be able to predict some of the ways that surgical treatments for cancer will develop in the future.

• Understand the value and limitations of chemotherapy in the treatment of cancer.

• Know about some of the new approaches, based on our understanding of the molecular and cellular biology of cancer, for creating biological treatments.

Prelude

Cancer is a common, often life-threatening, disease involving the uncontrolled growth and spread of abnormal cells. Cancer is one of the leading causes of death in the world, particularly in developed nations such as the United States. Cancer is really a group of diseases; it can arise in any organ of the body and has differing characteristics that depend on the site of the cancer, the degree of spread, and other factors. Mutations in certain genes within cells—called proto-oncogenes and tumor suppressor genes—are the primary cause of cancer (1).

Sadly, almost every college student has some knowledge of cancer, gained through experience with classmates, family members, or friends.

LEARNING OBJECTIVES

After reading this chapter, you should:

• Understand the role of vaccines in the prevention of disease.

• Understand the role of antibodies (Abs) in the immune system, and some of the ways that Abs can be used to prevent disease in humans.

• Understand the basic elements of Ab structure, and the difference in chemical structure between Ab classes.

• Understand the difference between monoclonal and polyclonal Abs.

• Understand how monoclonal antibodies (mAbs) are manufactured.

• Understand some of the basic approaches for vaccine development.

Prelude

The previous chapter introduced three of the major subjects of interest in biomolecular engineering: drug delivery, nanobiotechnology, and tissue engineering. This chapter focuses on additional applications of biomolecular engineering, particularly approaches for enhancing the function of the immune system. The most familiar application of biomedical engineering (BME) in immunology is the development of vaccines.

The development of vaccines that are both safe and effective has been one of the great achievements of modern medicine. Because of an effective vaccine, smallpox—a frequently fatal disease that claimed thousands of lives in previous centuries—has been eradicated, or eliminated as a natural infectious agent. Other severe infectious diseases, such as polio and influenza, are now in control in most countries of the world. There are, however, many diseases that have proven to be difficult for vaccine makers. Acquired immune deficiency syndrome (AIDS), which is caused by infection with human immunodeficiency virus (HIV), has killed millions of people worldwide (Figure 14.1), and there is still no effective vaccine available.

The field of biomedical engineering has expanded markedly in the past ten years. This growth is supported by advances in biological science, which have created new opportunities for development of tools for diagnosis of and therapy for human disease. This book is designed as a textbook for an introductory course in biomedical engineering. The text was written to be accessible for most entering college students. In short, the book presents some of the basic science knowledge used by biomedical engineers and illustrates the first steps in applying this knowledge to solve problems in human medicine.

Biomedical engineering now encompasses a range of fields of specialization including bioinstrumentation, bioimaging, biomechanics, biomaterials, and biomolecular engineering. Most undergraduate students majoring in biomedical engineering are faced with a decision, early in their program of study, regarding the field in which they would like to specialize. Each chosen specialty has a specific set of course requirements and is supplemented by wise selection of elective and supporting coursework. Also, many young students of biomedical engineering use independent research projects as a source of inspiration and preparation but have difficulty identifying research areas that are right for them. Therefore, a second goal of this book is to link knowledge of basic science and engineering to fields of specialization and current research.

As a general introduction to the field, this textbook assembles foundational resources from molecular and cellular biology and physiology and relates this science to various subspecialties of biomedical engineering.

LEARNING OBJECTIVES

After reading this chapter, you should:

• Understand the concepts of primary, secondary, tertiary, and quaternary structure in proteins.

• Understand the contribution of amino acid ionization to the structure of proteins.

• Understand the role of disulfide bonds in stabilizing protein structure.

• Recognize some of the methods used to determine the structure of proteins.

• Understand how post-translational modifications such as glycosylation and myristoylation contribute to protein structure and function.

• Understand the kinetics of enzyme action.

Prelude

Proteins are the workhorses of the cell (Figure 4.1): They provide structural support in the cytoskeleton, facilitate communication with other cells by acting as receptors, neutralize foreign pathogens, generate contraction forces in muscle, and most ubiquitously catalyze chemical reactions. Proteins are abundant in biological systems, such as eggs (Figure 4.2). Proteins are one of the major macronutrients in the human diet (Figure 4.3).

Some recombinant proteins now serve as therapeutic drugs for treatment or prevention of disease. Biomedical engineers also use recombinant proteins, such as growth factors, to promote growth and differentiation of cells in engineered tissues. Some biomedical engineers have been using techniques of protein engineering to design new biomaterials for use in tissue engineering, drug-delivery systems, or other medical applications.

This chapter describes the structure and function of proteins and also includes a brief introduction to some of the techniques used to determine protein structure, chiefly nuclear magnetic resonance (NMR) and x-ray crystallography. Researchers in the pharmaceutical industry use these protein structures in structure-guided drug design.

LEARNING OBJECTIVES

After reading this chapter, you should:

• Understand the concepts of an engineering system, system boundaries, and the differences between open and closed systems.

• Be familiar with the concepts of homeostasis and steady state and be able to distinguish equilibrium from steady state.

• Understand the concepts of external and internal respiration.

• Be familiar with air volumes and flow rates in the lungs.

• Understand how oxygen is carried by blood and the quantitative relationships describing oxygen concentration.

• Understand the relationship between carbon dioxide, bicarbonate ion, and pH in body fluids.

• Understand the diffusing capacity of the lung and how it relates to the properties of the respiratory membrane.

• Understand how the structure of the digestive organs (stomach, small intestine, large intestine, pancreas, and liver) is related to their functions in digestion.

• Understand the role of enzymes in digestion, and the importance of enzyme activation after secretion (i.e., the value of zymogens).

• Understand the role of reactor models in understanding digestion and absorption of nutrients.

Prelude

Humans eat, drink, and breathe to bring into their bodies the raw materials for growth, repair, and generation of the energy necessary for life and the actions that bring pleasure to life. This chapter provides an overview of human nutrition and respiration from the perspective of biomedical engineering (BME). The human body is an elegant machine that requires inputs for sustained operation. What are the processes responsible for input of nutrients and raw materials? How are molecular nutrients extracted from ingested materials? How are these processes controlled?

LEARNING OBJECTIVES

After reading this chapter, you should:

• Understand that the circulatory system consists of a circulating fluid, a system of vessels, and a pump.

• Know the composition of blood and the role of cells in determining blood's physical properties.

• Understand the general structure of the vascular system.

• Understand the relationship between vessel radius, resistance to flow, and pressure drop.

• Understand the function of capillaries in the distribution of flow throughout tissues and transport of molecules.

• Understand the anatomy of the heart and the electrical system that generates coordinated contractions.

• Understand the events in the cardiac cycle and how pressure is generated within the chambers and the aorta.

Prelude

Our bodies appear, from the outside, to be solid masses that are slow to change but, just beneath the surface, the body's fluids are in constant motion. Blood moves at high velocity throughout the body within an interconnected and highly branched network of vessels (Figure 8.1). The human circulatory system is responsible for the movement of fluid (and therefore vital nutrients contained in the fluid) throughout the body.

The purpose of the circulatory system is a familiar one to engineers and bakers; it provides mixing, and good mixing is an essential element of many successful enterprises. Cakes are made from flour, eggs, sugar, and milk (among other things); your birthday will be ruined (or at least a bit tarnished) if the chef does not mix these ingredients well. But why must humans be mixed?