## The y strain

**LETTER TO THE EDITOR**

**Origin of the “Y strain” of Trypanosoma cruzi**

São Paulo, May 13, 2010

Trypanosoma cruzi is the protozoan causal agent of Chagas disease, an important endemic parasite in several Latin American countries. In many studies conducted on this disease, this microorganism is commonly used to obtain new knowledge. It can be maintained in laboratories through culture in artificial media or in susceptible animals. It presents variable aggressivity and a highly virulent form has been isolated, denominated the “Y strain”. It is often used in investigations because it possesses this particular trait.

I am well acquainted with much of the history concerning the “Y strain”. It seems appropriate to tell it, since the strain is frequently used and mentioned, but few of us know its origin, including many intensively active researchers.

In 1953, I was a resident physician at the Division of Infectious and Parasitic Diseases ( Divisão de Moléstias Infecciosas e Parasitárias ) of the Clinics Hospital of São Paulo ( Hospital das Clínicas de São Paulo ) and during my activities I admitted a Japanese woman or one of Japanese descent. She was sick and it was important to establish a diagnosis, with fever as the dominant manifestation. The woman asked that her seven-month-old daughter be permitted to stay with her and the request was granted. Both had originated from a farm located in the rural area of Marília in the State of São Paulo.

Diagnosis was achieved rapidly and recognized as Chagas disease in its acute phase. Concomitantly, we perceived that the child was also feverish and she was attended. It was not long before it was clear that she, like her mother, had Chagas disease, also in the initial period, when the quantity of parasites in the blood is usually large.

The Trypanosoma cruzi isolated from these patients showed peculiarities that were carefully verified in the Department of Parasitology of the São Paulo School of Medicine ( Departamento de Parasitologia da Faculdade de Medicina de São Paulo ). Further studies determined marked mortality among inoculated animals; thus, proving the highly expressive virulence of the strain. Due to this trait, the protozoan in question was the target of special characterization. It received the designation of “Y” strain from the first letter of the young patient’s name.

The number of experimental scientific studies based on the “Y strain” is enormous, because its behavior helps to achieve almost irrefutable conclusions. As an example, I can recall studies that evaluated the efficacy of pharmaceuticals in treatment protocols.

The subject has a second part, which I also participated in.

My dear friend and colleague, Professor Rubens Campos decided to go to Marília. The home address, a farm, was noted in the hospital medical records. He was successful, since the family still lived on the property. He encountered the girl, aged 25 years-old. He explained the reason for his visit, managed to get her to understand and, in the spirit of cooperation, she promised to go to São Paulo. She made two requests: she would submit to exams from 8 am to the end of the afternoon; and, since she was engaged, her future husband could not know the underlying medical situation. Regarding Chagas disease, the recommended, conventional treatment had been followed. The results: happily, everything was normal. In summary, after 25 years inside the human organism, the “Y strain” had caused no manifestations or disorders, despite the virulence mentioned above.

The parasite recovered from the young woman was forwarded to the Laboratory of Protozoology of the São Paulo Institute of Tropical Medicine ( Laboratório de Protozoologia do Instituto de Medicina Tropical de São Paulo ), to verify its behavior in animals over a long time period; however, the strain was eventually lost.

The “Y strain” appears in innumerous scientific texts concerning Chagas disease, although even researchers that use it do not know the specific facts of its origin.

Prof. Vicente Amato Neto

Laboratório de Investigação Médica, Parasitologia – LIM 46

Av. Dr. Enéas de Carvalho Aguiar 470

05403-000 São Paulo, SP, Brasil

E-mail: [email protected]

All the contents of this journal, except where otherwise noted, is licensed under a Creative Commons Attribution License

Av. Dr. Enéas de Carvalho Aguiar, 470

05403-000 – São Paulo – SP – Brazil

Tel. +55 11 3061-7005

The y strain LETTER TO THE EDITOR Origin of the “Y strain” of Trypanosoma cruzi São Paulo, May 13, 2010 Trypanosoma cruzi is the protozoan causal agent of Chagas disease, an

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## Mechanics of Materials: Strain

#### Strain

So far, we’ve focused on the stress within structural elements. When you apply stress to an object, it **deforms**. Think of a rubber band: you pull on it, and it gets longer – it **stretches**. Deformation is a measure of how much an object is stretched, and **strain** is the ratio between the deformation and the original length. Think of strain as **percent elongation** – how much bigger (or smaller) is the object upon loading it.

Just like stress, there are two types of strain that a structure can experience: 1. **Normal Strain** and 2. **Shear Strain**. When a force acts perpendicular (or “normal”) to the surface of an object, it exerts a normal stress. When a force acts parallel to the surface of an object, it exerts a shear stress.

Let’s consider a rod under uniaxial tension. The rod elongates under this tension to a new length, and the **normal strain** is a ratio of this small deformation to the rod’s original length.

Strain is a **unitless** measure of how much an object gets bigger or smaller from an applied load. **Normal strain** occurs when the elongation of an object is in response to a normal stress (i.e. perpendicular to a surface), and is denoted by the Greek letter **epsilon.** A positive value corresponds to a **tensile** strain, while negative is **compressive**. Shear strain occurs when the deformation of an object is response to a shear stress (i.e. parallel to a surface), and is denoted by the Greek letter **gamma**.

#### Mechanical Behavior of Materials

Clearly, stress and strain are related. Stress and strain are related by a **constitutive law**, and we can determine their relationship experimentally by measuring how much stress is required to stretch a material. This measurement can be done using a **tensile test.** In the simplest case, the more you pull on an object, the more it deforms, and for small values of strain this relationship is linear. This linear, elastic relationship between stress and strain is known as **Hooke’s Law**. If you plot stress versus strain, for small strains this graph will be linear, and the slope of the line will be a property of the material known as **Young’s Elastic Modulus**. This value can vary greatly from 1 kPa for Jello to 100 GPa for steel. For most engineering materials, the linear region of the stress-strain diagram only occurs for very small strains ( Generalized Hooke’s Law

In the last lesson, we began to learn about how stress and strain are related – through Hooke’s law. But, up until this point we’ve only considered a very simplified version of Hooke’s law: we’ve only talked about stress or strain in one direction. In this lesson, we’re going to consider the generalized Hooke’s law for homogenous, isotropic, and elastic materials being exposed to forces on more than one axis.

First things first, even just pulling (or pushing) on most materials in **one direction** actually causes deformation in **all three orthogonal directions**. Let’s go back to that first illustration of strain. This time, we will account for the fact that pulling on an object **axially** causes it to compress **laterally** in the transverse directions:

So, pulling on it in the *x*-direction causes it to shrink in the *y* & *z* directions. This property of a material is known as **Poisson’s ratio**, and it is denoted by the Greek letter **nu**, and is defined as:

Or, more mathematically, using the axial load shown in the above image, we can write this out as an equation:

Since Poisson’s ratio is a ratio of two strains, and strain is dimensionless, Poisson’s ratio is also unitless. **Poisson’s ratio is a material property**. Poisson’s ratio can range from a value of -1 to 0.5. For most engineering materials, for example steel or aluminum have a Poisson’s ratio around 0.3, and rubbers have a Poisson’s ratio around 0.5, which are referred to as “incompressible”. Incompressible simply means that any amount you compress it in one direction, it will expand the same amount in it’s other directions – hence, its volume will not change.

There has been some very interesting research in the last decade in creating *structured materials* that utilize geometry and elastic instabilities (a topic we’ll cover briefly in a subsequent lecture) to create auxetic materials – materials with a negative Poisson’s ratio. Physically, this means that when you pull on the material in one direction it expands in all directions (and vice versa):

This principle can be applied in 3D to make expandable/collapsible shells as well:

Through Poisson’s ratio, we now have an equation that relates strain in the *y* or *z* direction to strain in the z direction. We can in turn relate this back to stress through Hooke’s law. This is an important note: pulling on an object in **one direction causes stress in only that direction**, and **causes strain in all three directions**. So, sigma_{y} = sigma_{z} = 0. Let’s write out the strains in the *y* and *z* direction in terms of the stress in the *x* direction.

Remember, up until this point, we’ve only considered **uniaxial deformation**. In reality, structures can be simultaneously loaded in multiple directions, causing stress in those directions. A helpful way to understand this is to imagine a very tiny “cube” of material within an object. That cube can have **stresses** that are **normal to each surface**, like this:

So, applying a load in the *x* direction causes a normal stress in that direction, and the same is true for normal stresses in the *y* and *z* directions. And, as we now know, **stress in one direction causes strain in all three directions**. So now we incorporate this idea into Hooke’s law, and write down equations for the strain in each direction as:

These equations look harder than they really are: strain in each direction (or, each component of strain) depends on the normal stress in that direction, and the Poisson’s ratio times the strain in the other two directions. Now we have equations for how an object will change shape in three orthogonal directions. Well, if an object changes shape in all three directions, that means it will change its **volume**. A simple measure for this volume change can be found by adding up the three normal components of strain:

Now that we have an equation for volume change, or **dilation**, in terms of normal strains, we can rewrite it in terms of normal stresses.

A very common type of stress that causes dilation is known as hydrostatic stress. This is just simply a pressure that acts equally on the entire material. Since it is acting equally, that means:

So, in the case of hydrostatic pressure we can reduce our final equation for dilation to the following:

This final relationship is important, because it is a constitutive relationship for how a material’s volume changes under hydrostatic pressure. The prefactor to *p* can be rewritten as a material’s **bulk modulus**, *K*.

Finally, let’s get back to the idea of “incompressible” materials. What happens to *K* – the measure of how a material changes volume under a given pressure – if Poisson’s ratio for the material is 0.5?

### Hooke’s Law in Shear

In the previous section we developed the relationships between normal stress and normal strain. Now we have to talk about shear. Let’s go back to that imaginary cube of material. In addition to external forces causing stresses that are normal to each surface of the cube, the forces can causes stresses that are parallel to each cube face. And, as we know, stresses parallel to a cross section are **shear stresses**

Now that cube of material looks a lot more complicated, but it’s really not too bad. On each surface there are two shear stresses, and the subscripts tell you which direction they point in and which surface they are parallel to. For instance, take the right face of the cube. Stresses normal to this face are normal stresses in the *x* direction. There are two stresses parallel to this surface, one pointing in the *y* direction (denoted tau_{xy}) and one pointing in the z direction (denoted tau_{xz}). In order for the cube to be in equilibrium, tau_{xy} = tau_{yx} (otherwise, the cube would rotate). Therefore, there are now **six stresses** (sigma_{x}, sigma y , sigma z , tau_{xy,} tau_{yz,} tau_{xz}) that characterize the state of stress within a homogenous, isotropic, elastic material.

So, how do these shear stresses relate to shear strains? Hooke’s law in shear looks very similar to the equation we saw for normal stress and strain:

In this equation, the proportionality between shear stress and shear strain is known as the **shear modulus** of a material. That’s the equation in its general form, but we can rewrite it more explicitly in terms of its components of *x,y*, and *z*. Doing so will give us the **generalized Hooke’s law** for homogenous, isotropic, elastic materials.

In our generalized Hooke’s law we have our six components of stress and strain, and three material properties. A natural question to as is how do these three material properties relate to each other? That relationship is given by the following equation:

### Summary

We’ve introduced the concept of strain in this lecture. Strain is the deformation of a material from stress. It is simply a ratio of the change in length to the original length. Deformations that are applied perpendicular to the cross section are **normal strains**, while deformations applied parallel to the cross section are **shear strains**. For linear, elastic materials, stress is linearly related to strain by Hooke’s law. The proportionality of this relationship is known as the material’s **elastic modulus**. Using Hooke’s law, we can write down a simple equation that describes how a material deforms under an externally applied load.

Additionally, we learned about **multiaxial loading** in this section. In particular, we learned that stress in **one direction causes deformation in three directions**. This occurs due to a material property known as **Poisson’s ratio** – the ratio between lateral and axial strains. The strains occurring in three orthogonal directions can give us a measure of a material’s **dilation** in response to multiaxial loading. In particular, a material can commonly change volume in response to changes in external pressure, or **hydrostatic stress**. This lead to a definition of a materials resistance to volume change under hydrostatic stress – the **bulk modulus**. By inspecting an imaginary cubic element within an arbitrary material, we were able to envision stresses occurring normal and parallel to each cube face. This gave us **six stresses** and **six strains** (three normal and three shear) that we related to each other using a **generalized Hooke’s law** for **homogenous**, **isotropic**, and **elastic** materials. These components of multiaxial stress and strain are related by three material properties: **Young’s elastic modulus**, the **shear modulus**, and **Poisson’s ratio**.

This material is based upon work supported by the National Science Foundation under Grant No. 1454153. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

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