7.3 The Vertebral Column

Learning objectives.

By the end of this section, you will be able to:

  • Describe each region of the vertebral column and the number of bones in each region
  • Discuss the curves of the vertebral column and how these change after birth
  • Describe a typical vertebra and determine the distinguishing characteristics for vertebrae in each vertebral region and features of the sacrum and the coccyx
  • Define the structure of an intervertebral disc
  • Determine the location of the ligaments that provide support for the vertebral column

The vertebral column is also known as the spinal column or spine ( Figure 7.20 ). It consists of a sequence of vertebrae (singular = vertebra), each of which is separated and united by an intervertebral disc . Together, the vertebrae and intervertebral discs form the vertebral column. It is a flexible column that supports the head, neck, and body and allows for their movements. It also protects the spinal cord, which passes down the back through openings in the vertebrae.

Regions of the Vertebral Column

The vertebral column originally develops as a series of 33 vertebrae, but this number is eventually reduced to 24 vertebrae, plus the sacrum and coccyx. The vertebral column is subdivided into five regions, with the vertebrae in each area named for that region and numbered in descending order. In the neck, there are seven cervical vertebrae, each designated with the letter “C” followed by its number. Superiorly, the C1 vertebra articulates (forms a joint) with the occipital condyles of the skull. Inferiorly, C1 articulates with the C2 vertebra, and so on. Below these are the 12 thoracic vertebrae, designated T1–T12. The lower back contains the L1–L5 lumbar vertebrae. The single sacrum, which is also part of the pelvis, is formed by the fusion of five sacral vertebrae. Similarly, the coccyx, or tailbone, results from the fusion of four small coccygeal vertebrae. However, the sacral and coccygeal fusions do not start until age 20 and are not completed until middle age.

An interesting anatomical fact is that almost all mammals have seven cervical vertebrae, regardless of body size. This means that there are large variations in the size of cervical vertebrae, ranging from the very small cervical vertebrae of a shrew to the greatly elongated vertebrae in the neck of a giraffe. In a full-grown giraffe, each cervical vertebra is 11 inches tall.

Curvatures of the Vertebral Column

The adult vertebral column does not form a straight line, but instead has four curvatures along its length (see Figure 7.20 ). These curves increase the vertebral column’s strength, flexibility, and ability to absorb shock. When the load on the spine is increased, by carrying a heavy backpack for example, the curvatures increase in depth (become more curved) to accommodate the extra weight. They then spring back when the weight is removed. The four adult curvatures are classified as either primary or secondary curvatures. Primary curves are retained from the original fetal curvature, while secondary curvatures develop after birth.

During fetal development, the body is flexed anteriorly into the fetal position, giving the entire vertebral column a single curvature that is concave anteriorly. In the adult, this fetal curvature is retained in two regions of the vertebral column as the thoracic curve , which involves the thoracic vertebrae, and the sacrococcygeal curve , formed by the sacrum and coccyx. Each of these is thus called a primary curve because they are retained from the original fetal curvature of the vertebral column.

A secondary curve develops gradually after birth as the child learns to sit upright, stand, and walk. Secondary curves are concave posteriorly, opposite in direction to the original fetal curvature. The cervical curve of the neck region develops as the infant begins to hold their head upright when sitting. Later, as the child begins to stand and then to walk, the lumbar curve of the lower back develops. In adults, the lumbar curve is generally deeper in females.

Disorders associated with the curvature of the spine include kyphosis (an excessive posterior curvature of the thoracic region), lordosis (an excessive anterior curvature of the lumbar region), and scoliosis (an abnormal, lateral curvature, accompanied by twisting of the vertebral column).

Disorders of the...

Vertebral column.

Developmental anomalies, pathological changes, or obesity can enhance the normal vertebral column curves, resulting in the development of abnormal or excessive curvatures ( Figure 7.21 ). Kyphosis, also referred to as humpback or hunchback, is an excessive posterior curvature of the thoracic region. This can develop when osteoporosis causes weakening and erosion of the anterior portions of the upper thoracic vertebrae, resulting in their gradual collapse ( Figure 7.22 ). Lordosis, or swayback, is an excessive anterior curvature of the lumbar region and is most commonly associated with obesity or late pregnancy. The accumulation of body weight in the abdominal region results an anterior shift in the line of gravity that carries the weight of the body. This causes in an anterior tilt of the pelvis and a pronounced enhancement of the lumbar curve.

Scoliosis is an abnormal, lateral curvature, accompanied by twisting of the vertebral column. Compensatory curves may also develop in other areas of the vertebral column to help maintain the head positioned over the feet. Scoliosis is the most common vertebral abnormality among girls. The cause is usually unknown, but it may result from weakness of the back muscles, defects such as differential growth rates in the right and left sides of the vertebral column, or differences in the length of the lower limbs. When present, scoliosis tends to get worse during adolescent growth spurts. Although most individuals do not require treatment, a back brace may be recommended for growing children. In extreme cases, surgery may be required.

Excessive vertebral curves can be identified while an individual stands in the anatomical position. Observe the vertebral profile from the side and then from behind to check for kyphosis or lordosis. Then have the person bend forward. If scoliosis is present, an individual will have difficulty in bending directly forward, and the right and left sides of the back will not be level with each other in the bent position.

Interactive Link

Osteoporosis is a common age-related bone disease in which bone density and strength is decreased. Watch this video to get a better understanding of how thoracic vertebrae may become weakened and may fracture due to this disease. How may vertebral osteoporosis contribute to kyphosis?

General Structure of a Vertebra

Within the different regions of the vertebral column, vertebrae vary in size and shape, but they all follow a similar structural pattern. A typical vertebra will consist of a body, a vertebral arch, and seven processes ( Figure 7.23 ).

The body is the anterior portion of each vertebra and is the part that supports the body weight. Because of this, the vertebral bodies progressively increase in size and thickness going down the vertebral column. The bodies of adjacent vertebrae are separated and strongly united by an intervertebral disc.

The vertebral arch forms the posterior portion of each vertebra. It consists of four parts, the right and left pedicles and the right and left laminae. Each pedicle forms one of the lateral sides of the vertebral arch. The pedicles are anchored to the posterior side of the vertebral body. Each lamina forms part of the posterior roof of the vertebral arch. The large opening between the vertebral arch and body is the vertebral foramen , which contains the spinal cord. In the intact vertebral column, the vertebral foramina of all of the vertebrae align to form the vertebral (spinal) canal , which serves as the bony protection and passageway for the spinal cord down the back. When the vertebrae are aligned together in the vertebral column, notches in the margins of the pedicles of adjacent vertebrae together form an intervertebral foramen , the opening through which a spinal nerve exits from the vertebral column ( Figure 7.24 ).

Seven processes arise from the vertebral arch. Each paired transverse process projects laterally and arises from the junction point between the pedicle and lamina. The single spinous process (vertebral spine) projects posteriorly at the midline of the back. The vertebral spines can easily be felt as a series of bumps just under the skin down the middle of the back. The transverse and spinous processes serve as important muscle attachment sites. A superior articular process extends or faces upward, and an inferior articular process faces or projects downward on each side of a vertebrae. The paired superior articular processes of one vertebra join with the corresponding paired inferior articular processes from the next higher vertebra. These junctions form slightly moveable joints between the adjacent vertebrae. The shape and orientation of the articular processes vary in different regions of the vertebral column and play a major role in determining the type and range of motion available in each region.

Regional Modifications of Vertebrae

In addition to the general characteristics of a typical vertebra described above, vertebrae also display characteristic size and structural features that vary between the different vertebral column regions. Thus, cervical vertebrae are smaller than lumbar vertebrae due to differences in the proportion of body weight that each supports. Thoracic vertebrae have sites for rib attachment, and the vertebrae that give rise to the sacrum and coccyx have fused together into single bones.

Cervical Vertebrae

Typical cervical vertebrae , such as C4 or C5, have several characteristic features that differentiate them from thoracic or lumbar vertebrae ( Figure 7.25 ). Cervical vertebrae have a small body, reflecting the fact that they carry the least amount of body weight. Cervical vertebrae usually have a bifid (Y-shaped) spinous process. The spinous processes of the C3–C6 vertebrae are short, but the spine of C7 is much longer. You can find these vertebrae by running your finger down the midline of the posterior neck until you encounter the prominent C7 spine located at the base of the neck. The transverse processes of the cervical vertebrae are sharply curved (U-shaped) to allow for passage of the cervical spinal nerves. Each transverse process also has an opening called the transverse foramen . An important artery that supplies the brain ascends up the neck by passing through these openings. The superior and inferior articular processes of the cervical vertebrae are flattened and largely face upward or downward, respectively.

The first and second cervical vertebrae are further modified, giving each a distinctive appearance. The first cervical (C1) vertebra is also called the atlas , because this is the vertebra that supports the skull on top of the vertebral column (in Greek mythology, Atlas was the god who supported the heavens on his shoulders). The C1 vertebra does not have a body or spinous process. Instead, it is ring-shaped, consisting of an anterior arch and a posterior arch . The transverse processes of the atlas are longer and extend more laterally than do the transverse processes of any other cervical vertebrae. The superior articular processes face upward and are deeply curved for articulation with the occipital condyles on the base of the skull. The inferior articular processes are flat and face downward to join with the superior articular processes of the C2 vertebra.

The second cervical (C2) vertebra is called the axis , because it serves as the axis for rotation when turning the head toward the right or left. The axis resembles typical cervical vertebrae in most respects, but is easily distinguished by the dens (odontoid process), a bony projection that extends upward from the vertebral body. The dens joins with the inner aspect of the anterior arch of the atlas, where it is held in place by the transverse ligament.

Thoracic Vertebrae

The bodies of the thoracic vertebrae are larger than those of cervical vertebrae ( Figure 7.26 ). The characteristic feature for a typical midthoracic vertebra is the spinous process, which is long and has a pronounced downward angle that causes it to overlap the next inferior vertebra. The superior articular processes of thoracic vertebrae face anteriorly and the inferior processes face posteriorly. These orientations are important determinants for the type and range of movements available to the thoracic region of the vertebral column.

Thoracic vertebrae have several additional articulation sites, each of which is called a facet , where a rib is attached. Most thoracic vertebrae have two facets located on the lateral sides of the body, each of which is called a costal facet (costal = “rib”). These are for articulation with the head (end) of a rib. An additional facet is located on the transverse process for articulation with the tubercle of a rib.

Lumbar Vertebrae

Lumbar vertebrae carry the greatest amount of body weight and are thus characterized by the large size and thickness of the vertebral body ( Figure 7.28 ). They have short transverse processes and a short, blunt spinous process that projects posteriorly. The articular processes are large, with the superior process facing backward and the inferior facing forward.

Sacrum and Coccyx

The sacrum is a triangular-shaped bone that is thick and wide across its superior base where it is weight bearing and then tapers down to an inferior, non-weight bearing apex ( Figure 7.29 ). It is formed by the fusion of five sacral vertebrae, a process that does not begin until after the age of 20. On the anterior surface of the older adult sacrum, the lines of vertebral fusion can be seen as four transverse ridges. On the posterior surface, running down the midline, is the median sacral crest , a bumpy ridge that is the remnant of the fused spinous processes (median = “midline”; while medial = “toward, but not necessarily at, the midline”). Similarly, the fused transverse processes of the sacral vertebrae form the lateral sacral crest .

The sacral promontory is the anterior lip of the superior base of the sacrum. Lateral to this is the roughened auricular surface, which joins with the ilium portion of the hipbone to form the immobile sacroiliac joints of the pelvis. Passing inferiorly through the sacrum is a bony tunnel called the sacral canal , which terminates at the sacral hiatus near the inferior tip of the sacrum. The anterior and posterior surfaces of the sacrum have a series of paired openings called sacral foramina (singular = foramen) that connect to the sacral canal. Each of these openings is called a posterior (dorsal) sacral foramen or anterior (ventral) sacral foramen . These openings allow for the anterior and posterior branches of the sacral spinal nerves to exit the sacrum. The superior articular process of the sacrum , one of which is found on either side of the superior opening of the sacral canal, articulates with the inferior articular processes from the L5 vertebra.

The coccyx, or tailbone, is derived from the fusion of four very small coccygeal vertebrae (see Figure 7.29 ). It articulates with the inferior tip of the sacrum. It is not weight bearing in the standing position, but may receive some body weight when sitting.

Intervertebral Discs and Ligaments of the Vertebral Column

The bodies of adjacent vertebrae are strongly anchored to each other by an intervertebral disc. This structure provides padding between the bones during weight bearing, and because it can change shape, also allows for movement between the vertebrae. Although the total amount of movement available between any two adjacent vertebrae is small, when these movements are summed together along the entire length of the vertebral column, large body movements can be produced. Ligaments that extend along the length of the vertebral column also contribute to its overall support and stability.

Intervertebral Disc

An intervertebral disc is a fibrocartilaginous pad that fills the gap between adjacent vertebral bodies (see Figure 7.24 ). Each disc is anchored to the bodies of its adjacent vertebrae, thus strongly uniting these. The discs also provide padding between vertebrae during weight bearing. Because of this, intervertebral discs are thin in the cervical region and thickest in the lumbar region, which carries the most body weight. In total, the intervertebral discs account for approximately 25 percent of your body height between the top of the pelvis and the base of the skull. Intervertebral discs are also flexible and can change shape to allow for movements of the vertebral column.

Each intervertebral disc consists of two parts. The anulus fibrosus is the tough, fibrous outer layer of the disc. It forms a circle (anulus = “ring” or “circle”) and is firmly anchored to the outer margins of the adjacent vertebral bodies. Inside is the nucleus pulposus , consisting of a softer, more gel-like material. It has a high water content that serves to resist compression and thus is important for weight bearing. With increasing age, the water content of the nucleus pulposus gradually declines. This causes the disc to become thinner, decreasing total body height somewhat, and reduces the flexibility and range of motion of the disc, making bending more difficult.

The gel-like nature of the nucleus pulposus also allows the intervertebral disc to change shape as one vertebra rocks side to side or forward and back in relation to its neighbors during movements of the vertebral column. Thus, bending forward causes compression of the anterior portion of the disc but expansion of the posterior disc. If the posterior anulus fibrosus is weakened due to injury or increasing age, the pressure exerted on the disc when bending forward and lifting a heavy object can cause the nucleus pulposus to protrude posteriorly through the anulus fibrosus, resulting in a herniated disc (“ruptured” or “slipped” disc) ( Figure 7.30 ). The posterior bulging of the nucleus pulposus can cause compression of a spinal nerve at the point where it exits through the intervertebral foramen, with resulting pain and/or muscle weakness in those body regions supplied by that nerve. The most common sites for disc herniation are the L4/L5 or L5/S1 intervertebral discs, which can cause sciatica, a widespread pain that radiates from the lower back down the thigh and into the leg. Similar injuries of the C5/C6 or C6/C7 intervertebral discs, following forcible hyperflexion of the neck from a collision accident or football injury, can produce pain in the neck, shoulder, and upper limb.

Watch this video to learn about a herniated disc. Watch this second video to see one possible treatment for a herniated disc, removing the damaged portion of the disc. How could lifting a heavy object produce pain in a lower limb?

Ligaments of the Vertebral Column

Adjacent vertebrae are united by ligaments that run the length of the vertebral column along both its posterior and anterior aspects ( Figure 7.31 ). These serve to resist excess forward or backward bending movements of the vertebral column, respectively.

The anterior longitudinal ligament runs down the anterior side of the entire vertebral column, uniting the vertebral bodies. It serves to resist excess backward bending of the vertebral column. Protection against this movement is particularly important in the neck, where extreme posterior bending of the head and neck can stretch or tear this ligament, resulting in a painful whiplash injury. Prior to the mandatory installation of seat headrests, whiplash injuries were common for passengers involved in a rear-end automobile collision.

The supraspinous ligament is located on the posterior side of the vertebral column, where it interconnects the spinous processes of the thoracic and lumbar vertebrae. This strong ligament supports the vertebral column during forward bending motions. In the posterior neck, where the cervical spinous processes are short, the supraspinous ligament expands to become the nuchal ligament (nuchae = “nape” or “back of the neck”). The nuchal ligament is attached to the cervical spinous processes and extends upward and posteriorly to attach to the midline base of the skull, out to the external occipital protuberance. It supports the skull and prevents it from falling forward. This ligament is much larger and stronger in four-legged animals such as cows, where the large skull hangs off the front end of the vertebral column. You can easily feel this ligament by first extending your head backward and pressing down on the posterior midline of your neck. Then tilt your head forward and you will fill the nuchal ligament popping out as it tightens to limit anterior bending of the head and neck.

Additional ligaments are located inside the vertebral canal, next to the spinal cord, along the length of the vertebral column. The posterior longitudinal ligament is found anterior to the spinal cord, where it is attached to the posterior sides of the vertebral bodies. Posterior to the spinal cord is the ligamentum flavum (“yellow ligament”). This consists of a series of short, paired ligaments, each of which interconnects the lamina regions of adjacent vertebrae. The ligamentum flavum has large numbers of elastic fibers, which have a yellowish color, allowing it to stretch and then pull back. Both of these ligaments provide important support for the vertebral column when bending forward.

Use this tool to identify the bones, intervertebral discs, and ligaments of the vertebral column. The thickest portions of the anterior longitudinal ligament and the supraspinous ligament are found in which regions of the vertebral column?

Career Connection

Chiropractor.

Chiropractors are health professionals who use nonsurgical techniques to help patients with musculoskeletal system problems that involve the bones, muscles, ligaments, tendons, or nervous system. They treat problems such as neck pain, back pain, joint pain, or headaches. Chiropractors focus on the patient’s overall health and can also provide counseling related to lifestyle issues, such as diet, exercise, or sleep problems. If needed, they will refer the patient to other medical specialists.

Chiropractors use a drug-free, hands-on approach for patient diagnosis and treatment. They will perform a physical exam, assess the patient’s posture and spine, and may perform additional diagnostic tests, including taking X-ray images. They primarily use manual techniques, such as spinal manipulation, to adjust the patient’s spine or other joints. They can recommend therapeutic or rehabilitative exercises, and some also include acupuncture, massage therapy, or ultrasound as part of the treatment program. In addition to those in general practice, some chiropractors specialize in sport injuries, neurology, orthopaedics, pediatrics, nutrition, internal disorders, or diagnostic imaging.

To become a chiropractor, students must have 3–4 years of undergraduate education, attend an accredited, four-year Doctor of Chiropractic (D.C.) degree program, and pass a licensure examination to be licensed for practice in their state. With the aging of the baby-boom generation, employment for chiropractors is expected to increase.

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  • Authors: J. Gordon Betts, Kelly A. Young, James A. Wise, Eddie Johnson, Brandon Poe, Dean H. Kruse, Oksana Korol, Jody E. Johnson, Mark Womble, Peter DeSaix
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2.6: Laboratory Activities and Assignment

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  • Page ID 53542

  • Rosanna Hartline
  • West Hills College Lemoore

Laboratory Activities and Assignment

Part 1: getting to know the microscope.

1. Label the parts of the compound microscope below using the terms listed.

2. Match the names of the microscope parts with their descriptions:

3. Pick up your microscope and physically move it to a new location. Bring it close enough that you can look into it comfortably from where you are sitting. Arrange it so that the stage is facing you and the eyepiece is rotated towards you. What part of the microscope did you grab in order to pick it up and move it?

4. Where are the locations of the two stage adjustment knobs on your microscope?

5. Where is the location of the coarse focus knob?

6. Where is the location of the fine focus knob?

7. Is there a condenser adjustment knob? If so, where is it located?

8. Find the diaphragm lever. Looking in the hole in the center of the stage, what happens when you move the diaphragm lever clockwise?

9. Still looking down at the hole in the center of the stage, what happens when you slide the diaphragm lever counterclockwise?

Part 2: Magnifications of the Microscope

1. Write down the magnification factor for the eyepiece lenses (ocular lenses) on the microscope in front of you.

2. Using the microscope in front of you, write out all the words and numbers written on each objective on your microscope. There are probably three or four objectives. Start with the smallest objective and move through them in order of increasing size:

  • Objective one:
  • Objective two:
  • Objective three:
  • Objective four:

3. In the above list, for each objective, circle just the magnification factor for that objective. Remember, the magnifying factor is a whole number, and differs for each different objective.

4. Write down the total magnification (ocular lens magnification x objective lens magnification) when using each objective on the microscope in front of you.

  • Total magnification - objective one:
  • Total magnification - objective two:
  • Total magnification - objective three:
  • Total magnification - objective four:

**Magnified images in textbooks, activities, and assignments always refer to the TOTAL magnification . To determine the objective lens you will need to use when given instructions in future labs, multiply the magnification written on each objective by the magnification of the ocular lens to determine the total magnification.**

5. If you observed two features on a slide with your naked eye that were 0.5 mm apart, how far apart would they appear to be if you observed them with the microscope in front of you, using the second objective?

Part 3: Comparing the Real Image (Naked Eye) with the Magnified Virtual Image

1. Get an “e” slide. If it is already under your microscope, rotate the lowest-power objective into place, use the coarse focus to lower the stage, and remove the slide.

2. Look at the unmagnified “e” on the slide by eye. Rotate the slide around in your hand so that the “e” is right side up. Now clip the slide onto the microscope stage with the stage clips so that the “e” is facing you right side up when you look at it with your unaided eye.

3. In the right-hand circle below, draw what the “e” looks like when you are looking at it right side up with the unaided eye. Assume the circle below is the size of the entire coverslip. Draw the “e” you see unaided in the correct proportion to the coverslip. (The unmagnified “e” will take up a tiny portion of the coverslip area.)

magnified "e" "e" with the unaided eye

4. Position the slide into slide clips on your microscope stage so that the “e” is still facing you right side up. Get the “e” into your field of view and in focus.

5. In the left-hand circle above, draw what the “e” looks like when viewing it through the microscope under the lowest-power objective. Under the circle, write the total magnification of the image.

6. When viewed under a microscope, how is a specimen rotated?

7. Look at the stage and slide directly (not through the eyepieces). Move the stage control knob that causes the slide to move away from you on the stage, then move it back to its original position.

8. Now move the stage control knob the exact same way you just did, but view the “e” through the eyepiece. When the stage is moving away from you, what direction does the virtual image appear to be moving?

9. Again, look at the stage and slide directly (not through the eyepiece.) This time, move the stage control knob that causes the slide to move to your right, then move it back to its original position.

10.Now move the stage control knob the exact same way you just did, but view the “e” through the eyepiece. When the stage is moving to your right, what direction does the virtual image appear to be moving?

11.The field of view is the entire area you can see when looking through an eyepiece. Use the stage control knobs to move the virtual image of your “e” to one side of the field of view. Keep most of the “e” in the field of view, but move it to one side or the other.

12.Now switch to the next-power objective. Do not skip objectives. To get to the next-power objective, and not the highest-power objective, which way did you have to rotate the objectives, clockwise or counterclockwise?

13.Using only the fine focus knob (you do NOT use the coarse focus knob on any objective other than the lowest objective), get the “e” in focus.

14.Move away from the eyepieces and look at the distance between the slide and the bottom of the objective. Rotate back to the lowest power objective. Now rotate to the next objective (do not rotate to the highest-power objective by accident). Now rotate to the third-highest objective. What happens to the distance between the slide and the bottom of the objective as you rotate to higher power objectives?

15.With the third-highest power objective still in place, how much space is there between the slide and the bottom of the objective?

16.Notice there is a danger of smashing the objective lens into the slide if you were to use the coarse focus. Why are you instructed to only use the coarse focus with the lowest- power objective?

Part 4: Making Illustrations of Magnified Specimens

Instructions for making illustrations of magnified specimens.

You do not have to be a great artist to make a diagram of the cells and structures you see under a microscope. You only have to be careful to draw something that is approximately the same size and shape as what you see. Follow the following guidelines:

  • Only draw what you actually see. Even if you expect to see something, if it is not there you should not draw it. Do not base your drawings on what the textbook or some other source tells you should be there. Do not draw things in the shapes that texts or other sources tell you to expect unless you actually see those shapes.
  • Keep things as simple as possible. Draw strong unbroken lines. Avoid shading or cross- hatching unless there is a very good reason to add them.
  • Feel free to simplify reality by leaving out unnecessary details. Draw what is of interest, but leave out background material, debris, or any other distracting items. Just be careful that, if you are leaving something out, that it isn’t something that is an important part of what you are drawing.

You should always have a basic understanding of what you are looking for before looking in the microscope. Tissues and other microscopic specimens can be confusing and cluttered. If you know in general what you are looking for, and, sometimes more importantly, what you are not looking for, it will make it much easier to find what you want to draw and it will make it much easier to decide how to draw it.

Just remember, what you see under the microscope may look quite different from the perfect specimens that are usually found in the figures put into textbooks and websites. Use the idealized images to track down what you are looking for, but draw the specimen as it actually is, regardless of your expectations.

For instance, in most textbooks, neurons, the most common cell found in nervous tissue, are drawn to look like variations of the drawing in the figure below:

Above: (A) Textbook illustration of a neuron. (B) Microscopic image of a neuron.

In the typical diagram of a neuron that appears in texts and on websites, there usually is a clear nucleus, and often a nucleolus visible, too. The dendrites are typically short and branched. There almost always is a single, easily-identifiable axon that is longer than all the dendrites and branches as it ends. An actual neuron as viewed through a microscope may look different from a “typical” neuron. In fact, often actual specimens look very little like their textbook counterparts. Draw what you see, not what you think you are supposed to see. Just make sure you are looking at what you are supposed to be finding (for instance, a neuron and not a piece of dirt or cell debris), and then draw it as it is.

Most students feel they “cannot draw” and are reluctant to sketch what they are seeing under a microscope. Don’t let what you believe to be a lack of artistic skills stop you! Use the following tips:

  • Draw an outline that approximates the item you want to draw. Don’t obsess about making it match perfectly. Approximate is ok.
  • Try to get the proportions approximately right. If something is half as big, or as third as big, as something else, make it that way in the drawing, too.
  • Do not draw everything you see. Improve on reality by only drawing the parts of the specimen you are interested in. You do not have to draw every bit of debris or dirt. Decide what the important parts of your specimen are and draw only those.

Practice Making Illustrations of Magnified Specimens

1. Get a human blood smear slide. Rotate your lowest power objective into place on your microscope.

2. Follow the directions for focusing on a sample until you are viewing the blood smear at 400x magnification (using the 40x objective).

3. You will see mostly red blood cells. They will probably be pinkish and they will be the circles without nuclei. Occasionally, some will appear to have blank circles in their centers, but these are not nuclei. If you search around your slide using your stage controls, you will find the rare circular cells with nuclei. These are white blood cells. There will be less than one white blood cell for every 100 red blood cells. These white blood cells will probably be light blue or grey and have purple or dark blue nuclei. The nuclei of white blood cells will not always be round.

4. Find a section of your slide with two or more white blood cells among all the red blood cells.

5. In the circle below, draw four or five representative red blood cells (do not draw all the red blood cells you see) and draw all the white blood cells in your field of view. Pay careful attention to drawing the white blood cell nuclei as accurately as possible.

Part 5: Approximating the Size of a Magnified Specimen

Measure the microscopic fields of view.

1. Set the TOTAL magnification of the microscope to 40x or the lowest magnification objective.

2. Place a transparent ruler across the stage of the microscope on top of the stage clips so that the metric side of the ruler is in the light (metric ruler lines can be seen when you look through the oculars).

3. Use the course focus knob to focus on the ruler.

4. Count the number of spaces between the lines on the ruler (each space is a millimeter (mm)) to determine the length of the diameter of the field of view of the compound microscope (see figure below). Record this length in the table below.

5. Switch the microscope to the next highest magnification objective (commonly 100x TOTAL magnification) and adjust the focus using the fine focus knob.

6. Count the number of spaces between the lines on the ruler to determine the length of the diameter of the field of view of the compound microscope. Record this length in the table below.

7. Move to the next highest magnification (usually 400x total magnification) and adjust the focus using the fine focus knob. Can you see the spaces/lines on the ruler to measure the diameter?

8. Calculate the diameter at the magnification from step 7. The difference between 40x and 400x is a magnitude of 10, so there will be a magnitude of 10 difference between the diameter of the field of view at 40x and 400x. To calculate, the diameter of the field of view at 40x is divided by 10 to determine the field of view diameter at 400x:

field of view at 400x (mm) = field of view at 40x (mm) ÷ 10

9. Convert the field of view diameters from mm to µm and record in the table below.

10. Describe the relationship between the total magnification and the field of view diameter . Use your answers from the table above.

Use Field of View Diameters to Approximate Sizes of Microscopic Objects

Imagine the black circle in the figure below is the field of view of the microscope. The blue line across shows the entire diameter of the field of view. There is no actual diameter line in the field of view, nor are there markings that show the percentage of the diameter as shown below - this is where your imagination must come into play to estimate the size of objects in the microscope.

The yellow circle below represents some object magnified by the microscope that you wish to measure. You can see that the yellow circle takes up about 50% of the entire diameter at this magnification. To estimate the size of the yellow circle, use the table above with the diameters of the field of view using the following process:

1. Determine what the total magnification you are viewing the object with and use the table above to determine what the diameter of the field of view is at that total magnification .

2. Estimate the percentage of the diameter of field of view the object you are measuring takes up.

3. Multiply the diameter of the field of view at that magnification in micrometers (µm) by the percentage you determined in part 2:

estimate of object size (µm) = % of field of view diameter x diameter of the field of view at that mag. (µm)

diagram showing how to estimate how large a cell is as a percentage of the microscope view diameter

For example, let's say that the yellow circle is an object magnified by 400x (total magnification). Let's say that in the previous section you calculated the diameter of the field of view at 400x to be 0.5 mm or 500 µm (this value may or may not correspond with your actual measurements and calculations from above - this is for this example only). It is estimated that at 400x, the yellow circle takes up 50% of the diameter of the field of view. The size of the yellow circle is therefore calculated:

Yellow circle size (µm) = 50% x 500 µm = 250 µm

Let's do one more example to show how the magnification changes the calculation.

Use the green circle above to represent another object that is viewed using the microscope at a lower magnification (100x). Let's say in the previous section, it was determined that the diameter of the field of view at 100x was 2 mm or 2,000 µm (this value may or may not correspond with your actual measurements and calculations from above - this is for this example only). It is estimated that at 100x, the green circle is 25% of the diameter of the field of view. The size of the green circle is therefore calculated:

Green circle size (µm) = 25% x 2,000 µm = 500 µm

Use the instructions above to calculate estimated sizes for the objects below at the magnifications given with their corresponding fields of view:

Part 6: Examining, Measuring, & Illustrating Magnified Specimens

Examine, measure, and illustration the epithelial tissue layer of the skin.

1. Obtain a slide of skin and focus on the sample using the techniques you learned in this laboratory.

2. Identify the epithelial tissue layer of the skin (see figure below) on the slide.

3. Measure the thickness of the epithelial tissue layer of the skin in micrometers (µm) as you learned to do in the previous section. Write your calculation and put your estimated measurement in the space provided:

Estimated thickness of the epithelial tissue layer of the skin:_______ µm

4. Make an illustration of the sample in the space below and indicate the magnification of your illustration:

Examine, Measure, and Illustrate Cheek Epithelial Cells

1. Make a wet mount of cheek epithelial cells. Watch this video for instructions for making a wet mount of cheek epithelial cells.

a. Set a new slide on the benchtop.

b. Put a very small drop of saline (0.85% - 0.9% NaCl) in the center of the slide.

c. GENTLY scrape the inside of your cheek with a toothpick to obtain cheek epithelial cells.

d. Swirl the same side of the toothpick that scraped the inside of your cheek in the drop of saline on the slide.

e. Dispose of the toothpick in a biological waste container or in a container of bleach water.

f. Place one small drop of methylene blue (stain) on top of the saline/cheek cell solution on the slide.

g. Place one edge of a cover slip toward the edge of the fluid on the slide at about a 45 degree angle and dip in the fluid.

h. Release the cover slip onto the fluid on the slide. The fluid should spread out underneath the cover slip.

i. Use a paper towel or KimWipe at the edge of the cover slip to wick off excess fluid.

2. Focus on the cheek epithelial cell sample using the techniques you learned in this laboratory.

3. Identify the cheek epithelial cells on the slide. Make sure you are looking at cheek epithelial cells and not other debris on the slide. See the video linked above to examine what cheek epithelial cells should look like.

4. Measure the size of a cheek epithelial cell in micrometers (µm) as you learned to do in the previous section. Write your calculation and put your estimated measurement in the space provided:

Estimated size of a cheek epithelial cell:_______ µm

5. Make an illustration of the sample in the space below and indicate the magnification of your illustration:

Attributions

  • "Anatomy and Physiology I Lab" by Victoria Vidal is licensed under CC BY 4.0
  • "BIOL 250 Human Anatomy Lab Manual SU 19" by Yancy Aquino , Skyline College is licensed under CC BY-NC-SA 4.0
  • "Anatomy and Physiology Lab Reference" by Laird C Sheldahl , OpenOregonEducational Resources , Mt. Hood Community College is licensed under CC BY-SA 4.0

Exploring WCAG 2.1 — 2.5.3 Label in Name

Our series of new WCAG 2.1 Success Criteria continues with the next success criterion within the new 2.5 Input Modalities guideline: 2.5.3 Label in Name .

Guideline 2.5 Input Modalities

Make it easier for users to operate functionality through various inputs beyond keyboard.

Success Criterion 2.5.3 Label in Name (Level A)

For user interface components with labels that include text or images of text , the name contains the text that is presented visually.

Note: A best practice is to have the text of the label at the start of the name.

Terminology

To understand this success criterion we need to review the difference between a label and a name. 

The label identifies the control to all users. It is generally visible text. Examples of labels are the label element on a form control or the text of a link. The label is often used as the name as shown in the example search field below.

HTML code for search field:

The label is, “Search.”

The name is what assistive technology uses to identify the control to the user. This means it can be programmatically determined and why it is often referred to as the accessible name. The accessible name is not related to the name attribute on input elements. 

A control may have both an accessible name and a label. The name may be the same as the label as in the search field example above.  Or, the name may not be detectable on the page unless you are using an assistive technology. Examples include the alt-text and the aria-label, and aria-labelledby attributes. The image below of the red coffee mug has the alt text of, “red coffee mug with large black polka dots.” The alt text is the accessible name that screen readers will speak. 

assignment quick check labeling 2.1

Who Benefits?

People who use speech input benefit from this success criterion. A user must speak the accessible name of the component for the speech input software to know which one to activate. If the accessible name does not match or start with the visible name, a user does not know the correct name to speak.

A proper behavior benefits people who can see, especially when they also are screen reader users. A screen reader speaks the accessible name. It confuses users when the visible label is not the same as the name, and they do not hear what they see on the screen.

The simple example below lists several kitchen products for sale. The button next to each product has the label, “Buy.” A speech input user would say “Buy,” but the speech software doesn’t know what item to add.  The underlying code has an aria-label (which is the accessible name) of “Buy <item name> for <amount> .” The speech software expects to hear that text, but the sighted speech input user cannot see that name. 

Kitchen Tools – Poor Example

We have the following kitchen tools available to buy:

assignment quick check labeling 2.1

Kitchen Tools – Better Example

To solve this issue, make the label and the accessible name the same. If that is not possible, have the visible label text at the beginning of the accessible name. 

In this example, the accessible name that a screen reader user hears is “Buy <item name> for <amount> .” The speech input user sees and speaks, “Buy <item name> ,” and the software can activate the correct button.

Make labels visible, unique, and descriptive when possible. In this case, the label is the accessible name.  If you need more details in the accessible name, make it start with the same text as the visual label and make sure each label is unique.

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Image Labeling by Assignment

Profile image of Stefania PETRA

Journal of Mathematical Imaging and Vision

Related Papers

Stefania PETRA

We introduce a novel geometric approach to the image labeling problem. A general objective function is defined on a manifold of stochastic matrices, whose elements assign prior data that are given in any metric space, to observed image measurements. The corresponding Riemannian gradient flow entails a set of replicator equations, one for each data point, that are spatially coupled by geometric averaging on the manifold. Starting from uniform assignments at the barycenter as natural initialization, the flow terminates at some global maximum, each of which corresponds to an image labeling that uniquely assigns the prior data. No tuning parameters are involved, except for two parameters setting the spatial scale of geometric averaging and scaling globally the numerical range of features, respectively. Our geometric variational approach can be implemented with sparse interior-point numerics in terms of parallel multiplicative updates that converge efficiently.

assignment quick check labeling 2.1

We study the inverse problem of model parameter learning for pixelwise image labeling, using the linear assignment flow and training data with ground truth. This is accomplished by a Riemannian gradient flow on the manifold of parameters that determines the regularization properties of the assignment flow. Using the symplectic partitioned Runge–Kutta method for numerical integration, it is shown that deriving the sensitivity conditions of the parameter learning problem and its discretization commute. A convenient property of our approach is that learning is based on exact inference. Carefully designed experiments demonstrate the performance of our approach, the expressiveness of the mathematical model as well as its limitations, from the viewpoint of statistical learning and optimal control.

We introduce a novel algorithm for estimating optimal parameters of linearized assignment flows for image labeling. An exact formula is derived for the parameter gradient of any loss function that is constrained by the linear system of ODEs determining the linearized assignment flow. We show how to efficiently evaluate this formula using a Krylov subspace and a low-rank approximation. This enables us to perform parameter learning by Riemannian gradient descent in the parameter space, without the need to backpropagate errors or to solve an adjoint equation, in less than 10 seconds for a 512 Ă— 512 image using just about 0.5 GB memory. Experiments demonstrate that our method performs as good as highly-tuned machine learning software using automatic differentiation. Unlike methods employing automatic differentiation, our approach yields a lowdimensional representation of internal parameters and their dynamics which helps to understand how networks work and perform that realize assignmen...

Lecture Notes in Computer Science

We introduce and study the unsupervised self-assignment flow for labeling image data (euclidean or manifold-valued) without specifying any class prototypes (labels) beforehand, and without alternating between data assignment and prototype evolution, which is common in unsupervised learning. Rather, a single smooth flow evolving on an elementary statistical manifold is geometrically integrated which assigns given data to itself. Specifying the scale of spatial regularization by geometric averaging suffices to induce a low-rank data representation, the emergence of prototypes together with their number, and the data labeling. Connections to the literature on low-rank matrix factorization and on data representations based on discrete optimal mass transport are discussed.

Reza Babanezhad

We consider the stochastic optimization of finite sums where the functions are smooth and convex on a Riemannian manifold. We present MASAGA, an extension of SAGA on Riemannian manifolds. SAGA is a variance reduction technique that often performs faster in practice compared to methods that rely on updating the expensive full gradient frequently such as SVRG. However, SAGA typically requires extra memory proportional to the size of the dataset to store stale gradients. This memory footprint can be reduced when the gradient vectors have a structure such as sparsity. We show that MASAGA achieves a linear convergence rate when the objective function is smooth, convex, and lies on a Riemannian manifold. Furthermore, we show that MASAGA achieves faster convergence rate with non-uniform sampling than the uniform sampling. Our experiments show that MASAGA is faster than the RSGD algorithm for finding the leading eigenvector corresponding to the maximum eigenvalue.

Proceedings / CVPR, IEEE Computer Society Conference on Computer Vision and Pattern Recognition. IEEE Computer Society Conference on Computer Vision and Pattern Recognition

In this paper, we propose a novel algorithm for computing an atlas from a collection of images. In the literature, atlases have almost always been computed as some types of means such as the straightforward Euclidean means or the more general Karcher means on Riemannian manifolds. In the context of images, the paper&#39;s main contribution is a geometric framework for computing image atlases through a two-step process: the localization of mean and the realization of it as an image. In the localization step, a few nearest neighbors of the mean among the input images are determined, and the realization step then proceeds to reconstruct the atlas image using these neighbors. Decoupling the localization step from the realization step provides the flexibility that allows us to formulate a general algorithm for computing image atlas. More specifically, we assume the input images belong to some smooth manifold M modulo image rotations. We use a graph structure to represent the manifold, an...

We present a smooth geometric approach to discrete tomography that jointly performs tomographic reconstruction and label assignment. The flow evolves on a submanifold equipped with a Hessian Riemannian metric and properly takes into account given projection constraints. The metric naturally extends the Fisher-Rao metric from labeling problems with directly observed data to the inverse problem of discrete tomography where projection data only is available. The flow simultaneously performs reconstruction and label assignment. We show that it can be numerically integrated by an implicit scheme based on a Bregman proximal point iteration. A numerical evaluation on standard test-datasets in the few angles scenario demonstrates an improvement of the reconstruction quality compared to competitive methods.

Hans Knutsson

We study optimization problems over Riemannian manifolds using Stochastic Derivative-Free Optimization (SDFO) algorithms. Riemannian adaptations of SDFO in the literature use search information generated within the normal neighbourhoods around search iterates. While this is natural due to the local Euclidean property of Riemannian manifolds, the search information remains local. We address this restriction using only the intrinsic geometry of Riemannian manifolds. In particular, we construct an evolving sampling mixture distribution for generating non-local search populations on the manifold. This is done within a consistent mathematical framework using the Riemannian geometry of the search space and the geometry of mixture distributions over Riemannian manifolds. We first propose a generalized framework for adapting SDFO algorithms on Euclidean spaces to Riemannian manifolds, which encompasses known methods such as Riemannian Covariance Matrix Adaptation Evolutioanry Stragegies (Ri...

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