Learning Center: The Fick Equation and You


Base Training, The Fick Equation and You

-Written by Joe Rubio

After the season ends, thoughts for the competitive runner turn to the traditional annual build up of miles in preparation for the coming season. The goal in the base training stage is to increase the functional work capacity of the athlete. If we are successful in accomplishing this goal during the initial stages of the season, the groundwork for future success is laid and the potential for improved race performances during the championship season is the end result.

What specifically should be the emphasis of base training be if this is the goal? Is easy mileage the only type of running needed? For a possible answer we look to the Fick Equation.

The Fick Equation

Maximum oxygen uptake or VO2max is considered the recognized standard of cardiovascular, pulmonary, and muscular aerobic fitness. VO2max is the maximum oxygen consumption that can be used per minute, representing any individual's upper limit of aerobic metabolism. Raising the VO2max levels of an athlete through systematic training invariably leads to significant gains in distance running performance. This is the reason why nearly all top-level competitive runners target specific training on raising their VO2max much of the year.

With proper training, an athlete can increase their VO2max as well as the ability to run for longer periods at any percentage of their VO2max. Still, knowing that increasing VO2max results in faster race times means little if you do not understand the components that make up VO2max. The Fick Equation is a mathematical estimation of an athlete's theoretical VO2max. Understanding the individual components that comprise VO2max can help us determine the specific types of workouts we should focus on to increase this important training variable. The formula for determining VO2max through the Fick Equation is represented as:

VO2 max = Q(CaO2-CvO2)
Q is cardiac output,
CaO2 = arterial oxygen content,
CvO2 = venous oxygen content.

The Fick Equation states that VO2max equals the amount of blood pumped per heart beat at maximum heart rate times the amount of oxygen the working muscles are able to extract from the blood passing through them. The maximal heart rate times the volume of blood pumped per beat is referred to as maximal cardiac output, while the amount of oxygen being extracted by the working skeletal muscles is called the Arterio-Venous Oxygen difference (A-V O2 Difference) and is classified as the difference between the oxygen delivered to a working muscle (the arterial concentration) and the oxygen levels of the blood leaving the working muscles (the venous concentration).

In functional terms, to increase VO2max we must:

  1. Increase the cardiac output or the amount of energy (oxygen) made available to the working muscles.
  2. Increase the A-V O2 Difference, meaning (1) increase the delivery and/or (2) improve the efficiency with which the working muscles make use of the available oxygen to produce energy.

To gain continued improvement in a distance runner's performances season after season, we must seek ways to increase the amount of available energy to the working muscles. Additionally, we must improve the delivery of the available energy to the specific muscles that require additional energy and increase the percentage of the available energy they can effectively use. The base period is the ideal time to lay the groundwork for improvement in all of these areas.

Running Physiology 101

Air containing oxygen enters the lungs through breathing and once in the air sacs of the lungs, oxygen passes into the blood stream where it binds with hemoglobin within red blood cells. The oxygen-rich blood is pumped by the heart through arteries which branch into smaller capillaries that surround the working muscles. The thin walls of the capillaries allow oxygen carried by the red blood cells to pass through to working muscles where they are utilized by the working muscles to produce energy as well as remove the waste products produced as a result of metabolism.

Increasing the Amount of Energy Available to Working Muscles

Increasing the amount of energy available for use by the working muscles is the first goal to be met in increasing VO2max. Oxygen is the primary source of energy and is used to convert carbohydrates and lipids into usable energy by the working muscles. At the most basic level, the greater the amount of oxygen available in the blood stream, the greater the potential for improved distance running performances.

There are two primary factors that an athlete can influence which typically will have a positive affect on the amount of oxygen available in the blood stream at any one time. These include:

  1. The amount of blood pumped by the heart.
  2. The amount of available hemoglobin within the blood.

While many believe that increasing lung capacity will help in this area, research suggests that a healthy human has more than enough available oxygen in their lungs to supply their needs. Lung capacity is not a factor that limits performance and therefore actively training to improve lung capacity will not result in improved performance.

Increasing The Amount of Blood Pumped

The primary piece of the oxygen supply puzzle is the actual volume of blood that can be pumped by the heart that is called cardiac output. If the athlete can pump a greater volume of blood through their blood system for a set period of time, the effect is to increase the amount of oxygen that is made available at any one time to working muscles thus increasing the potential for improved performances.

Cardiac Output = Max Heart Rate x Stroke Volume

Cardiac output can be increased in one of two ways. Either through an increase in the number of beats per minute of the heart or by an increase in the amount of blood pumped with each beat of the heart. The number of beats per minute is referred to as the maximum heart rate of an athlete. Unfortunately, this factor is limited by heredity and cannot be influenced through training.

The amount of blood pumped with each beat of the heart is referred to stroke volume. Fortunately, stroke volume can be greatly influenced by proper training. The result of increasing stroke volume is to increase the amount of oxygen that is made available to working muscles at any one time, which corresponds to a potential increase in the work capacity of that athlete. The primary training adaptation that increases VO2max and ultimately leads to faster race times is through training that leads to an enlargement of the left ventricle of the heart as well as an improvement in the ability of the heart to contract. Increasing stroke volume has the greatest potential for in improving running performance above every other training means. Development of this area should not be overlooked.

Increasing the Amount of Available Hemoglobin

An important area to look at when addressing the available oxygen in the blood stream is the make up of the blood itself, specifically the amount of hemoglobin present within the red blood cells. If the athlete has a lower than normal level of hemoglobin in the blood stream, this results in less oxygen which can be transported to the working muscles. The condition of having lower than normal levels of hemoglobin is known as anemia and results in decreased performances. The greater the amount of hemoglobin in the blood stream, the greater the amount of oxygen there is to be transported to the working muscles. If an athlete can effectively increase the available hemoglobin in their blood system to normal or above normal levels, the result should be a potential for increased performances. Living for extended periods of time at altitude will positively affect the amount of hemoglobin in the blood stream, but this is not a realistic option for many athletes. One area that any runner can address is diet that can greatly influence a positive change in hemoglobin levels.

Every attempt should be made to have the athlete focus specific attention upon establishing and maintaining a diet that specifically addresses providing the proper amount of iron intake from natural food sources in combination with other foods that encourage iron absorption, plus ensuring an adequate calorie intake are good places to start to help avoid anemia. Base training is the ideal time to establish a sound routine of nutrition. Good eating habits established early in the season and maintained will help increase the performances of the athlete down the road by ensuring maximum levels of hemoglobin is available for oxygen transport.

Training to Improve the Availability of Oxygen

Increasing cardiac output is the only available means to increase the availability of red blood cells to working muscles. The idea of how exactly to accomplish this feat is far from new. Dr Reindell and Dr Gerschler in the 1930's discovered that shorter, somewhat intense bouts of fast running, followed by a recovery period repeated several times in the same training session resulted in an increase in stroke volume and thus, the cardiac output of the athlete over time. The training method Reindell and Gerschler invented was termed "interval" training because of the recovery "interval" taken following a short, fast bout of running. This form of training resulted in the monumental improvements in distance running performances starting in the 1940's and continuing through to the present day.

Gerschler and Reindell's original method required periods of effort lasting from 30 to 70 seconds, at an intensity that elevated the heart rate to about 170-180 beats per minute. The hard effort phase was followed by sufficient recovery time to allow the heart rate to return to 120-140 beats/min. The process of raising and lowering the heart rate was repeated many times.

The significant part of the process was not necessarily the fast running, but the recovery interval, which actually provided the training effect. It is during the recovery phase that the heart rate declines at a proportionally greater rate than the return of blood to the heart, resulting in a brief increase in stroke volume. The repeated nature of short interval resulted in a greater training stimulus for stroke volume development than does a run at a set intensity but lacks recovery periods.

Real World Training Application

Performing short intervals such as 200's, 300's and 400's on a flatter surface or hill reps of the same 200-400m length at roughly 1500-3k with a short recovery jog of roughly the same time or distance run is the proper effort and recovery needed to increase stroke volume over time.

Over the years, short intervals have been a consistent element in nearly every top distance runner's schedules. Zatopek, Bikila, Edelen, Keino, Ryun, Shorter, Rodgers, Meyer, Waitz, Barrios, Jones, DeCastella ? it doesn't really matter if they are a middle distance, long distance or marathon athlete, the top distance runners do these regularly throughout the entire training year. If an athlete is serious about improving as a competitive distance runner, there is little question they should incorporate them consistently into their schedule year round.

Do these short intervals need to be all out? Actually no, all out efforts are counter-productive during the base phase. ItÍs much better to do a larger number controlled, versus a smaller amount out of hand. Primarily 1500-3k effort is whatÍs needed to elicit the greatest training effect, but 5k efforts produce solid benefits as well and are much more appropriate for those coming off an injury or extended breaks (i.e. masters). Short intervals should be included into a training schedule at least every other week, and preferably once or twice a week most of the year to address stroke volume improvements.

Examples include:

  1. 40-60 min easy + 8 x 200 at 3k effort w/ 200 jog
  2. 20-30 min easy + 9 x 250m hill reps at 3k effort w/ jog down recoveries + 10-15 min
  3. 30-40 min + 8 x 300 on grass at 1500-3k effort w/ easy 300m jog + 10-15 min
  4. 15-20 min easy + 10 x 60 seconds on/off at 3k effort + 15-20 min
  5. 6-8 mile run on rolling hills. Surge uphill at XC/5k race effort
  6. Masters or return from injury version: 15-20 min + 30 sec on/60 sec off + 15-20 min

Improving the Efficiency of Oxygen Usage

Improving the delivery and efficiency with which the muscles make use of the available oxygen in the blood stream is the second goal to be met in increasing the functional work capacity of an athlete. It's not enough to have a large amount of oxygen available for the muscles to use. For the athlete to gain the ability to race faster, the delivery and utilization of a greater percentage of available oxygen by the working muscles is a key factor in determining if an athlete reaches their potential as a competitive distance runner.

There are 3 primary areas to address when increasing energy utilization and improving energy delivery:

  1. Increasing the number and size of mitochondria
  2. Increasing the aerobic enzyme activity
  3. Increasing the capillary network surrounding working muscles

One of the main goals in the pursuit of increasing oxygen utilization is improving the muscle fiber's ability and capacity to use a larger percentage of available oxygen to burn sugars and lipids. The mitochondria are the powerhouse of the cell that specializes in the production of ATP (energy) within the aerobic system. Increasing oxygen utilization is achieved by increasing the number and size of mitochondria as well as the activity of the aerobic enzymes that are found within the mitochondria. The amount of oxygen used and the amount of ATP produced is directly proportional to the activity of these enzymes and the number of mitochondria. Therefore to increase the efficiency of the athlete requires an increase in the number and size of mitochondria as well as increasing the aerobic activity of the enzymes located within the mitochondria.

Additionally improving the delivery of oxygen to working muscles via an increase in the number of capillaries surrounding the working muscles has the potential to increase performance. Capillaries supply muscles directly with oxygen. An increase in the number of capillaries results in an increase in the supply of oxygen that can reach the working muscles and a net increase in that athlete's potential.

Training to Improve Efficiency of Energy Usage

To improve the delivery and efficiency with which the athlete uses the available oxygen, we must improve three areas: increase the number and size of mitochondria, increase the aerobic enzyme activity, and increase the capillary network around the working muscles. How is this accomplished? Sustained runs performed at 70-90% of VO2max elicit all of these necessary reactions in the working muscles. Sustained runs which range anywhere from an easier long run to a faster 4 mile tempo run and everything in between performed at roughly 70-90% of an athlete's current 5k pace have been shown to greatly increase the number and size of the working muscles mitochondria and the activity of aerobic enzymes, plus they increase the number and density of the capillaries surrounding the working muscles thereby increasing the delivery of available oxygen.

Performing these types of runs season after season allows greater adaptations and is a key factor in answering why developed athletes can spend a large percentage of their weekly mileage in the upper end of the 70-90% range. Improvements in this area increase the athlete's ability to run for longer periods at any percentage of their VO2max. This equates to faster race times at every race distance, plus improved finishing kicks at the end of races even without any improvements in overall leg speed.

Real World Application

What training paces are we talking about to increase efficiency of energy usage? For a 15:00 5k runner: 7 minute pace down to 5:30 pace. For a 17:00 runner; 7:45 pace down to 6:00, for a 19:00 5k person; 8:30 down to 6:30. As these paces indicate, the effort is not easy, but neither is it all out or race like. Ideally runs focusing on improving efficiency are kept strong and controlled for a longer period of time. Base training really should be of a more relaxed nature in the 70-75% range early on in a career where the athlete runs by feel more than by a set pace, but as the athlete matures and is better able to tolerate the added stress, more running should occur in the 80-90% range. What it is important though is that the runs be of a stronger, controlled, sustained nature and for an extended period of time.


  1. Long easy to moderate run of 90-120 min at 70-75% of 5k
  2. 30-40 min at 80-85% of 5k
  3. Progressive run starting easy, making each mile faster and ending the last mile at 90%
  4. 60-90 min in the hills working the up hills at a strong effort and running the final 40-50 minutes home at 75-80%.
  5. Fartlek with the fast portions at roughly 90% effort and following that with an easier jog for recovery at 70-75%. 2-5 min on/off with 10-20 minutes total harder running.
  6. 20-30 min at 90% (tempo)

There have been countless athletes over the years with extremely high VO2max values, but sadly race times that were not very good. This is because their utilization of the available oxygen was low. The reason for their proportionally slow race times most likely was the result of not consistently training for extended lengths of time at paces that range between the very easy recovery jogs and faster interval workouts. Runs that range anywhere between 70-90% of an athlete's current 5k fitness fill this important gap and play an enormous role in determining how fast an athlete can ultimately race distance events.

Over time, performing many, many miles over many, many seasons at 70-90% of 5k pace results in an increase in the athlete's ability to utilize more available energy. These physiological improvements allow the athlete to perform at a greater percentage of their VO2max for a longer period of time. This equates to faster overall race times at ALL distances, sprints included.


The summer months are the ideal time to lay the groundwork for future success. A higher than normal volume of weekly mileage is a key component, but not to be overlooked is the addition of regularly scheduled short intervals each week plus several other days each week of runs in the 70-90% of 5k pace range. These two types of workouts perform absolutely essential functions in the continued improvement in race times. Short intervals increase the stroke volume of the athlete and make more oxygen available, while 70-90% efforts improve the ability to utilize this added oxygen through an increase in the number and size of mitochondria, an increase in the activity of the aerobic enzymes located within the mitochondria, and increase the capillary network that surround the working muscles all of which improve the fractional utilization of oxygen thus forming the necessary groundwork for continued improvement in distance running performances over time.


Current Est. Fitness 65% 70% 75% 80% 85% 90% 95% 100% 105%
5k/10k Very Easy Easy Moderate Strong MP Tempo 10k 5k:VO2 3k
14:00/29:35 6:50+ 6:25 6:00 5:36 5:20 5:00 4:44 4:30 4:18
14:20/30:00 7:00+ 6:32 6:08 5:44 5:24 5:04 4:48 4:35 4:22
14:35/30:40 7:10+ 6:40 6:12 5:48 5:28 5:12 4:54 4:40 4:26
14:48/31:15 7:20+ 6:48 6:20 5:56 5:36 5:16 5:00 4:44 4:30
15:05/31:40 7:30+ 6:54 6:28 6:00 5:40 5:20 5:04 4:50 4:34
15:25/32:30 7:40+ 7:00 6:32 6:08 5:48 5:28 5:12 4:56 4:38
15:35/32:55 7:50+ 7:08 6:40 6:16 5:52 5:32 5:16 5:00 4:42
16:02/34:10 7:55+ 7:16 6:48 6:24 6:00 5:40 5:24 5:08 4:50
16:25/34:35 8:05+ 7:30 7:00 6:32 6:12 5:48 5:32 5:16 4:58
16:40/35:00 8:15+ 7:36 7:08 6:40 6:16 5:56 5:36 5:20 5:02
17:05/35:50 8:25+ 7:48 7:16 6:48 6:24 6:04 5:44 5:28 5:10
17:30/36:40 8:35+ 8:00 7:28 7:00 6:36 6:12 5:54 5:36 5:18
17:55/37:40 8:45+ 8:12 7:40 7:12 6:48 6:24 6:04 5:45 5:26
18:20/38:30 8:55+ 8:24 7:52 7:20 6:56 6:32 6:12 5:52 5:34
18:45/39:20 9:05+ 8:34 8:00 7:30 7:04 6:40 6:20 6:00 5:42

Basic Outline

Use the chart above as a guide in setting your various workout paces for the bulk of the summer or winter months. Every training day should have a purpose. The chart above should help keep your paces as intended so the system we are looking to train that day is in fact being addressed. Running significantly faster or slower than the pace outlined for the day will work a different system, which is not ideal at this stage of training. We are looking for overall aerobic development that the following outline addresses. Base training is about setting the groundwork for future success, much of which lays in consistent work at all relevant aerobic paces outlined above.

Stick to the paces outlined above and base them on your CURRENT fitness, not your PR. Stay at the level indicated until you have a recent race result that indicates a higher level of fitness. By using race results, you ensure your body is in fact at level X. It is much, much better to train conservatively at this stage and err to the safe side in terms of paces.

70% or less: VERY EASY: AM Runs, Easy & Recovery Runs.
70-75%: EASY TO MODERATE: Most runs, includes weekend long run.
75-80%: STRONG: Mid Week Long Run. Last 40-50 min at 75-80%
80-85%: MARATHON PACE: Medium Length Tempos (30-40 min):
85-90%: TEMPO: Short, Fast Tempos (20-30 min)
90-95%: 10K EFFORT: Long Intervals: 3-5 min.
95-100%: 5K EFFORT: Medium Length Intervals 2-3 min.
100-105%: 3K EFFORT: Short Intervals: 30 sec-2 min

Joe Rubio is a former 2:18 marathoner, and head coach of the Asics Aggies Running Club. He has a MS in Physical Education and is co-owner of Running Warehouse. He can be reached at joe@runningwarehouse.com