Computational models have spurred on great advancements in the field of biomechanical engineering. From advanced prosthetic design to cardiac tissue modeling – practices in biomechanical modeling and computational biomechanics are making tremendous headway towards the delivery of successful medical intervention in humans. In this article, you’ll learn why physiological variation must be quantified for biomechanical engineering’s continued advancement as a field.


This success, however, depends heavily on the biomechanical engineer’s ability to reliably predict trends across a population. Human biomechanics variability is inherent in our physical dimensions, our material properties and our individual statures, functions, and pathological conditions. For continued advancement in biomechanical engineering, this physiological variation must be quantified and integrated into the biomechanical modeling processes. This is precisely the work being done by Dr. Douglas Cook over at New York University.

Physiological variation must be quantified for biomechanical engineering’s continued advancement.

Dr. Douglas Cook teaches Computational Biomechanics at NYU in the United Arab Emirates. His recent studies promote the advancement of biomechanics research by implementing advanced statistics to quantify, predict, and integrate physiological variation in the biomechanical modeling process. Continue reading to learn more about the computational approaches he uses in solving complex problems in biomechanical models and systems.

1. Can you elaborate on how the field of statistics has been useful in helping you understand physiological variability?

First, as you’ve already mentioned, there are numerous physiological variables.

For each variable, two important aspects are critical.

  • First, the distribution of the variable among the human population (a simplistic example would be the vertical height of each person, for which there is a global distribution, but there are also distributions by ethnicity, region, etc.).
  • Second, since all biological variables are just one component of a complex system, the relationships between a given variable and other variables also are important. To extend the height example, the global, ethnic, and regional variables of height and weight are related (you could say correlated) in certain ways.

These relationships result from numerous physical/biological relationships between the two variables, which explains why a scatter plot of height vs. weight almost always reveals a cloud of data rather than a nice, tight relationship as is typical in non-biological systems such as physics experiments, engineering data, etc.

2. What techniques do you use to examine the relationships between physiological variables? What is the greatest obstacle to incorporating information about these relationships into your studies?

The relationships described above can be examined through a variety of techniques, including experimentation and physics-based modeling. Incorporating such information is extremely difficult because typical experiments and studies normally measure or report only a small number of variables simultaneously. The sheer number of variables and relationships is daunting.

For example, a simplistic twenty-variable model of a biological system (n) will exhibit 190 two-variable relationships (m), most of which may not be linear relationships (m = (n^2-n)/2). Of course there are higher-order relationships, and most biological systems consist of considerably more than 20 variables. So you can see that there is a great deal of work to be done.

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3. What inspired you to take a statistical approach to solving the biomechanical variability problem? Was there something that the classic “average” model methods could not do for you?

That’s a really interesting question…. I’m not sure I can pinpoint a particular moment of “inspiration”. The more I’ve thought about biological variation, the more I’ve been able to imagine how all the components are inter-related, and that our models and techniques cannot ignore this complexity if we really want to solve real-world problems.

Fortunately engineers are pretty practical folks. We realize we can’t model everything, so I don’t think we’ll get too wrapped up in chasing every little loose end, but right now many engineers seem to underestimate the complexity of biological systems. As a community, we’re treating our biomechanical models like designed engineering systems which, are typically complicated (i.e. many components and features), but are not complex.

Complex systems have been classified as having four important qualities:

  1. Features of a complex system are diverse (i.e. high levels of variation),
  2. Connected,
  3. Interdependent, and;
  4. Adaptable

A typical engineering system like a car doesn’t have diversity (all the parts are nearly identical), and while the parts are definitely connected and affect each other, they aren’t interdependent (i.e. tire pressure will affect performance of the system, but it won’t affect any of the other features of the car directly). Finally, a car is not adaptable (i.e. it does not adapt to a changing environment).

It is the realization of these differences between engineering systems and biomechanical systems that caused me to start looking for alternative approaches. Complex systems and physiological variation must be quantified for biomechanical engineering continued advancement.

4. What are a few examples of “best practices” for biomechanical modeling? Do you think statistics could be incorporated to improve any of these best practices?

The “best practices” are currently borrowed from other, more developed fields. Our community hasn’t yet established our own set of best practices, and this is needed.

However, some of the relevant best practices include:

  1. Reporting variable distributions instead of just average variable values
  2. Reporting relationships between variables, and even better;
  3. Uploading data for others to use (since the types of relationships we observe often depend upon what aspect of the problem we’re interested in).

It obviously isn’t possible to report every relationship in a scientific paper. When creating models, we need to perform more simultaneous variation of parameters, and perform sensitivity analyses to better understand our models’ comprehensive behaviors. Statistical approaches are important in all of these issues, except perhaps the uploading of data.

5. Were there any statistics resources that you found particularly useful when working to quantify physiological variability in humans? If so, what are those resources?

We first need to quantify variation, then we can use those quantities as inputs to our models so that our models can then predict the levels of variation, and extents of likely variation in proposed treatments. Virtually the entire field of statistics is important for accomplishing this goal.

For example, we need descriptive statistical methods to quantify the fundamental distributions, then we can use correlation to make simplistic models between two variables. Adding complexity, we can use multiple regression, nonlinear regression, and more advanced techniques to describe relationships between multiple variables. We use hypothesis testing to determine if certain variables affect model outcomes, and so on.

I think it’s important for us to be familiar with a broad range of methods so that we aren’t limited by a narrow view of how to approach the problems we’re working on.

We first need to quantify variation, then we can use those quantities as inputs to our models so that our models can then predict the levels of variation, and extents of likely variation in proposed treatments. Virtually the entire field of statistics is important for accomplishing this goal.

6. What is the biggest statistics or biomechanical engineering design challenge you have faced in your career, and how did you overcome this challenge?

That’s an interesting question. I think the biggest challenge right now is the lack of data that matches the complexity of the systems we’re studying.

Such data is nearly impossible to obtain in human biomechanics, since the data must contain information about several, likely-correlated variables involved (i.e. we need a full set of data for each specimen: geometry, material properties, etc.). This typically requires a complete dis-assembly of the system. This obviously isn’t possible for human subjects research unless we obtain a large number of cadavers, which are expensive. Even if we had the specimens, measuring a full set of properties is almost overwhelming.

We’re addressing this problem by turning to a model system instead of measuring human specimens. The model system we have chosen is the corn stalk, which has remarkable topological similarities to human bone. Studying the corn stalk not only addresses a problem of economic importance (corn is the world’s #1 crop, and breeding efforts to increase yield are currently limited by stalk strength), but it will eventually allow us to harvest comprehensive data with large sample sizes. This isn’t possible in human biomechanics.

7. What are your top 3 predictions for how advances in biomechanical engineering will improve people’s quality of life over the next 20 years?

This is a tough question. There’s an old saying that scientist’s predictions of what is possible with our current technologies are pretty reliable, but that no one is particularly good at predicting the potential of new technologies.

I would say that the current ability to both collect and share large quantities of data will have a great influence on our ability to create more robust models in the near future. Sensitivity analysis and systems thinking are rising in prominence, and these will have a great positive impact on the insights we can gain from both our data and our model predictions.

I think we’ll see great advances in biomedical therapies, particularly in the development of new tissues and organs grown to replace our diseased or damaged tissues… I guess my goal right now is to promote the use of techniques that I can see will enable such progress. I believe that my contribution is to promote these tools, which I hope will have a greater positive impact than if I just use them myself on a narrow research topic.


Cook, D., et al., Biological variability in biomechanical engineering research: Significance and meta-analysis of current modeling practices. Journal of Biomechanics (2014),

This is a contribution that I originally made to Statistics Views website.

Lillian Pierson, P.E.

Hi, I'm Lillian Pierson, PE (CEO of Data-Mania). I’m a data leader that supports data professionals to get ahead in their own data careers by developing data leadership capabilities. To date, I’ve trained over 1 million workers on the topics of AI and data science. Since 2013, Data-Mania, LLC has provided high-impact training to data-driven professionals so they can support their organizations in making major digital transformations. Additionally, we offer powerful online programs designed to transform data professionals into data leaders.

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