04(16): Why 1 kg weight loss takes away 4 kg-equivalent of stress from the hip – a tango between medicine and Newtonian mechanics

INTRODUCTION

It has been a while (about 1.5 months) since my previous blog post, in which I discussed a medical condition where the patient sheds ‘crocodile tears’. Well, that condition (Borogad syndrome) is pretty esoteric, and I wrote about it largely only because I wanted to share some fascinating trivia I had encountered in my casual reading.

In contrast, for the sake of this blog post, I would like to share something which I feel is important and clinically relevant. I only learnt this after participating in a tutorial which I attended a few days ago. It was a didactic tutorial held on 23 Nov, Wednesday, and it was led by Emeritus Consultant A/Prof Low Boon Yong, an orthopaedic surgeon who works at Changi General Hospital (CGH), a hospital within the SingHealth cluster.

Just to provide some context, my fellow clinical groupmates and I are currently on our orthopaedic surgery posting (our third major clinical posting as part of the curriculum for third-year undergraduate medical students at NUS). The focus of the tutorial was that of essential knowledge pertaining to the hip that medical students are expected to possess. It was evident to me, at least, that A/Prof Low is indeed highly knowledgeable even as he briefly walked us through an extensive amount of background information prior to even broaching the hip per se. He shared with us the implications of human beings being bipedal, the advantages and disadvantages of being bipedal, a short segment on the Neanderthals, the mechanism of how losing 1 kg of body mass takes away 4 kg -equivalent of pressure from the lower limb joints, and a conceptual understanding on what constitutes an antalgic gait.

It is beyond the scope of this blog post to elaborate on everything that A/Prof Low covered. So, I will only be elaborating on what I deem to be the highlight of the tutorial. It is valuable knowledge and deserves to be shared.

All credit for the explanation of the mechanism of the stress/pressure offloading to A/Prof Low, and do kindly consider any error (if present) to be mine.

WHY EVEN CONSIDER THE EFFECT OF WEIGHT LOSS?

Before we even get to the mechanism as to why 1 kg of weight loss leads to a disproportionate reduction in equivalent pressure from one’s lower limb joints, it is necessary to discuss why we may even need to consider the effect of 1 kg of weight loss.

The reality is that intentional weight loss remains the cornerstone of the management of virtually all chronic metabolic diseases such as obesity, essential hypertension, dyslipidaemia, and diabetes mellitus (along with all its associated acute complications, chronic microvascular complications, and chronic macrovascular complications). Moreover, intentional weight loss remains one of the key strategies which many rely on to boost their level of physical attractiveness, an objective which is desirable by many in society.

The prevalence of obesity has been steadily increasing, and this constitutes a worrisome threat to the fiscal viability of healthcare systems around the globe. The obesity epidemic is thus perhaps more appropriately termed the obesity pandemic, as it doesn’t just affect developed countries such as the United States, the United Kingdom, or Australia, where highly processed foods, high fructose corn syrup, artificial sweeteners, excessively salty, fatty, and oily foods all abound.

Even our island home hasn’t been spared. According to a press release by MOH in 2014, “Singapore’s obesity prevalence increased 0.7 percentage point a year since 2004 to reach nearly 11% in 2010, only one percentage lower than the global average obesity prevalence of 12%.” I’m not sure what the latest figures are, but given that it’s 12 years on from 2010, I’m certain that the prevalence of obesity is greater than the already-dismal 11%.

For the past few decades, the obesity pandemic has not spared developing countries due to the far-reaching tentacles of globalisation. In fact, the affliction of the obesity pandemic in developing countries is often harsher due to the dearth of relevant health and food safety regulations, thus allowing unbridled capitalism to hold the reins of the industries of local sustenance.

With the unfettered proliferation of unhealthy diets across the globe, people are increasingly getting horizontally challenged (pardon that sad attempt to cruise along the euphemism treadmill). Obesity has numerous complications which ultimately contribute to a reduced quality of life for patients, and one such complication is the acceleration of the progression of osteoarthritis of the weight-bearing joints, which manifests clinically as progressively worsening mechanical pain.

Osteoarthritis may be defined as a disorder characterised by chronic progressive degeneration of articular cartilage within synovial joints, resulting in the loss of joint space that is often asymmetric, and the formation of subchondral cysts. Osteophytosis (the formation of new bone and cartilage at the joint margins), sclerosis of subchondral bone, and formation of new connective tissue in the form of capsular fibrosis all occur as part of the body’s attempt at counteracting the degenerative process.

Acceleration of osteoarthritis as a complication of obesity is unsurprising because as one might imagine: with an abnormally high body mass, there is a pathologically high amount of stress or pressure on weight-bearing joints such as the hips and knees, which increases the rate of the degeneration of these joints due to greater tendency and magnitude of the wear-and-tear associated with the articular surfaces grinding against each other.

It is thus no surprise that when we talk about the management of osteoarthritis, for which there are nonoperative options (further classified as nonpharmacological and pharmacological) and operative options, chief among the nonpharmacological options would be intentional and sustainable weight loss, which would reduce the rate of osteoarthritis progression.

Specifically for the typical patient (whether suffering from osteoarthritis or not) of Asian ethnicity in Singapore, this would ideally entail getting the BMI to <23.5 and ensuring that the waist circumference is also <80 cm (if female) and <90 cm (if male), as per local guidelines. Of course, what I’ve listed here is just general advice for educational purposes only. For appropriate management in your specific circumstances, please consult your doctor.

THE MECHANISM UNDERLYING A DISPROPORTIONATE REDUCTION IN EQUIVALENT PRESSURE FROM THE WEIGHT-BEARING JOINTS OF THE LOWER LIMBS IN WEIGHT LOSS

Now that we’ve discussed why people may even be interested in the idea of weight loss in the first place, let’s now explore the mechanism underlying a disproportionate reduction in equivalent pressure from the weight-bearing joints of the lower limb.

A/Prof Low used fundamental physics principles to illustrate how one could arrive at a factor of 4 regarding the offloading of pressure from the weight-bearing hip joint (though a similar calculation could be modified and tailored to other weight-bearing joints of the lower limb) for each unit of weight loss.

Consider the principle of moments which is a staple of Newtonian mechanics in any physics syllabus, whether at the O-level, A-level, or even within an introductory physics module at university. The principle of moments may be defined as follows: “the resultant torques due to a number of forces applied about a point is equal to the sum of the contributing torques”.

From this definition, it follows that when an object is in rotational equilibrium, one can determine the relative magnitude of a particular force if the other variables are known. A/Prof Low shared with us how we can use this well-known physics principle to better understand the anatomy and mechanics of the human hip and the clinical implications of this.

As we all know, the hip can be thought of as a ball-and-socket joint, with the head of the femur constituting the ball of the hip joint, while the acetabulum constitutes the socket of the hip joint. Whilst a gross simplification of the actual mechanics within the human body, the following framework is nevertheless sufficiently robust for both clinicians and patients alike to conceptualise the positive effect that intentional and sustainable weight loss can have on weight-bearing joints:

  • Consider a vertical plane passing through the centre of mass of the femoral head to correspond to the position of an imaginary fulcrum.
  • The gluteus medius, the main abductor of the hip, attaches to the greater trochanter of the femur.
  • The vertical plane containing the ‘average’ origin (because after all, the actual origin of the gluteus medius is not a mere simple point, but rather, a relatively large region) of the gluteus medius can be taken to be approximately some perpendicular distance ‘a‘ from the femoral capital vertical plane.
  • Next consider another vertical plane which runs through the centre of mass of the patient, which would roughly correspond to the sagittal plane of the patient.
  • Based on standard anatomic proportions, when in the anatomic position, the perpendicular distance between this new vertical plane (i.e. the sagittal plane) and the femoral capital vertical plane is roughly ‘3a‘ (i.e. the perpendicular distance between the vertical plane containing the point of the patient’s centre of mass and the femoral capital vertical plane, is approximately three times the perpendicular distance between femoral capital vertical plane and the vertical plane containing the ‘average’ origin of the ipsilateral gluteus medius).

Do you see where I am going with this?

Let ‘F’ represent the weight of the patient.

Considering just the abovementioned force and distances, one can certainly mathematically determine the average force (or tension) present within a contracted gluteus medius when the patient is in balance.

Let T represent the tension within the contracted gluteus medius in the abovementioned system. Using the principle of moments, we can construct the following equation:

T (a) = F (3a)

Thus, T = 3F;

Going one step further, assuming the patient is in a state of not just rotational equilibrium (i.e. no net torque about the femoral head; constant angular momentum), but also translational equilibrium (i.e. no net force acting on the femoral head; constant momentum), we can use Newton’s third law to determine the force, Z, exerted on the femoral head.

By Newton’s third law, for the system to be in translational equilibrium, Z = T + F = 3F + F = 4F.

Z = 4F.

Incredible, isn’t it?

In fact, A/Prof Low used this relationship between the various forces and perpendicular distances to explain why the classic antalgic gait is the way it is. In an attempt to minimise the magnitude of the downward forces acting on the femoral head (which would of course be counteracted by the reactionary normal force due to Newton’s third law; note that a similar system/reasoning can be employed if the source of the antalgic gait is another part of the lower limb), the patient will ’tilt’ towards the unaffected side during the stance phase of the unaffected limb (see the second image given below, where the patient’s left lower limb is affected and presents with an antalgic gait).

Why is this so?

Well, when this ’tilt’ happens (see the second image presented below, which is a screen capture at 0:23 from a YouTube video illustrating antalgic gait), the ratio of the perpendicular distance between the plane containing patient’s centre of mass and the femoral capital vertical plane, to the perpendicular distance between the femoral capital vertical plane and the plane containing the ‘average’ origin of the gluteus medius, is effectively reduced (i.e. less than ‘3’ instead of approximately 3). Consequently, this would lead to a reduction in the tension within the gluteus medius (i.e. T < 3F), which would result in the sum of the downward forces on the femoral head being reduced (i.e. Z < 3F + F ; Z < 4F), which would theoretically reduce the intensity of mechanical pain on the affected ipsilateral lower limb.

CONCLUSION

You can probably see why I enjoyed the tutorial so much to the extent that I might even want to write an entire post on it. People who have known me for a long time know that for a rather substantial period of time, I have always wanted to pursue something related to physics (e.g. obtaining a physics degree, becoming a physics teacher). Being able to work things out from first principles fascinates me, and physics is a field where this practice routinely abounds.

Simply put, I am absolutely enamoured with A/Prof Low’s explanation because it theoretically illustrated an experimentally confirmed relationship using fundamental first principles in physics in a manner that most people who have had even just prior secondary school-level instruction in Newtonian mechanics can comprehend.

I consider it a privilege to have had A/Prof Low teach my colleagues and I on Wednesday, and hope you have enjoyed reading this article as much as I have enjoyed writing this!

Nic
27 Nov 2022 (Sun)


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3 thoughts on “04(16): Why 1 kg weight loss takes away 4 kg-equivalent of stress from the hip – a tango between medicine and Newtonian mechanics

  1. Hello nick! Great post. Your posts and your credentials have given me the impression that you are someone who is academically strong. Could you shed some light on the reasons as to why you did not pass M3 last year? Would love to hear your response, and keep up the good work.

    1. Hey Alan, thanks for your comment. It’s encouraging to learn that people read and enjoy reading my musings on this blog. Encouraging indeed.

      You are correct that I did not pass M3 in the previous academic year. As for why it occurred, it’s probably something that many people wonder (though not many have asked me directly about it). I don’t think it’d do the complexity of the issue justice to elaborate on the reasons in a single comment in this context but in essence, it’s nuanced and multifactorial.

      It is actually my intention, for now at least, to address that issue in a comprehensive post some time in the future. I believe it’d be a useful exercise of introspection, and I trust that it’d be of great utility to my colleagues and juniors in order to learn from the unique path I trodded.

      Best regards,
      Nic
      12/12/22

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