Urinary Glucose Is Mass: A Mass-Balance Critique of the Energy-Centric Explanation for Attenuated Weight Loss in Type 2 Diabetes

1. The Claim

Patients with type 2 diabetes (T2D) typically lose less weight on GLP-1-based therapies than patients with obesity but without diabetes [1,2]. Hall proposes that this gap is substantially explained by two glycemia-dependent processes: (i) the reduction of UGE as plasma glucose falls, and (ii) a concurrent decline in energy expenditure [3]. Both are treated as energy-side phenomena that offset the negative energy balance induced by reduced intake. The model is Hall’s previously validated energy-balance model, modified to include hyperglycemia effects on expenditure and UGE [3].

Hall’s central quantitative claims are these. In T2D patients without background SGLT2i therapy, UGE falls from approximately 20 g/day at baseline to zero, and energy expenditure falls by approximately 175 kcal/day. In patients on stable background SGLT2i therapy, UGE falls from approximately 125 g/day to approximately 40 g/day. These reductions are presented as the principal explanation for why T2D patients lose less weight than patients with obesity alone [3].

2. Urinary Glucose Is Mass

Hall’s equation 1 computes UGE as

$$\mathrm{U}\mathrm{G}\mathrm{E}=\mathrm{e}\mathrm{G}\mathrm{F}\mathrm{R}\times (G-\mathrm{R}\mathrm{T}),G>\mathrm{R}\mathrm{T},$$

with eGFR in ml/min, and G and RT in mg/dl. A unit analysis settles what this equation computes.

The product of eGFR and G – RT has units

$${\displaystyle \frac{\mathrm{m}\mathrm{l}}{\mathrm{m}\mathrm{i}\mathrm{n}}}\times {\displaystyle \frac{\mathrm{m}\mathrm{g}}{\mathrm{d}\mathrm{l}}}={\displaystyle \frac{\mathrm{m}\mathrm{l}}{\mathrm{m}\mathrm{i}\mathrm{n}}}\times {\displaystyle \frac{\mathrm{m}\mathrm{g}}{100\mathrm{m}\mathrm{l}}}={\displaystyle \frac{1}{100}}·{\displaystyle \frac{\mathrm{m}\mathrm{g}}{\mathrm{m}\mathrm{i}\mathrm{n}}}.$$

The result is a mass flux: milligrams of glucose per minute. With the conversion factor \(1/100\) absorbed into the numerical evaluation, and with the standard conversion from mg/min to g/day, Hall’s equation yields exactly the quantities he reports: 20 g/day at baseline, 125 g/day on SGLT2i therapy, and so on [3]. The model’s own calculation is mass-based. The quantity that enters the simulation is a mass flux.

Yet Hall describes UGE as “an energy sink” [3] and incorporates it into an energy-balance equation. This is a category error. Energy is not a substance that can be excreted. What is excreted is glucose – a quantity of mass with a carbon skeleton, a stoichiometric composition, and a measurable mass flux. The energy content of that glucose is a derived property, obtained by multiplying its mass by a heat-of-combustion coefficient. It is not an independent quantity.

The point is not interpretive. It is internal to Hall’s own method. The equation he writes computes mass. The units confirm it. Whatever role UGE plays in his simulation, the quantity he has calculated is a mass flux, and its most direct consequence is a reduction in total body mass.

The substitution is not neutral. To convert UGE to an energy sink and then back to a mass prediction requires two auxiliary assumptions: the energy density of glucose (~3.75 kcal/g) and the energy density of the body tissue lost or gained. Neither is measured in Hall’s study. The first is a physical constant; the second is a model assumption that varies with tissue composition. In a mass-balance formulation, UGE enters directly as an outflow term in the continuity equation,

$${\displaystyle \frac{dM}{dt}}={\dot{m}}_{\mathrm{i}\mathrm{n}}-{\dot{m}}_{\mathrm{o}\mathrm{u}\mathrm{t}},$$

where m_out includes urinary glucose, fecal mass, and all other mass effluxes. No conversion to kilocalories is required. The mass effect is direct; the energy effect is a consequence of the mass effect, not its cause.

This distinction matters because it changes which quantities are primary. In Hall’s framework, UGE is a secondary energy term whose mass effect is recovered through assumptions. In a mass-balance framework, UGE is a primary mass term whose energy content is a derived property. The two frameworks make different predictions when tissue composition changes – as it does during both weight loss and weight gain.

3. The Circularity Problem

Hall’s model belongs to the class of energy-balance formulations in which an energy imbalance is translated into a mass change by means of assumed or semi-empirical energy densities of tissue. The structure of the inference is as follows:

1. An energy imbalance ∆E is posited, including contributions from reduced intake, reduced expenditure, and reduced UGE (converted to kcal).

2. ∆E is converted to a mass change ∆M via an assumed energy density p: ∆M = ∆E/p.

3. The predicted ∆M is compared with observed weight loss in the STEP UP T2D trial.

4. Agreement is presented as evidence that the energy-side mechanisms are correct.

Step 2 is not an independent prediction. It is a definitional mapping. The model defines mass change as a function of the energy imbalance it already assumes. When the comparison in step 3 succeeds, it confirms that the assumed p is approximately correct – not that the energy-side mechanisms are the correct explanation.

Hall’s procedure partially mitigates this by fitting appetite parameters to obesity-only data (STEP UP) and then fixing them for the T2D simulation [1]. This is a genuine predictive step. But the energy-to-mass conversion remains calibrated on the same class of data being predicted: both the obesity and T2D comparisons depend on the same assumed p. A systematic error in p – say, from an incorrect assumption about the fat-to-lean ratio of lost tissue – will affect both predictions in the same direction and may either mask or exaggerate the UGE effect.

The procedure is therefore not formally tautological. But it contains a closed loop that limits its independent confirmatory power. Agreement between predicted and observed weight loss is a weaker test of the underlying physiology than is commonly claimed.

4. What a Mass-Balance Account Supplies

A mass-balance formulation begins with the continuity equation for body mass and treats every significant outflow – including UGE – as a mass flux [4,5,6]. Changes in glycemic control alter the magnitude of that flux; the effect on body mass follows directly, without intermediate energy conversions.

Hall’s own numbers illustrate the point. The UGE reduction in non-SGLT2i patients is 20 g/day. In SGLT2i patients, it is 85 g/day. These are mass fluxes. A mass-balance model asks directly: what mass flux difference is required to produce the observed weight-loss gap?

The STEP UP T2D trial reports an attenuated weight loss of approximately 7 percentage points at 72 weeks relative to STEP UP [ref]. For a 100 kg patient, this is approximately 7 kg over 72 weeks, or about 14 g/day of sustained mass difference. The non-SGLT2i UGE reduction of 20 g/day is the correct order of magnitude. The SGLT2i UGE reduction of 85 g/day is substantially larger, consistent with the model’s prediction of greater attenuation in that subgroup.

Within this frame, the attenuated weight loss in T2D patients on GLP-1 therapy is expected once the reduction in urinary mass loss is acknowledged. No additional energy-side offset needs to be invoked to generate the qualitative phenomenon. Energy expenditure and its possible modulation by glycemia remain relevant, but they enter as secondary influences on the energy content of the retained mass rather than as the primary drivers of the mass trajectory.

This is the core of the mass-balance model (MBM) developed elsewhere [4,5,6]. The MBM tracks macronutrient mass directly, without intermediate energy-unit conversions, and treats energy balance as a consequence of mass balance rather than as its cause [4,5,6]. It has been shown to outperform energy-balance models in external validation across multiple datasets. Applying the same logic to UGE is not an additional assumption; it is the natural extension of an already-superior framework.

5. Implications for the Hall Model

Four concrete implications follow.

First, UGE should be modeled as a mass flux, not an energy sink. Hall’s own equation computes it as a mass flux. Converting it to kilocalories and then back to mass introduces unnecessary assumptions that can be eliminated. The mass effect of UGE is direct and does not require an energy-density assumption.

Second, the comparison between predicted and observed weight loss should be reframed. Under the energy-balance approach, agreement is partly built in through the energy-to-mass conversion. Under a mass-balance approach, the model predicts mass change from mass fluxes, and the comparison with observed mass change is a genuine test – one that can fail if the mass fluxes are wrong.

Third, the role of energy expenditure should be re-examined. Hall models a reduction of 175 kcal/day in energy expenditure [1]. In a mass-balance framework, this effect is mediated through changes in the composition of retained mass, not through a separate “energy balance” channel. The 175 kcal/day figure may be correct, but its explanatory weight is different: it modifies the relationship between mass intake and mass retention, not the total mass balance directly.

Fourth, the SGLT2i subgroup analysis should be reported as a mass-balance prediction. Hall’s model predicts the greatest attenuation in SGLT2i patients because their baseline UGE is highest and falls most. This prediction can be tested directly by measuring UGE and body mass in that subgroup – without any energy conversion. Such a test would be more informative than the current comparison, which depends on assumptions about energy density.

6. Predictions That Distinguish the Frameworks

The two frameworks make different predictions in at least three testable respects.

Prediction 1: Composition-dependence of the energy-to-mass conversion. If the energy-balance framework is correct, the relationship between energy imbalance and mass change should be stable across individuals with different tissue compositions. If the mass-balance framework is correct, this relationship should vary systematically with composition, because the same energy imbalance produces different mass changes depending on the fat-to-lean ratio of the tissue gained or lost.

Prediction 2: Direct proportionality of UGE and mass change. In a mass-balance framework, UGE reduction translates directly into attenuated mass loss, with no intermediate energy term. In an energy-balance framework, the translation depends on the assumed energy density of the lost tissue. Direct measurement of UGE and body mass in the same individuals can distinguish these predictions.

Prediction 3: Asymmetry between gain and loss. In a mass-balance framework, the effect of UGE on mass change is symmetric: a given mass flux produces the same mass change whether the patient is gaining or losing. In an energy-balance framework, the effect depends on the energy density of the tissue being gained or lost, which may differ. Longitudinal studies that include both weight gain and weight loss phases can test this.

7. Conclusion

Urinary glucose excretion is a mass outflow. Hall’s own model computes it as one. Models that treat it primarily as an energy sink, convert the resulting energy imbalance into a mass prediction, and then present the match with observed weight loss as evidence, invert the natural order of explanation and introduce a degree of circularity.

A mass-balance approach restores the correct order: mass fluxes are accounted for directly, and energy appears only as a property of the mass that remains. The clinical observation that patients with T2D lose less weight on GLP-1 receptor agonists is thereby given a simpler and less assumption-laden interpretation.

The dispute is not merely methodological. It concerns which quantity – mass or energy – is the proper primary variable in the analysis of body weight regulation. Mass is what is measured on a scale. Mass is what is excreted in urine. Mass is what changes. Energy is a derived property. Models that begin with energy and recover mass through auxiliary assumptions begin in the wrong place.