Testing Computer Models Predicting Human Responses to a High-Salt Diet: Implications for Understanding Mechanisms of Salt-Sensitive Hypertension

Both QCP and HumMod correctly predicted that in normal subjects, moving from a moderately low salt diet to a high salt diet for 5 days produces little or no blood pressure increase.

“Both models also accurately predicted the results from the study of Ishii et al which showed that in normal subjects,16 switching from a moderately low salt diet (~100 mmol NaCl/day) to a high salt diet (~275 mmol/day) for 5 days causes little or no increase in blood pressure. (data not shown).”

• cites [16] sourceSupported

Schmidlin et al found that when normal subjects moved from a very low salt diet to a high salt diet, mean arterial pressure fell by 5% during the first 12 to 48 hours and then returned to baseline by day 5.

“In the study of Schmidlin et al,15 switching from a very low salt diet to a high salt diet induced a 5% decrease in mean arterial pressure during the first 12 to 48 hours of salt loading, followed by a return of mean arterial pressure to baseline by the 5th day of salt loading (Figure 3).”

• cites [15] sourcePartly supported

  The Hemodynamic Effects of LS and HS Diets section reports a 5% fall in mean arterial pressure within 9 hours of salt loading in salt-resistant subjects, persisting through day 4 before returning toward low-salt levels. The claim leaves out that this response was specific to the salt-resistant group: mean arterial pressure instead rose in salt-sensitive subjects. The text also does not establish an exact return to baseline by day 5. (LLM, conf=0.89)

  Experimental — accuracy not yet measured

In Clemmer and colleagues' simulations, salt sensitivity was defined by blood pressure responses to massive, clinically unrealistic salt intakes, exceeding a 30-fold increase to 1000 mmol per day.

“In the simulation studies performed by Clemmer and colleagues, salt sensitivity was defined according to blood pressure responses to massive, clinically unrealistic increases in salt intake (> 30 fold increase in salt intake to 1000 mmol/day).13”

• cites [13] sourceSupported

The omission of the pressure-natriuresis relationship as a blood pressure driver in HumMod and other contemporary models aligns with Beard's warning to stop teaching and promoting physiologic concepts based on tautological thinking.

“The omission of the pressure-natriuresis relationship as a driver of blood pressure outcomes in HumMod, and in other contemporary models,35–38 agrees with Beard’s admonition to stop teaching and promoting physiologic concepts that are based on tautological thinking.39”

• cites [35] sourcePartly supported

  In “Establishment of a new mathematical model for long-term control of arterial pressure” (page unavailable), the authors reject pressure–natriuresis as an overriding determinant of long-term blood pressure. But they explicitly say their proposed model will include a pressure–natriuresis relationship, primarily as a back-up mechanism; the paper therefore does not support describing the relationship as omitted. Beard’s admonition has a separate citation in the citing sentence and is not assessed here. (LLM, conf=0.84)

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• cites [36] sourceSupported
• cites [37] sourcePartly supported

  The Introduction and Discussion say this paper’s model produces hypertension without making arterial pressure the driver of sodium excretion, while still reproducing the observed pressure–natriuresis relationship. That supports the point for this model, but these passages do not establish the claimed omission in HumMod or other contemporary models. Beard’s admonition has a separate citation in the citing sentence and is not attributed to this source. (LLM, conf=0.84)

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• cites [38] sourceCould not verify

  The Introduction questions whether the kidney’s pressure-natriuresis relationship determines long-term arterial pressure, but our copy does not admonish readers to stop teaching or promoting concepts based on tautological thinking. A separate Beard article titled “Tautology vs. Physiology in the etiology of hypertension” appears in the References; its title does not establish what admonition it makes. Searched the indexed paper for tautology, teaching, and promoting. (LLM, conf=0.73)

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• cites [39] sourceSupported

Neither Guyton and his colleagues nor most other researchers investigating salt sensitivity abnormalities published studies measuring sodium balance, cardiac output, and systemic vascular resistance during salt loading in healthy people or animals.

“Also surprisingly,18, 19, 26 neither Guyton and his colleagues, nor most other investigators searching for abnormalities mediating salt sensitivity, published studies of sodium balance, cardiac output, and systemic vascular resistance responses to salt-loading in normal humans or animals.”

• cites [18] sourcePartly supported

  In “The Lack of Appropriate Normal Controls in Studies of Salt-Induced Increases in Blood Pressure” (page unavailable), the paper says studies cited for the volume-loading theory did not compare salt-sensitive subjects with normal controls on sodium balance, cardiac output, and systemic vascular resistance during salt loading. That supports the concern about missing normal-control comparisons, but it does not establish that Guyton and his colleagues, or most other investigators, published no studies measuring those responses in normal humans or animals. (LLM, conf=0.78)

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• cites [19] sourceNot checked — no full text of the source
• cites [26] sourcePartly supported

  In ‘How Does Salt Initiate the Increased BP…’ (page unavailable), the paper says Guyton’s studies lacked cardiac-output and systemic-vascular-resistance measurements in normal controls. It also describes other salt-loading studies that measured sodium balance and hemodynamic responses in normal controls, but does not establish that most other investigators omitted such studies. (LLM, conf=0.84)

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The pressure-natriuresis relationship was included as a critical blood pressure determinant in early Guyton circulation models.

“Although the “pressure natriuresis relationship” was incorporated as a critical determinant of blood pressure in early Guyton models of the circulation, investigators involved in the development of HumMod have recently stated that “In HumMod, there is no equation that describes the renal function curve or pressure natriuresis relationship per se.”13”

• cites [13] sourcePartly supported

  The Discussion (§ “Renal function curve”; page unavailable) says Guyton’s computer simulations predicted that long-term arterial pressure could change only with the pressure-natriuresis relationship or salt intake, supporting its critical role. It does not establish that the relationship itself was incorporated into the early circulation models; the curves used to illustrate the concept were based on empirical data rather than simulations. (LLM, conf=0.78)

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Montani and Van Vliet identified the pressure-natriuresis relationship and blood flow autoregulation as central features of the 1972 Guyton model that continued as core concepts during its evolution.

“Specifically, Montani and Van Vliet noted that the “pressure-natriuresis relationship” and “blood flow autoregulation” are main features of the 1972 Guyton model that “remained as core concepts” as the model evolved.9”

• cites [9] sourceSupported

Clemmer and colleagues used HumMod 3.0.4 to simulate cardiovascular, renal, and neurohormonal responses to very large salt loads in normal subjects and in subjects with various experimental manipulations.

“In a recent effort to “test hypotheses of salt sensitivity,” Clemmer and colleagues at the University of Mississippi used HumMod 3.0.4 to simulate responses of cardiovascular, renal, and neurohormonal variables to massive degrees of salt-loading in normal subjects, and in subjects with various experimental manipulations.13”

• cites [13] sourcePartly supported

  The Abstract describes HumMod simulations of systemic hemodynamic, renal, and neurohormonal responses under normal renal function and several experimental conditions. The Methods (Protocols) specify salt intakes up to 1,000 mmol/day. The Methods identify the simulator as HumMod, but our copy does not identify it as version 3.0.4. (LLM, conf=0.86)

  Experimental — accuracy not yet measured

The historical Guyton model and its modern derivatives have been used for many years to investigate hypotheses about how abnormalities in sodium excretion, cardiac output, and vascular resistance might mediate pressor responses to short- and long-term salt loading.

“Despite the lack of model validation studies in salt loaded normal controls, these models have been used for many years to probe hypotheses about the possible role of abnormalities in sodium excretion, cardiac output, and vascular resistance in mediating pressor responses to both short-term and long-term salt loading.5, 6, 13, 24, 25”

• cites [5] sourceNot checked — no full text of the source
• cites [6] sourceNot checked — no full text of the source
• cites [13] sourceSupported
• cites [24] sourceNot checked — no full text of the source
• cites [25] sourcePartly supported

  The Introduction identifies HumMod as a derivative of the Guyton model, and the Results (§3.1; page unavailable) report blood-pressure, cardiac-output, and vascular-resistance responses to three weeks of salt loading. The Introduction also discusses disturbed renal sodium handling, but the paper does not establish that these models were used to investigate the specified mechanisms under both short- and long-term salt loading. (LLM, conf=0.85)

  Experimental — accuracy not yet measured

Osborn and colleagues and Beard and colleagues deliberately excluded the pressure-natriuresis curve as the main blood pressure controller in their modern arterial pressure models.

“Further, Osborn and colleagues35–37 and Beard and colleagues38 pointedly chose not to include the pressure natriuresis curve as the main controller of blood pressure in their modern models of arterial pressure regulation.”

• cites [35] sourceSupported
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• cites [36] sourceSupported
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• cites [37] sourceSupported
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• cites [38] sourceSupported
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In salt-sensitive individuals, the rises in sodium balance and cardiac output after acute salt loading are no larger than those seen in salt-resistant healthy controls.

“While increases in sodium balance and cardiac output occur in response to acute salt loading, the increases that occur in salt sensitive subjects are not greater than those that occur in salt resistant normal controls.18, 19, 26”

• cites [18] sourcePartly supported

  In “The Natriuretic and Hemodynamic Responses of Salt-Sensitive Subjects to Increases in Salt Intake” (page not provided), the paper says sodium retention and cardiac-output increases in salt-sensitive subjects are usually no greater than in normal controls. The claim omits “usually” and states the comparison categorically for salt-sensitive individuals, while the paper’s direct comparison focuses on normotensive salt-sensitive humans. (LLM, conf=0.86)

  Experimental — accuracy not yet measured
• cites [19] sourceNot checked — no full text of the source
• cites [26] sourcePartly supported

  The section on how salt initiates increased BP says that, during initiation of salt loading, sodium-balance and transient cardiac-output increases are no greater than in salt-resistant normal controls for most salt-sensitive normotensive subjects tested. The claim omits both “most” and “normotensive,” extending that finding to salt-sensitive individuals generally; the section on normotensive subjects notes that studies in hypertensive subjects have differed. (LLM, conf=0.87)

  Experimental — accuracy not yet measured

In light of the current studies and previous animal and human experiments, the use of these models by Guyton and colleagues to reorient understanding of hypertension causes appears to have been overreaching.

“However, in light of the results of the current studies with the 1972 Guyton model and its derivatives, together with those of previous experimental studies in animals47–50 and humans,15, 18, 51, 52 the use of the models by Guyton and colleagues to “reorient understanding” of the causes of hypertension appears to have been overreaching.”

• cites [47] sourceNot checked — no full text of the source
• cites [48] sourceSupported
• cites [49] sourceNot checked — no full text of the source
• cites [50] sourceNot checked — no full text of the source
• cites [15] sourceSupported
• cites [18] sourceSupported
• cites [51] sourceNot checked — no full text of the source
• cites [52] sourceSupported

A literature review found no validation studies that tested whether the models accurately predict sodium balance, cardiac output, and vascular resistance responses of normal subjects to dietary salt increases within the real-life range of human salt intake.

“In reviewing the literature on the 1972 Guyton model and the most evolved derivatives of the Guyton model, we could not find validation studies testing the capacity of the models to accurately predict sodium balance, cardiac output, and vascular resistance responses of normal subjects to increases in dietary salt within the real life range of salt intake in humans.”

The 1972 Guyton model also fails to accurately predict the usual changes in sodium balance, cardiac output, and systemic vascular resistance in normal subjects when salt intake is increased to clinically realistic levels.

“Neither model, nor the 1972 Guyton model, accurately predicts the usual changes in sodium balance, cardiac output, and systemic vascular resistance that normally occur in response to clinically realistic increases in salt intake.”

Both QCP and HumMod correctly predicted that in normal subjects, moving from a very low salt diet to a high salt diet for 5 to 7 days produces only minimal blood pressure increases above baseline.

“Both models accurately predicted that in normal subjects, switching from a very low salt diet to a high salt diet for 5 to 7 days causes minimal increases in blood pressure above baseline (Figure 3).”

Neither QCP nor HumMod accurately predicted the temporary drop in mean arterial pressure that occurs when normal subjects switch from a very low salt diet to a high salt diet.

“Neither QCP nor HumMod accurately predicted this reduction in mean arterial pressure that is transiently induced upon switching normal subjects from a very low salt diet (~ 30 mmol NaCl/70 kg body weight/day) to a high salt diet (~250 mmol NaCl/70 kg body weight/day) (Figure 3).”

Despite both being extensions of the 1972 Guyton model, HumMod 3.0.4 and QCP 2005 make major inconsistent predictions about sodium balance and hemodynamic responses of normal subjects to short-term and long-term salt loading.

“testing revealed major inconsistencies between model predictions with respect to sodium balance and hemodynamic responses of normal subjects to short-term and long-term salt loading.”

• Also stated in: § Introduction · boosted

  “testing revealed major inconsistencies between the predictions made by these models with respect to cardiovascular and sodium metabolic responses to acute and chronic increases in salt intake.”

QCP 2005 significantly underestimates the usual fall in systemic vascular resistance caused by salt loading in normal subjects.

“The simulation results from the QCP model significantly underestimate the usual salt-induced increases in cardiac output and salt-induced decreases in systemic vascular resistance (Figures 4 and 5).”

The 1972 Guyton model clearly overestimates how much arterial pressure rises with salt loading compared with HumMod 3.0.4 and normal humans.

“The 1972 Guyton model clearly overestimates the extent to which arterial pressure increases in response to salt loading in HumMod 3.0.4 and in normal humans (Figures S7 and S8).”

In 1972 Guyton model simulations, salt-induced increases in cardiac output and sodium balance are much smaller than in HumMod 3.0.4 simulations.

“In simulations with the 1972 Guyton model, the salt-induced increases in cardiac output and sodium balance are much smaller than those in simulations with HumMod 3.0.4 (Figure 6 and Figure S7).”

QCP 2005 significantly underestimates the usual rise in cardiac output caused by salt loading in normal subjects.

“The simulation results from the QCP model significantly underestimate the usual salt-induced increases in cardiac output and salt-induced decreases in systemic vascular resistance (Figures 4 and 5).”

The 1972 Guyton model greatly underestimates the sodium balance levels that normally occur when clinically realistic salt loading begins in normal salt-resistant normotensive humans.

“In addition, the 1972 Guyton model greatly underestimates the levels of sodium balance, and greatly overestimates the levels of blood pressure and systemic vascular resistance that usually occur with initiation of clinically realistic degrees of salt loading in normal humans (salt resistant normotensive humans).”

For subjects with normal renal function, the original 1972 Guyton model predicts much larger salt-induced blood pressure increases than HumMod 3.0.4.

“In subjects with normal renal function, the original 1972 Guyton model predicts the occurrence of much greater salt-induced increases in blood pressure than those predicted by HumMod 3.0.4, the most recent extension of the Guyton model.”

HumMod 3.0.4 greatly overestimates the usual rise in cardiac output caused by salt loading in normal subjects.

“The simulation results from HumMod 3.0.4 markedly overestimate the usual salt-induced increases in cardiac output (Figure 4), and markedly overestimate the usual salt-induced decreases in systemic vascular resistance (Figure 5).”

In normal subjects, moderate salt loading causes little or no blood pressure rise because they usually vasodilate strongly and lower systemic vascular resistance enough to offset the pressor effect of the accompanying large increase in cardiac output.

“Specifically, both models show that in normal subjects, non-extreme salt loading induces relatively little or no increase in blood pressure because normal subjects usually undergo robust vasodilation and reduce systemic vascular resistance sufficiently to offset the potential pressor effects of substantial salt-induced increases in cardiac output.”

In 1972 Guyton model simulations, changing from a low-salt to a high-salt diet increased the variable ARM, defined as the vasoconstrictor effects of all types of autoregulation, by more than 50%.

“In simulations with the 1972 Guyton model, switching from a low salt diet to a high salt diet, induced a greater than 50% increase in the variable “ARM” defined as “the vasoconstrictor effects of all types of autoregulation” (for the ARM data, see online data supplement file labeled “Guyton_1972_Fortran_output”).”

The 1972 Guyton model greatly overestimates the blood pressure levels that normally occur when clinically realistic salt loading begins in normal salt-resistant normotensive humans.

“In addition, the 1972 Guyton model greatly underestimates the levels of sodium balance, and greatly overestimates the levels of blood pressure and systemic vascular resistance that usually occur with initiation of clinically realistic degrees of salt loading in normal humans (salt resistant normotensive humans).”

In HumMod testing, salt-loading simulations produced strikingly different results in male versus female subjects.

“In the testing of HumMod, we also observed strikingly different results between simulations of salt loading in male subjects versus those in female subjects.”

The 1972 Guyton model greatly overestimates the systemic vascular resistance levels that normally occur when clinically realistic salt loading begins in normal salt-resistant normotensive humans.

“In addition, the 1972 Guyton model greatly underestimates the levels of sodium balance, and greatly overestimates the levels of blood pressure and systemic vascular resistance that usually occur with initiation of clinically realistic degrees of salt loading in normal humans (salt resistant normotensive humans).”

Simulations of long-term salt loading produced conflicting results between the contemporary models for hemodynamic, sodium balance, and fluid volume responses.

“Computer simulations of hemodynamic, sodium balance, and fluid volume responses to long-term salt loading also produced conflicting results between the contemporary models (see results in online data supplement).”

HumMod 3.0.4 greatly overestimates the usual fall in systemic vascular resistance caused by salt loading in normal subjects.

“The simulation results from HumMod 3.0.4 markedly overestimate the usual salt-induced increases in cardiac output (Figure 4), and markedly overestimate the usual salt-induced decreases in systemic vascular resistance (Figure 5).”

In simulations of subjects with normal kidney function, moving from a very low NaCl diet to a high salt diet produces much larger short-term and long-term blood pressure increases in the original 1972 Guyton model than in HumMod 3.0.4.

“In simulations of subjects with normal kidney function, switching from a very low NaCl diet to a high salt diet induces far greater short-term and long-term increases in blood pressure in the original 1972 Guyton model than in HumMod 3.0.4 (Figure 6 and Figure S7).”

HumMod simulations of female subjects differed strikingly from its simulations of male subjects.

“In addition, HumMod simulations of female subjects yielded striking differences from those of male subjects (see results in online data supplement).”

The HumMod and QCP models predict very different acute and chronic salt-induced changes in cardiac output, blood volume, interstitial fluid volume, plasma protein concentrations, and systemic vascular resistance.

“In addition to failing validation testing, the HumMod and QCP models predict vastly different results with respect to acute and chronic salt-induced changes in cardiac output, blood volume, interstitial fluid volume, plasma protein concentrations, and systemic vascular resistance.”

The current findings raise doubts about how studies of salt sensitivity that use the various Guyton models should be interpreted.

“Accordingly, the present results raise concerns about the interpretation of studies of salt sensitivity with the various Guyton models.”

Assessing how well mathematical models predict experimental outcomes is a useful method for judging the soundness of the mechanistic hypotheses they contain.

“Testing the validity of mathematical models, by assessing their ability to predict experimental outcomes, provides a useful way of determining the soundness of the mechanistic hypotheses inherent in the models.2”

• cites [2] sourceNot checked — no full text of the source

The findings reveal important limitations in the hypotheses built into Guyton models about how sodium balance, cardiac output, and vascular resistance are normally regulated when salt intake rises in salt-resistant humans.

“These results demonstrate significant limitations with the hypotheses inherent in Guyton models regarding the usual regulation of sodium balance, cardiac output and vascular resistance in response to increased salt intake in normal salt-resistant humans.”

These comments indicate that the renal function curve, the main core determinant of long-term blood pressure control in early Guyton models, was not retained in HumMod 3.0.4 as a driver of blood pressure outcomes in the simulations.

“These comments indicate that the renal function curve (pressure natriuresis relationship), the main “core” determinant of long-term blood pressure control in the early Guyton models, has not been retained in HumMod 3.0.4 as a driver of blood pressure outcomes in the simulations.”

This vascular resistance response to salt-induced cardiac output increases is opposite to what blood flow autoregulation would predict.

“This type of vascular resistance response to salt-induced increases in cardiac output is opposite to the type of vascular resistance response expected to occur with “blood flow autoregulation.””

The current study tested model validity for predicting responses to salt intake changes under only a small number of experimental conditions.

“Thus, the current study only tested the validity of the models in predicting responses to changes in salt intake under a small number of experimental conditions.”

The 1972 Guyton model's greater salt sensitivity compared with HumMod or normal humans is not caused by greater sodium retention and cardiac output; it is caused by greater systemic vascular resistance.

“The greater salt sensitivity in the 1972 Guyton model than in HumMod or normal humans is not initiated by greater levels of sodium retention and cardiac output (Figures 6, S9, S10), but rather by greater levels of systemic vascular resistance (Figures 6, S11).”

The greater acute and chronic salt sensitivity in the 1972 Guyton model compared with HumMod 3.0.4 results from greater vascular resistance during salt loading in the 1972 model, not from greater sodium retention or cardiac output.

“The greater acute and chronic salt sensitivity in the 1972 Guyton model than in HumMod 3.0.4 is caused by strikingly greater levels of vascular resistance with salt loading in the 1972 model than in HumMod 3.0.4, not by greater levels of sodium retention and cardiac output (Figure 6, Figure S7, and raw data in online-only supplement).”

In the 1972 Guyton model, this rise in autoregulatory vasoconstrictor effects could help explain why systemic vascular resistance fails to decrease normally when salt-induced cardiac output rises.

“In the 1972 Guyton model, this increase in the “vasoconstrictor effects of all types of autoregulation” could contribute to the failure of systemic vascular resistance to normally decrease in response to salt-induced increases in cardiac output.”

The findings raise major doubts about the validity of the hypotheses built into Guytonian models concerning sodium balance regulation and hemodynamic responses to salt intake changes within the real-life range of human salt intake.

“These findings raise major questions about the validity of the hypotheses inherent in Guytonian models that pertain to the regulation of sodium balance and hemodynamic responses to changes in salt intake within the real-life range of salt intake in humans.”

Even if HumMod 3.0.4 accurately predicted how sodium balance and hemodynamics respond to such extreme salt loading, the relevance of those findings to usual human responses to clinically realistic salt loading would be questionable.

“Thus, even if simulations with HumMod 3.0.4 were to accurately predict the sodium balance and hemodynamic responses of normal subjects to such extreme degrees of salt loading, the relevance of such findings to the usual human responses to clinically realistic degrees of salt loading would be questionable.”

The large sustained falls in total peripheral resistance in HumMod simulations suggest that HumMod 3.0.4 did not retain the 1972 Guyton model's core blood flow autoregulation feature as a determinant of how systemic vascular resistance responds to clinically realistic salt intake in people with normal renal function.

“The large, sustained decreases in total peripheral resistance in the HumMod simulations suggest that the “core” feature of “blood flow autoregulation” in the 1972 Guyton model, has not been retained in HumMod 3.0.4 as a determinant of the systemic vascular resistance response to clinically realistic increases in salt intake in subjects with normal renal function”

During both the start and the maintenance of salt loading, the 1972 Guyton model's greater salt sensitivity compared with HumMod results from its much higher systemic vascular resistance.

“Throughout both the initiation and maintenance phases of salt loading, the greater salt sensitivity in the 1972 Guyton model simulation than in the HumMod simulation is a consequence of much greater levels of systemic vascular resistance in the 1972 Guyton model than in HumMod 3.0.4 (see Figures 6, Figure S7, and raw data in the online supplement).”

The present studies' results indicate that the 1972 Guyton model and its modern derivatives HumMod 3.0.4 and QCP 2005 embody an incomplete understanding of how the body regulates sodium balance, cardiac output, and systemic vascular resistance when salt intake rises to clinically realistic levels.

“Indeed, the results of the present studies indicate that the 1972 Guyton model, and its contemporary derivatives HumMod 3.0.4 and QCP 2005, reflect an incomplete understanding of the systems regulating sodium balance, cardiac output, and systemic vascular resistance in response to clinically realistic increases in salt intake.”