Rubidium paper tells us that the pumping of natrium out of...

Rubidium paper tells us  that the pumping of natrium out of  neurons takes a lot of energy and if energy is not produced enough the neurons are in danger of dying.
Diuretics work by eliminating natrium from our body. So they help also neurons to get rid of extra natrium and so there is less need for energy to ease the possible energy crisis. So they help also in AD prevention as seen below ( Tully et al 2016). Correspondingly eating also a lot of fruits and vegetables  help in AD prevention because they contain  lot of potassium and not much sodium.
So the epidemiological studies support "the energy crisis" to be behind AD symptoms.

But as we know, diuretics and fruit eating are beneficial also in prevention of  other diseases and evidently also by helping energy crisis in other organs than brain. It is very common to oder a kidney patient on low sodium diet and to heart patients it has been general recommendation for years without any knowledge about a possible mitochondrion problem.

See comment in PubMed Commons below
J Hypertens. 2016 Jun;34(6):1027-35. doi: 10.1097/HJH.0000000000000868.
Diuretic antihypertensive drugs and incident dementia risk: a systematic review, meta-analysis and meta-regression of prospective studies.

Tully PJ¹, Hanon O, Cosh S, Tzourio C.
Author information

• ¹aUniversity Bordeaux, Neuroepidemiology, UMR, Bordeaux, France bFreemasons Foundation Centre for Men's Health, Discipline of Medicine, School of Medicine, The University of Adelaide, Adelaide, Australia cINSERM, Service de Gériatrie, Université Paris Descartes, Hôspital Broca, Paris, France dSchool of Psychology, The University of Adelaide, Adelaide, Australia eINSERM, Neuroepidemiology, UMR, Bordeaux, France.

Abstract

OBJECTIVE:

Diuretic drugs have been a mainstay of hypertension treatment in the elderly however their dementia sparing effects are under-reported. The objective was to quantify dementia risk in relation to diuretic antihypertensive drugs.
METHODS:

Electronic databases were searched until June 2015.
ELIGIBILITY CRITERIA:

population, adults without dementia from primary care, community cohort, residential/institutionalized, or randomized controlled trial; exposure, diuretic antihypertensive drug; comparison, no diuretic drug, other or no antihypertensive drug, placebo-control; outcome, incident dementia diagnosed by standardized criteria. Adjusted hazard ratios (HR) with 95% confidence intervals (CI) were pooled in fixed-effects models with RevMan 5.3 (The Nordic Cochrane Centre, Copenhagen, Denmark) and the findings rated according to The Grading of Recommendations Assessment, Development and Evaluation criteria.
RESULTS:

A total of 15 articles were included (52 599 persons, 3444 dementia cases, median age 76.1 years) and median follow-up was 6.1 years. Diuretics were associated with reduced dementia risk (HR 0.83; 95% CI 0.76-0.91, P < 0.0001, I = 0) and Alzheimer's disease risk (HR 0.82; 95% CI 0.71-0.94, P = 0.004, I = 0). Stratified analysis indicated a difference between potassium sparing, thiazide and loop diuretics (P = 0.01). Risk estimates were generally consistent comparing monotherapy vs. combination therapy, study design and follow-up. Meta-regression showed that demographics, stroke, heart failure, diabetes, liver disease, attrition, mortality rate, cognitive function, and apolipoprotein E allele did not moderate the results.